problem solving with fractions decimals and percentages

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Fractions Decimals Percents Worksheets

Welcome to our Fractions Decimals Percents Worksheets page. Here you will find a wide range of printable Fraction Worksheets which will help your child understand and practice how to convert between fractions, decimals and percentages.

Looking to convert fractions to percentages or decimals; decimals to fractions or percentages; percentages to fractions or decimals?

Then look no further - we have what you need!

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• Fractions Decimals Percents Conversion Table

Fractions Decimals Percents Riddles

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Fractions Decimals Percents Online Quiz

Fractions decimals percents.

Below are some common conversions for fractions into decimals and percents.

Where a digit is underlined, it means that the number has been rounded to 3 decimal places, or to the nearest 0.1%.

We have split up our fractions decimals percents worksheets into several different sections to make it easier for you to choose the skill you want to practice.

• The first section is just converting fractions into decimals and percents.
• The second sections is about converting decimals to percents and fractions.
• The third section covers convertig percents to fractions and decimals.
• The last section involves converting between all three.

The sheets are carefully graded so that the supported and easier sheets come first, and the most difficult sheet is the last one.

Using these sheets will help your child to:

• convert between fractions decimals and percents.

These sheets are aimed at 5th, 6th and 7th graders.

Converting Fractions to Decimals and Percents

• Fractions to Decimals and Percents Sheet 1
• PDF version
• Fractions to Decimals and Percents Sheet 2

Fractions to Decimals and Percents Walkthrough Video

This short video walkthrough shows several problems from our Fractions to Decimals and Percents Worksheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Converting Decimals to Percents and Fractions

• Decimals to Percents and Fractions Sheet 1
• Decimals to Percents and Fractions Sheet 2

Converting Percents to Decimals and Fraction s

• Percents to Decimals and Fractions Sheet 1
• Percents to Decimals and Fractions Sheet 2

Convert Between Fractions Decimals Percents Worksheets

• Fractions Decimals and Percents Sheet 1
• Fractions Decimals and Percents Sheet 2
• Fractions Decimals and Percents Sheet 3
• Fractions Decimals and Percents Sheet 4

Now is your chance to practice your fractions decimals and percents problem solving skills with some fun riddles!

• Fraction Decimal Percent Riddle 1
• Fraction Decimal Percent Riddle 2
• Fraction Decimal Percent Riddle 3

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Equivalent Fractions

The printable fraction page below contains support, examples and practice using equivalent fractions.

• Finding Equivalent Fractions support page
• Equivalent Fractions Worksheets

Comparing Fractions

We have some carefully graded worksheets on comparing and ordering fractions.

You can choose from supported sheets with diagrams for students who need extra help to harder worksheets for those more confident.

• Comparing Fractions Worksheet page

Simplifying Fractions

Take a look at our Simplifying Fractions Practice Zone or try our worksheets for finding the simplest form for a range of fractions.

You can choose from proper fractions, improper fractions or both.

You can print out your results or benchmark your scores against future achievements.

Good for practising equivalent fractions as well as converting to simplest form.

Great for using with a group of children as well as individually.

• Simplify Fractions Practice Zone
• Simplifying Fractions Worksheet page

Fraction Riddles

Riddles are a great way to get children to apply their knowledge of fractions.

These riddles are a good way to start off a maths lesson, or also to use as a way of checking your child's understanding about fractions.

All the fraction riddles consist of 3 or 4 clues and a selection of 6 or 8 possible answers. Children have to read the clues and work out which is the correct answer.

The riddles can also be used as a template for the children to write their own clues for a partner to guess.

• Fraction Riddles for kids (easier)
• Free Printable Fraction Riddles (harder)

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Our quizzes have been created using Google Forms.

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This quick quiz tests your knowledge and skill at converting between fractions, decimals and percents.

Fun Quiz Facts

• This quiz was attempted 1,155 times in the last academic year.
• The average (mean) score was 13.4 out of 20 marks.
• Can you beat the mean score?

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Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

Here, have a play with it yourself:

Example Values

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:

Conversions!

From percent to decimal.

To convert from percent to decimal divide by 100 and remove the % sign.

An easy way to divide by 100 is to move the decimal point 2 places to the left :

Don't forget to remove the % sign!

From Decimal to Percent

To convert from decimal to percent multiply by 100%

An easy way to multiply by 100 is to move the decimal point 2 places to the right :

 Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

Example: Convert 2 5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

Answer: 2 5 = 0.4

From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

Example: To convert 0.75 to a fraction

From fraction to percentage.

