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Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

## Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

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Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

## Ratio Problem Solving

Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

## What is ratio problem solving?

Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,

- What is the ratio involved?
- What order are the quantities in the ratio?
- What is the total amount / what is the part of the total amount known?
- What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer.

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods we can use when given certain pieces of information.

When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation.

For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts.

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

This means that Charlie will get 15 sweets and David will get 25 sweets.

- Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

## Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

## Simplifying and equivalent ratios

- Simplifying ratios

Equivalent ratios

## Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

- If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
- The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

## How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

## Explain how to do ratio problem solving

## Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

## Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

- How to work out ratio
- Ratio to fraction
- Ratio scale
- Ratio to percentage

## Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?

Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?

Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).

We could write this as

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

## Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 (GBP) to Euros € (EUR).

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

We know that we have £520.

We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520 = €608.40.

## Example 3: writing a ratio 1:n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.

Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

So the ratio of plant food to water in the form 1:n is 1:4.

## Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?

We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

The total amount of pocket money is therefore 4+7+8=£19.

## Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

We need to simplify this ratio.

To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}

HCF (12,16,10) = 2

Dividing all the parts of the ratio by 2 , we get

Our solution is 6:8:5 .

## Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .

We know the two ratios

We are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.

## Example 7: using bar modelling

India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if we can find out this value, we can then find the total quantity.

From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.

We can find the value of one share by working out 75 \div 3=25g.

We can fill in each share to be 25g.

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

The total amount of popcorn was 125+50=175g.

## Common misconceptions

- Mixing units

Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.

- Ratio written in the wrong order

For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.

- Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

- Counting the number of parts in the ratio, not the total number of shares

For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.

- Ratios of the form \bf{1:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

## Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?

8-3=5 computer games sold for every 3 board games.

2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.

## Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

## Learning checklist

You have now learned how to:

- Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Make and use connections between different parts of mathematics to solve problems

## The next lessons are

- Compound measures
- Best buy maths

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## HOW TO SOLVE RATIO WORD PROBLEMS

In this section, you will learn how word problems on ratio can be solved.

Let us look at the stuff which are required to solve word problems on ratio.

For example,

If two persons A & B are earning $400 and $ 500 respectively per week, the ratio of their earnings is

A : B = 400 : 500

When we simplify, we get

A : B = 4 : 5

From the ratio 4:5, if we want to get the earning of A and B, we have to multiply the terms of the ratio 4 & 5 by 100.

From the above point, it is very clear that if we want to get original quantity from the ratio, we have to multiply both the terms of the ratio by the same number.

In the above problem, we know that we have to multiply by 100. In case, we do not know what number to be multiplied, we have to multiply by "x" or any alphabet.

For example, the ages of two persons are in the ratio

Age of the 1st person = 5x

Age of the 2nd person = 6x

(The value of 'x' to be found)

If a quantity increases or decreases in the ratio a : b, then new quantity is

= 'b' of the original quantity divided by 'a'

new quantity = (b x original quantity) / a

Increment Ratio :

In a ratio, if the second term is greater than the first term, it is called increment ratio.

Examples: 7 : 8 , 4 : 5, 1 : 5.

Decrement Ratio :

In a ratio, if the second term is smaller than the first term, it is called decrement ratio.

Examples : 8 : 7, 4 : 3, 9 : 7.

How to find increment ratio :

A quantity called 'A' has been increased to '3A'.

Now, to find the ratio in which it has been increased, just take the coefficient of A in the changed quantity '3A'. It is '3'.

Now we have to write this '3' as a fraction. That is 3/1. From the fraction '3/1', we have to form a increment ratio. Because, the original quantity has been increased.

Therefore, the increment ratio from '3/1' is 1 : 3.

How to find decrement ratio :

A quantity called 'A' has been decreased to '0.25A'.

Now, to find the ratio in which it has been decreased, just take the coefficient of A in the changed quantity '0.25A'. It is '0.25'.

Now we have to write this '0.25' as a fraction. That is '1/4'. From the fraction '1/4', we have to form a decrement ratio. Because, the original quantity has been decreased.

Therefore, the decrement ratio from '1/4' is

Let us see how the above explained stuff help us to solve the ratio word problem given below.

Find in what ratio, will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

Let us understand the given information. There are two information given in the question.

1. In a factory, there is a reduction in the number of workers in the ratio 15:11.

2. There is an increment in their wages in the ratio 22:25.

Target of the question :

In what ratio, will the total wages of the factory be increased or decreased ?

Let 'x' be the original number of workers

Let 'y' be the wages per worker.

Total wages = (No. of workers) x (wages per worker)

Before the given two changes,

Total wages = xy or 1xy

After reduction in the number of workers in the ratio

Number of workers in the factory is

= 11x / 15 (see stuff 2)

After increment in wages in the ratio

Wages per worker is

= 25y / 22 (see stuff 2)

After the two changes,

Total wages = (11x/15) x (25y/22)

Total wages = (5/6)xy = (0.833)xy

Total wages = 1xy ----(1)

After the given two changes,

Total wages = (0.83)xy ----(2)

Comparing (1) and (2), it is very clear that total wages has been decreased when the two changes are applied.

That is, total wages has been decreased from (1xy) to (0.83)xy

Now, to find the ratio in which it has been decreased, just take the coefficient of 'xy' in total wages after the two changes applied.

It is '0.83'.

Now we have to write this '0.83' as a fraction.

That is '5/6'.

From the fraction '5/6', we have to form a decrement ratio.

That is '5 : 6' (See stuff 4).

Therefore, the total wages of the factory will be decreased in the ratio

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## Word Problems: Ratios

When we solve word problems, we often encounter ratios. Whether we're aware of it or not, our universe contains many ratios -- including the so-called " golden ratio " that is so common in nature. When we understand how ratios work, it's easy to solve all kinds of real-world problems . Let's get started:

## What is a ratio?

A ratio is a comparison of two different values with the same units. We write these with colons. Here are a few examples: 5:1, 12:30, 1:2

The colon simply means "to," so "5:1" means a "five to one" ratio.

## Using our knowledge of ratios to solve word problems

Let's use our knowledge of ratios to tackle a few word problems:

Let's say we have 12 sunfish and 30 rainbow shiners in our backyard pond. What is the ratio of sunfish to rainbow shiners in its simplest form?

We can write the ratio 12:30 as the fraction 12 30 . Next, we can reduce this fraction to 2/5. Finally, we rewrite it as the ratio 2:5. We also know that the reverse is true, as the ratio of rainbow shiners to sunfish is 5:2.

Now let's say we have a classroom of 32 students with 20 girls. What is the ratio of boys to girls?

We know that the total is 32 -- but we can't make the mistake of giving 20/32 as our answer. This gives us the ratio of girls to the total number of students -- but it doesn't give us the ratio of girls to boys. To find the correct answer, we need the total number of boys.

30 - 18 = 12 boys

Therefore, the ratio of girls to boys is 20:12 or 5:3 in simplified terms.

Now let's say we're baking a cake using a recipe that calls for a butter-to-sugar ratio of 2:3. If we use 6 cups of butter, how many cups of sugar should we use?

We know that we're using three times as much butter as the original recipe (since 6 is three times 2), so all we need to do is multiply the original sugar amount by three as well.

3 × 3 = 9 cups of sugar.

So, if we use 6 cups of butter, we should use 9 cups of sugar to maintain the 2:3 butter-to-sugar ratio.

## Topics related to the Word Problems: Ratios

Equivalent Ratios

Word Problems

Golden Ratio

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## Ratio Word Problems

Here, we will learn to do some practical word problems involving ratios.

Amelia and Mary share $40 in a ratio of 2:3. How much do they get separately?

There is a total reward of $40 given. Let Amelia get = 2x and Mary get = 3x Then, 2x + 3x = 40 Now, we solve for x => 5x = 40 => x = 8 Thus, Amelia gets = 2x = 2 × 8 = $16 Mary gets = 3x = 3 × 8 = $24

In a bag of blue and red marbles, the ratio of blue marbles to red marbles is 3:4. If the bag contains 120 green marbles, how many blue marbles are there?

Let the total number of blue marbles be x Thus, ${\dfrac{3}{4}=\dfrac{x}{120}}$ x = ${\dfrac{3\times 120}{4}}$ x = 90 So, there are 90 blue marbles in the bag.

Gregory weighs 75.7 kg. If he decreases his weight in the ratio of 5:4, find his reduced weight.

Let the decreased weight of Gregory be = x kg Thus, 5x = 75.7 x = \dfrac{75\cdot 7}{5} = 15.14 Thus his reduced weight is 4 × 15.14 = 60.56 kg

A recipe requires butter and sugar to be in the ratio of 2:3. If we require 8 cups of butter, find how many cups of sugar are required. Write the equivalent fraction.