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

Example: Convert 3 8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 37.5%

Answer: 3 8 = 37.5%

From Percentage to Fraction

To convert a percentage to a fraction , first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

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3: Fractions, Decimals, and Percentages

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• 3.1: Visualize Fractions (Part 1) A fraction is a way to represent parts of a whole. The denominator b represents the number of equal parts the whole has been divided into, and the numerator a represents how many parts are included. The denominator, b, cannot equal zero because division by zero is undefined. A mixed number consists of a whole number and a fraction. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one.
• 3.2: Visualize Fractions (Part 2) Equivalent fractions are fractions that have the same value. When working with fractions, it is often necessary to express the same fraction in different forms. To find equivalent forms of a fraction, we can use the Equivalent Fractions Property. We can use the inequality symbols to order fractions. Remember that a > b means that a is to the right of b on the number line. As we move from left to right on a number line, the values increase.
• 3.3: Fraction Multiplication A fraction is considered simplified if there are no common factors, other than 1, in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors. To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.
• 3.4: Fraction Division The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To divide fractions, multiply the first fraction by the reciprocal of the second.
• 3.5: Add and Subtract Fractions with Matching (Common) Denominators To add fractions, add the numerators and place the sum over the common denominator. To subtract fractions, subtract the numerators and place the difference over the common denominator.
• 3.6: Add and Subtract Fractions with Different Denominators In fraction multiplication, you multiply the numerators and denominators together, respectively. To divide fractions, you multiply the first fraction by the reciprocal of the second. For fraction addition, add the numerators together and place the sum over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD. Likewise, for fraction subtraction, subtract the numerators and place the difference over the common denominator.
• 3.7: Percentages A percent is a ratio whose denominator is 100. Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100, so the denominator of the fraction is 100. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal. To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.
• 3.8: Solve General Applications of Percent We will solve percent equations by using the methods we used to solve equations with fractions or decimals. Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.
• 3.9: Decimals (Part 1) Decimals are another way of writing fractions whose denominators are powers of ten. To convert a decimal number to a fraction or mixed number, look at the number to the left of the decimal. If it is zero, the decimal converts to a proper fraction. If not, the decimal converts to a mixed number. The numbers to right of the decimal point become the numerator while the place value corresponding to the final digit represent to the denominator. Finally, simplify the fraction if possible.
• 3.10: Decimals (Part 2) Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line. To round a decimal, locate the given place value and mark it with an arrow. Underline the digit to the right of the place value and determine if it is greater than or equal to 5. If it is, add one to the digit in the given place value. If not, don't change the digit. Finally, rewrite the number, removing all digits to the right of the given place value.
• 3.11: Decimal Operations (Part 1) To add or subtract decimals, write the numbers vertically so the decimal points line up. Use zeros for place holders, as needed. Then, add or subtract the numbers as if they were whole numbers. Lastly, place the decimal in the answer under the decimal points in the given numbers. Multiplying decimals is like multiplying whole numbers—we just have to determine where to place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors.
• 3.12: Decimal Operations (Part 2) Just as with multiplication, division of decimals is very much like dividing whole numbers. To divide a decimal by a whole number, we place the decimal point in the quotient above the decimal point in the dividend and then divide as usual with long division. Sometimes we need to use extra zeros at the end of the dividend to keep dividing until there is no remainder. To divide decimals, we multiply both the numerator and denominator by the same power of 10 to make the denominator a whole number.

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PROBLEM SOLVING WITH FRACTIONS DECIMALS AND PERCENTAGES WORKSHEET

Problems with fractions.

(1)  A fruit merchant bought mangoes in bulk. He sold 5/8  of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy? 

(2)  A family requires 2 1/2 liters of milk per day. How much milk would family require in a month of 31 days?  

(3)  A ream of paper weighs 12 1/2 kg.  What is the weight per quire ?

(4)   It was Richard's birthday. He distributed 6 kg of candies to his friends. If he had given 1/8  kg of candies to each friend, how many friends were there ?

(5)  Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?

Answer Key :

(1)  960 mangoes

(2)   77 1/2 liter

(3)  5/8 kg

(4)   48 friends

(5)  1/5

Fraction Word Problems Mixed Operations

(1)  Linda walked 2 1/3 miles on the first day and 3 2/5   miles on the next day. How many miles did she walk in all ?                Solution

(2)   David ate 2 1/7 pizzas and he gave 1 3/14    pizzas to his mother. How many pizzas did David have initially ?