Thus, for every 2 cups of butter, we use 3 cups of sugar Here we are using 8 cups of butter, or 4 times as much So you need to multiply the amount of sugar by 4 3 × 4 = 12 So, we need to use 12 cups of sugar Thus, the equivalent fraction is ${\dfrac{2}{3}=\dfrac{8}{12}}$

Jerry has 16 students in his class, of which 10 are girls. Write the ratio of girls to boys in his class. Reduce your answer to its simplest form.

Total number of students = 16 Number of girls = 10 Number of boys = 16 – 10 = 6 Thus the ratio of girls to boys is ${\dfrac{10}{6}=\dfrac{5}{3}}$

A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the total number of chocolates in the bag.

Let the total number of chocolates be x

Then the two parts are:

${\dfrac{5x}{5+7}}$ and ${\dfrac{7x}{5+7}}$

${\dfrac{7x}{5+7}}$ = 84

=> ${\dfrac{7x}{12}}$ = 84

Thus, the total number of chocolates that were present in the bag was 144

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How to protect machines against random failures

UPDATE: The solutions can be read here

I’ve temporarily moved to Berkeley, California, where I am the “science communicator in residence” at the Simons Institute , the world’s leading institute for collaborative research in theoretical computer science.

One nano-collaboration is today’s puzzle – told to me by a computer scientist at Microsoft I befriended over tea. It’s about data centres – those warehouses containing endless rows of computers that store all our data.

One problem faced by data centres is the unreliability of physical machines. Hard drives fail all the time, and when they do, all their data may be lost. How do companies like Microsoft make sure that they can recover the data from failed hard drives? The solution to the puzzle below is, in essence, the answer to this question.

An obvious strategy that a data centre could use to protect its machines from random failures is for every machine to have a duplicate. In this case, if a hard drive fails, you recover the data from the duplicate. This strategy, however, is not used because it is very inefficient. If you have 100 machines, you would need another 100 duplicates. There are better ways, as you will hopefully deduce!

The disappearing boxes

You have 100 boxes. Each box contains a single number in it, and no two boxes have the same number.

1. You are told that one of the boxes at random will be removed. But before it is removed you are given an extra box , and allowed to put a single number in it. What number do you put in the extra box that guarantees you will be able to recover the number of whichever box is removed?

2. You are told that two of the boxes at random will be removed. But before it is removed you are given two extra boxes, and allowed to put one number in each of them. What (different) numbers do you put in these two boxes that guarantees you will be able to recover the numbers of both removed boxes?

I’ll be back with the answers at 5pm UK. Meanwhile, NO SPOILERS, please discuss your favourite hard drives.

UPDATE: The solutions can be read here.

The analogy here is that each box is a hard drive, the number in the box is the data, and the removal of a box is the failure of the hard drive. With one extra hard drive, we are secure against the random failure of a single hard drive, and with two, we are secure against the failure of two. It seems magical that we can protect such a lot of information against random failures with minimal back-up.

The field of “error-correcting codes” is a large body of beautiful theories that provide answers to questions such as how to minimise the number of machines needed to protect against random failures of hard drives. And the theories work! Data centres never lose your data because of mechanical failure.

My tea companion was Sivakanth Gopi, a Principal Researcher at Microsoft. He said: “The magic of error correcting codes allows us to build reliable systems using noisy and faulty components. Thanks to them, we can communicate with someone as far away as the ends of our solar system and store billions of terabytes of data safely in the cloud. We can forget about the noise and complexity of this world and instead enjoy its beauty.”

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me .

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## Unit 3: Ratios and rates

About this unit, intro to ratios.

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## Equivalent ratios

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## Ratio application

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## Intro to rates

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## AI helps boost creativity in the workplace but still can't compete with people's problem-solving skills, study finds

- Artificial intelligence is disrupting professional workplaces with systems like ChatGPT and Gemini.
- A study found that people mistrust AI for the wrong reasons while trusting it for tasks where it might mess up.
- AI boosts performance in creative tasks but performs poorly in problem-solving, the study found.

Artificial intelligence is coming to change your workplace .

The rapidly evolving technology has already started to disrupt day-to-day activities in professional settings, and leaders at the forefront of the AI revolution have been clear about how they hope to implement systems like ChatGPT and Gemini into the mainstream workflow.

But while many employees may be cautiously skeptical about the impending AI overhaul, a recent study found that people are actually mistrustful of artificial intelligence for the wrong reasons while frequently trusting in the technology for tasks it's more likely to mess up.

The September 2023 study, which is titled " How People Can Create—and Destroy—Value with Generative AI ," was spearheaded by François Candelon, the managing director and senior partner at consulting company Boston Consulting Group.

The study's findings are back in the news this week after Candelon sat down with the Wall Street Journal's Executive Insights podcast to discuss generative AI in the workplace.

Candelon partnered with talent from top universities like MIT, Wharton, Harvard Business School, and the University of Warwick, and used his consulting company's own employees to execute the experiment, which he told The Journal was inspired by his desire to figure out how humans and AI can work together to help businesses.

The more than 750 study participants were given real tasks, including "creative product innovation" assignments. The participants were instructed to use OpenAI tool GPT-4 to help them with tasks like pitching the shoe concepts to their boss, coming up with focus group questions, and executing a successful social media rollout, Candelon said.

The study found that people using AI faired much better than those working without it when it came to creative product innovation tasks. About 90% of the participants improved their performance when using AI for any task involving ideation and content creation.

Participants also converged on a performance level that was 40% higher than those working on the same task without GPT-4, according to the study.

The most benefits were seen when people didn't try to change or improve the technology's output suggestions, accepting GPT-4's suggestions as is, the study found.

But there are still some tasks where humans have the edge. People's problem-solving skills far outweigh the help offered by AI, Candelon said.

The study found that generative AI actually persuaded several participants to accept GPT's misleading output, even when they had been briefed on the possibility of wrong answers.

Participants who used AI for problem-solving tasks performed 23% worse than those who didn't use the tool at all, according to the study.

The "double-edged sword" that is generative AI, with its "relatively uniform output," can also reduce a group's diversity of thought by 41%, the study found.

But Candelon stressed to The Journal that AI is exceedingly powerful and, ultimately, unavoidable.

"There is this famous quote saying that humans won't get replaced by AI. They will get replaced by humans using AI," he told the outlet.

Candelon said the study shows that data will become even more important with generative AI in the workplace, forcing people to revisit their workflows and figure out places for human and AI collaboration.

## Watch: AI will drive personalization, not creativity, says Roku's VP of growth marketing, Sweta Patel

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## How do you solve a problem like a gopher? Fountain Valley is learning through experience

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How do you solve a problem like a gopher? In the city of Fountain Valley, rodents digging networks of subterranean tunnels that compromise the soil integrity of local parklands have been an ongoing challenge for public works employees.

“They burrow all day long, so there are shallow tunnels that can create risks if they do cave in,” said Mark Sprague, a field services manager for the city. “They mostly feed on the roots of plants. They also chew irrigation lines. It’s caused a lot of problems both privately and publicly.”

Visitors to Los Alamos Park, Harper Park and the city’s Sports Park near Mile Square Regional Park — identified by city staff as gopher “hot spots” — may have seen signs of the rodent’s presence in the area, including cones and markers placed near tunnels.

Officials have for years contracted with an area landscaping company to trap and remove the critters. But recently, an observed increase in gopher activity is popping up in residential neighborhoods.

Fountain Valley City Councilman Jim Cunneen said it’s common for residents to air gopher grievances at City Hall, sometimes speaking in public comments at council meetings, or to bring up the subject at local functions.

“It’s not unique to our city, but something has triggered a rise in the population of gophers in our parks,” he said Friday. “A lot of people in our neighborhood are dealing with gophers. You can see it in some of the front lawns of our neighbors.”

Cunneen has lived for the past three decades near the city’s Los Alamos Park on a street named La Marmota Avenue, the Spanish word for groundhog. Although he recalled having issues with the animals in the ’90s, his backyard was pretty calm until the recent population explosion.

“We have at least 30 holes gophers have chewed,” he said. “They take out a 3- to 4-inch diameter patch, and they’re also burrowing so the surface becomes uneven — it’s horrible.”

Gopher Mitigation Update https://t.co/zG5HUgmcwh pic.twitter.com/Njt8PAPLOr — City of Fountain Valley (@fv_cityhall) February 7, 2024

City officials reported last week on social media gopher mitigation efforts are in full swing at local parks. Where a typical month may bring in 15 to 20 animals, last month more than 40 trappings were logged, according to Sprague.

Cunneen said extermination companies tend not to deal with gophers, requiring residents to seek out services that offer to remove the animals by trapping them. It’s unclear, however, what happens once an animal is captured.

Representatives of Merchants Landscape Services, which handles landscaping for Fountain Valley and its more than 150 acres of park space under an $873,000 annual contract, did not immediately respond to a request for that information. But one local wildlife expert offered some advice.

Debbie McGuire, executive director of the nonprofit Wetlands & Wildlife Care Center in Huntington Beach, maintains state laws prohibit the relocation of many small animals and rodent species into different habitats. She said many removal companies end up humanely euthanizing the animals they trap.

One explanation for the rising gopher population may be a decline in the presence of predators who feed on them, such as bobcats and coyotes or birds of prey like barn owls.

“Gophers are really important for the ecosystem. They move the soil around and keep roots aerated so plants stay healthy,” McGuire said Friday. “But there are times when there are no predators to keep their population down, and they’ll get out of control.”

She suggested city employees or residents in Fountain Valley might look into installing nesting boxes in public parks and residential neighborhoods to attract animals like the barn owl, which prey on gophers but leave larger animals, like cats and dogs, undisturbed.

A number of organizations and resources can be found online, including the Barn Owl Box Co. , which sells nesting boxes and instructs people how to build their own.

“The best thing is to leave nature alone and let the circle of life take care of things,” McGuire advised.

All the latest on Orange County from Orange County.

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## How far can cities go to clear homeless camps? The U.S. Supreme Court will decide

Jennifer Ludden

A man named Frank sits in his tent with a river view in Portland, Ore., in 2021. A lawsuit originally filed in 2018 on behalf of homeless people in the Oregon city of Grants Pass is set to go before the U.S. Supreme Court in April. Paula Bronstein/AP hide caption

A man named Frank sits in his tent with a river view in Portland, Ore., in 2021. A lawsuit originally filed in 2018 on behalf of homeless people in the Oregon city of Grants Pass is set to go before the U.S. Supreme Court in April.

In April, the U.S. Supreme Court will hear a major case that could reshape how cities manage homelessness. The legal issue is whether they can fine or arrest people for sleeping outside if there's no shelter available. The 9th U.S. Circuit Court of Appeals has deemed this cruel and unusual punishment, and this case is a pivotal challenge to that ruling.

The high court declined to take up a similar case in 2019. But since then, homelessness rates have climbed relentlessly. Street encampments have grown larger and have expanded to new places, igniting intense backlash from residents and businesses. Homelessness and the lack of affordable housing that's helping to drive it have become key issues for many voters.

The case, Grants Pass v. Johnson , could have dramatic implications for the record number of people living in tents and cars across the United States.

## An Oregon town banned camping and the use of sleeping bags and stoves on public property

In the small city of Grants Pass, Ore. , homeless people say the city broke the law when it aggressively tried to push them out over the past decade. To discourage people from sleeping in public spaces, the city banned the use of stoves and sleeping bags or other bedding. But during several years when she had lost housing, Helen Cruz says she needed to live in city parks because they're close to the jobs she had cleaning houses.

"We're not out there because we want to be," she says. "We don't have a choice. There's no place to go."

Grants Pass has no homeless shelter that's open to everyone. A religious mission takes in a few who agree to attend services. That left Cruz racking up thousands of dollars in fines, which she remains unable to pay.

"And I keep getting mail from Josephine County court saying, 'You owe this. If you don't pay this, it's going to collections,'" she says, "which has destroyed my credit."

## Charges dropped against Ohio pastor who housed homeless people at his church

A lawsuit originally filed in 2018 on behalf of homeless people in Grants Pass said the situation there was part of a larger crisis, as homelessness rates around the U.S. were high and growing. It accused the city of trying to "punish people based on their status of being involuntarily homeless." The 9th Circuit agreed, saying the city could not ban people from sleeping outside with "rudimentary protection from the elements" when there was nowhere else for them to go.

The same appeals court also sided with homeless people in a landmark 2018 case out of Boise, Idaho, which the Supreme Court later declined to take up.

Critics say the Grants Pass ruling is a major expansion over the Boise one, since it forbids not just criminal penalties but civil ones. Advocates for homeless people don't see much difference, since some in Grants Pass who couldn't pay their fines were eventually jailed.

Grants Pass petitioned the Supreme Court. And its appeal has drawn support from dozens of local and state officials across the West and elsewhere who urged the justices to take this case. Among those filing such friend-of-the-court briefs are Republican -led states like Idaho, Montana and Nebraska and Democratic-led cities like Los Angeles and San Francisco, plus a separate brief from California Gov. Gavin Newsom .

## Officials say the law has paralyzed their efforts to manage a public safety crisis

States and cities contend these rulings have contributed to the growth of tent encampments.

"These decisions are legally wrong and have tied the hands of local governments as they work to address the urgent homelessness crisis," Theane Evangelis, the attorney representing Grants Pass , said in a statement. "The tragedy is that these decisions are actually harming the very people they purport to protect."

Evangelis and others say sprawling tent camps pose a threat to public health and safety. Those living in them often face theft or assault and are at risk of being hit by passing vehicles. And they note that encampments have led to fires, disease, environmental hazards and high numbers of people overdosing on drugs and dying on public streets.

## Homelessness in the U.S. hit a record high last year as pandemic aid ran out

## 'Frustration all across the board.' A day with homelessness outreach workers in LA

"It's just gone too far," California Gov. Gavin Newsom said last year at a Politico event in Sacramento. "People's lives are at risk. It's unacceptable what's happening on the streets and sidewalks. Compassion is not stepping over people on the streets."

Critics also say the 9th Circuit's rulings are ambiguous and have been interpreted too broadly, making them unworkable in practice.

"We need to have clarity," says Seattle City Attorney Ann Davison, who wrote a legal brief on behalf of more than a dozen other cities plus the National League of Cities.

For example, what exactly constitutes adequate shelter? And what about when a bed is open, but someone refuses to go? Local officials say that this happens a lot, and some acknowledge that people might have good reasons to not want to go to a shelter. Yet Davison says court rulings essentially require cities to build enough shelter for every person without housing, something many places can't possibly afford.

They also argue that homelessness is a complex problem that requires balancing competing interests, something local officials are better equipped to do than the courts.

"We are trying to show there's respect for the public areas that we all need to have," Davison says. "And we care for people, and we're engaging and being involved in the long-term solution for them."

## Advocates say punishing homeless people won't solve the problem

Attorneys and advocates for the homeless plaintiffs argue that the 9th Circuit rulings are far narrower and less restrictive than cities claim.

"It's interesting to me that the people in power have thrown up their hands and said, 'There's nothing we can do, and the only solution we can think of is to arrest people,'" says Jesse Rabinowitz of the National Homelessness Law Center. "That's simply not true."

He and others say the rulings do allow cities to regulate encampments. They can limit the time and place for them, ban the use of tents, even clear them out. And plenty of cities do that, though they often face lawsuits over the details of what's allowed.

## Housing is now unaffordable for a record half of all U.S. renters, study finds

Grants Pass did what's not allowed, which is ban camps everywhere all the time, says Ed Johnson of the Oregon Law Center, which represents those suing the city. He says that would basically make it illegal for people to exist.

"It's sort of the bare minimum in what a just society should expect, is that you're not going to punish someone for something they have no ability to control," he says.

The reason they can't control being homeless, Johnson says, is because Grants Pass — like so many cities around the U.S. — has a severe housing shortage and unaffordable rents. He says that cities are blaming the courts for decades of failed housing policies and that fining and jailing people only makes the problem worse.

"When we criminalize people, we know it impacts their ability to get a job," says Ann Oliva, CEO of the National Alliance to End Homelessness. "It impacts their ability to get housing in the long run if they have a criminal record."

Some cities that side with Grants Pass say they have invested heavily to create more affordable housing, even as homelessness rates keep going up. That's a long-term challenge they'll still face, whatever the Supreme Court decides.

- grants pass
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Read our research on: Immigration & Migration | Podcasts | Election 2024

## Regions & Countries

How americans view the situation at the u.s.-mexico border, its causes and consequences, 80% say the u.s. government is doing a bad job handling the migrant influx.

Pew Research Center conducted this study to understand the public’s views about the large number of migrants seeking to enter the U.S. at the border with Mexico. For this analysis, we surveyed 5,140 adults from Jan. 16-21, 2024. Everyone who took part in this survey is a member of the Center’s American Trends Panel (ATP), an online survey panel that is recruited through national, random sampling of residential addresses. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race, ethnicity, partisan affiliation, education and other categories. Read more about the ATP’s methodology .

Here are the questions used for the report and its methodology .

The growing number of migrants seeking entry into the United States at its border with Mexico has strained government resources, divided Congress and emerged as a contentious issue in the 2024 presidential campaign .

Americans overwhelmingly fault the government for how it has handled the migrant situation. Beyond that, however, there are deep differences – over why the migrants are coming to the U.S., proposals for addressing the situation, and even whether it should be described as a “crisis.”

## Factors behind the migrant influx

Economic factors – either poor conditions in migrants’ home countries or better economic opportunities in the United States – are widely viewed as major reasons for the migrant influx.

About seven-in-ten Americans (71%), including majorities in both parties, cite better economic opportunities in the U.S. as a major reason.

There are wider partisan differences over other factors.

About two-thirds of Americans (65%) say violence in migrants’ home countries is a major reason for why a large number of immigrants have come to the border.

Democrats and Democratic-leaning independents are 30 percentage points more likely than Republicans and Republican leaners to cite this as a major reason (79% vs. 49%).

By contrast, 76% of Republicans say the belief that U.S. immigration policies will make it easy to stay in the country once they arrive is a major factor. About half as many Democrats (39%) say the same.

For more on Americans’ views of these and other reasons, visit Chapter 2.

## How serious is the situation at the border?

A sizable majority of Americans (78%) say the large number of migrants seeking to enter this country at the U.S.-Mexico border is eithera crisis (45%) or a major problem (32%), according to the Pew Research Center survey, conducted Jan. 16-21, 2024, among 5,140 adults.

Related: Migrant encounters at the U.S.-Mexico border hit a record high at the end of 2023 .

- Republicans are much more likely than Democrats to describe the situation as a “crisis”: 70% of Republicans say this, compared with just 22% of Democrats.
- Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem.

In an open-ended question , respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with the immigration system.

Yet two concerns come up most frequently:

- 22% point to the economic burdens associated with the migrant influx, including the strains migrants place on social services and other government resources.
- 22% also cite security concerns. Many of these responses focus on crime (10%), terrorism (10%) and drugs (3%).

When asked specifically about the impact of the migrant influx on crime in the United States, a majority of Americans (57%) say the large number of migrants seeking to enter the country leads to more crime. Fewer (39%) say this does not have much of an impact on crime in this country.

Republicans (85%) overwhelmingly say the migrant surge leads to increased crime in the U.S. A far smaller share of Democrats (31%) say the same; 63% of Democrats instead say it does not have much of an impact.

## Government widely criticized for its handling of migrant influx

For the past several years, the federal government has gotten low ratings for its handling of the situation at the U.S.-Mexico border. (Note: The wording of this question has been modified modestly to reflect circumstances at the time).

However, the current ratings are extraordinarily low.

Just 18% say the U.S. government is doing a good job dealing with the large number of migrants at the border, while 80% say it is doing a bad job, including 45% who say it is doing a very bad job.

- Republicans’ views are overwhelmingly negative (89% say it’s doing a bad job), as they have been since Joe Biden became president.
- 73% of Democrats also give the government negative ratings, the highest share recorded during Biden’s presidency.

For more on Americans’ evaluations of the situation, visit Chapter 1 .

## Which policies could improve the border situation?

There is no single policy proposal, among the nine included on the survey, that majorities of both Republicans and Democrats say would improve the situation at the U.S.-Mexico border. There are areas of relative agreement, however.

A 60% majority of Americans say that increasing the number of immigration judges and staff in order to make decisions on asylum more quickly would make the situation better. Only 11% say it would make things worse, while 14% think it would not make much difference.

Nearly as many (56%) say creating more opportunities for people to legally immigrate to the U.S. would make the situation better.

Majorities of Democrats say each of these proposals would make the border situation better.

Republicans are less positive than are Democrats; still, about 40% or more of Republicans say each would improve the situation, while far fewer say they would make things worse.

Opinions on other proposals are more polarized. For example, a 56% majority of Democrats say that adding resources to provide safe and sanitary conditions for migrants arriving in the U.S. would be a positive step forward.

Republicans not only are far less likely than Democrats to view this proposal positively, but far more say it would make the situation worse (43%) than better (17%).

Building or expanding a wall along the U.S.-Mexico border was among the most divisive policies of Donald Trump’s presidency. In 2019, 82% of Republicans favored expanding the border wall , compared with just 6% of Democrats.

Today, 72% of Republicans say substantially expanding the wall along the U.S. border with Mexico would make the situation better. Just 15% of Democrats concur, with most saying either it would not make much of a difference (47%) or it would make things worse (24%).

For more on Americans’ reactions to policy proposals, visit Chapter 3 .

## Facts are more important than ever

In times of uncertainty, good decisions demand good data. Please support our research with a financial contribution.

## Report Materials

Table of contents, fast facts on how greeks see migrants as greece-turkey border crisis deepens, americans’ immigration policy priorities: divisions between – and within – the two parties, from the archives: in ’60s, americans gave thumbs-up to immigration law that changed the nation, around the world, more say immigrants are a strength than a burden, latinos have become less likely to say there are too many immigrants in u.s., most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

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## VIDEO

## COMMENTS

3+5=8 3 + 5 = 8 40 \div 8=5 40 ÷ 8 = 5 Then you multiply each part of the ratio by 5. 5. 3\times 5:5\times 5=15 : 25 3 × 5: 5 × 5 = 15: 25 This means that Charlie will get 15 15 sweets and David will get 25 25 sweets. There can be ratio word problems involving different operations and types of numbers.

In this video I'll show you how to solve multiple types of Ratio Word Problems using 5 examples. We'll start simple and work up to solving the most complex problems. Here are the...

0:00 / 3:50 Solving Ratio Word Problems (the easy way!) vinteachesmath 26.9K subscribers Subscribe Subscribed 1.4K 118K views 8 years ago This video focuses on how to solve ratio word...

Step 1: Assign variables: Let x = number of red sweets. Write the items in the ratio as a fraction. Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x Isolate variable x Answer: There are 90 red sweets. Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue.

part: whole = part: sum of all parts To write a ratio: Determine whether the ratio is part to part or part to whole. Calculate the parts and the whole if needed. Plug values into the ratio. Simplify the ratio if needed. Integer-to-integer ratios are preferred. [Example: Part to whole] [Examples: Simplifying ratios]

About Transcript Discover how to solve ratio problems with a real-life example involving indoor and outdoor playtimes. Learn to use ratios to determine the number of indoor and outdoor playtimes in a class with a 2:3 ratio and 30 total playtimes. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted

Activities How do we find a missing value in two equivalent ratios? Express each ratio of two quantities by writing its numerical values as a fraction. Remember, that's one of the three ways to...

Ratio Worksheets. Columns: Rows: (These determine the number of problems) Level: Level 1: write a ratio. Level 2: write a ratio and simplify it. Numbers used (only for levels 1 & 2): Range from to with step. Level 3: word problems.

3 + 5 = 8 40 ÷ 8 = 5 Then we multiply each part of the ratio by 5. 3 x 5:5 x 5 = 15:25 This means that Charlie will get 15 sweets and David will get 25 sweets. Dividing ratios Step-by-step guide: Dividing ratios (coming soon) Ratios and fractions (proportion problems) We also need to consider problems involving fractions.

Math > 6th grade > Ratios > Equivalent ratios Equivalent ratio word problems Google Classroom A fruit basket is filled with 8 bananas, 3 oranges, 5 apples, and 6 kiwis. Complete the ratio. For every 3 kiwis, there are 4 Select a fruit . Stuck? Review related articles/videos or use a hint. Report a problem Do 4 problems

http://www.mathtestace.comhttp://www.mathtestace.com/fraction-word-problems/Need help solving word problems with ratios and fractions? This video will walk y...

How to solve Ratio Word Problems with three terms? Example: A piece of string that is 63 inches long is cut into 3 parts such that the lengths of the parts of the string are in the ratio of 5 to 6 to 10. Find the lengths of the 3 parts. Show Video Lesson.

IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Use tape diagrams to solve ratio word problems" and thousands of other math skills.

This calculator has 1 input. What 3 formulas are used for the Ratio Word Problems Calculator? a:b ratio means a + b = c total options Expected Number of A = a * n/c Expected Number of B = b * n/c For more math formulas, check out our Formula Dossier What 3 concepts are covered in the Ratio Word Problems Calculator? fraction

Stuff 1: For example, If two persons A & B are earning $400 and $ 500 respectively per week, the ratio of their earnings is. A : B = 400 : 500. When we simplify, we get. A : B = 4 : 5. From the ratio 4:5, if we want to get the earning of A and B, we have to multiply the terms of the ratio 4 & 5 by 100.

A ratio is a comparison of any two quantities. It can be written as a to b, a: b or a/b. Percent is a ratio. Percent should be viewed as a part-to-whole ratio that compares a number to a whole divided into 100 equal parts. In these lessons, we will learn how to solve ratio word problems and how to use ratios to help us solve percent word problems.

Math Homework. Do It Faster, Learn It Better. Word Problems: Ratios When we solve word problems, we often encounter ratios. Whether we're aware of it or not, our universe contains many ratios -- including the so-called "golden ratio" that is so common in nature.

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Write the ratio of girls to boys in his class. Reduce your answer to its simplest form. Solution: Total number of students = 16. Number of girls = 10. Number of boys = 16 - 10 = 6. Thus the ratio of girls to boys is 10 6 = 5 3. A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the ...

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Pre-algebra 15 units · 179 skills. Unit 1 Factors and multiples. Unit 2 Patterns. Unit 3 Ratios and rates. Unit 4 Percentages. Unit 5 Exponents intro and order of operations. Unit 6 Variables & expressions. Unit 7 Equations & inequalities introduction. Unit 8 Percent & rational number word problems.

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This video focuses on how to solve ratio word problem in algebra 1. I show how to carefully translate the verbal portions of the problem in algebraic express...

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