(3)   Mr. A has 3 2/3 acres of land. He gave 1 1/4 acres of land to his friend. How many acres of land does Mr. A have now ?          Solution

(4)   Lily added 3 1/3 cups of walnuts to a batch of trail mix. Later she added 1 1/3 cups of almonds. How many cups of nuts did Lily put in the trail mix in all? 

(5)   In the first hockey games of the year, Rodayo played 1 1/2 periods and 1 3/4 periods. How many periods in all did he play ?         Solution

(6)   A bag can hold 1 1/2 pounds of flour. If Mimi has 7 1/2 pounds of flour, then how many bags of flour can Mimi make ?        Solution

(7)   Jack and John went fishing Jack caught 3 3/4 kg of fish and while John  caught 2 1/5 kg of fish. What is the total weight of the fish they caught?

(8)   Amy has 3 1/2 bottles in her refrigerator. She used 3/5 bottle in the morning 1 1/4 bottle in the afternoon. How many bottles of milk does Amy have left over ?  

(9)   A tank has 82 3/4 liters of water. 24 4/5 liters of water were used and the tank was filled with another 18 3/4 liters. What is the final volume of the water in the tank ?

(10)   A trader prepared 21 1/2 liters of lemonade. At the end of the day he had 2 5/8 liters left over. How many liters of lemonade was sold by the Trader? 

Answer key :

Problems on Decimals

(1)  A chemist mixed 6.35 grams of one compound with 2.45 grams of another compound. How many grams were there in the mixture.      Solution

(2)   If the cost of a pen is $10.50, a book is $25.75 and a bag is $45.50, the  find the total cost of 2 books, 3 pens and 1 bag.         Solution

(3)    John wants to buy a bicycle that cost $ 450.75. He has saved $ 125.35. How much more money must John save in order to have enough money to buy the bicycle ?

(4)   Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?

(5)   The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.          Solution

(6)   A copy of English book weighs 0.45 kg. What is the weight of 20 copies ?          Solution

(7)   Find the weight of 25.5 meters of copper wire in kilograms, if one meter weighs 10 grams.          Solution

(8)   Robert paid $140 for 2.8 kg of cooking oil. How much did 1 kg of the cooking oil cost ?         Solution

(9)   If $20.70 is earned in 6 hours, how much money will be earned in 5 hours ?            Solution

(10)   A pipe is 76.8 meters long. What will the greatest number of pieces of pipe each 8 meters long that can be cut from this pipe ?          Solution

Answers Key :

Problems on Percentage

(1)  In a particular store the number of TV's sold the week of Black Friday was 685. The number of TVs sold the following week was 500. TV sales the week following Black Friday were what percent less than TV sales the week of Black Friday ?

(A)  17%   (B)  27%   (C)  37%   (D)  47%

(2)  In March, a city zoo attracted 32000 visitors to its polar bear exhibit. In April, the number of visitors to the exhibit increased by 15%. How many visitors did the zoo attract to its polar bear exhibit in April ?

(A)  32150   (B)  32480   (C)  35200  (D)  36800

(3)  A charity organization collected 2140 donations last month. With the help of 50 additional volunteers, the organization collected 2690 donations this month. To the nearest tenth of a percent, what was the percent increase in the number of donations the charity organization collected ?

(A) 20.4%   (B)  20.7%    (C)  25.4%   (D)  25.7%

(4)  The discount price of a book is 20% less than the retail price. James manages to purchase the book at 30% off the discount price at the special book sale. What percent of the retail price did James pay ?

(A)  42%   (B)  48%    (C)  50%   (D)  56%

(5)  Each day, Robert eats 40% of the pistachios left in his jar at the time. At the end of the second day, 27 pistachios remain. How many pistachios were in the jar at the start of the first day ?

(A)  75   (B)  80   (C)  85  (D)  95

(6) Joanne bought a doll at a 10 percent discount off the original price of $105.82. However, she had to pay a sales tax of x% on the discounted price. If the total amount she paid for the doll was $100, what is the value of x ?

(A)  2   (B)  3   (C)  4  (D)  5

(7)  In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 2010, how many were built in Town B ?

(A)  56   (B)  50    (C)  48   (D)  20

(8)  Over two week span, John ate 20 pounds of chicken wings and 15 pounds of hot dogs. Kyle ate 20 percent more chicken wings and 40 percent more hot dogs. Considering only chicken wings and hot dogs, Kyle ate approximately x percent more food, by weight, than John, what is x (rounded to the nearest percent) ?

(A)  25   (B)  27    (C)  29   (D)  30

(9) Due to deforestation, researchers, expect the deer population to decline by 6 percent every year. If the current deer population is 12000, what is the approximate expected population size in 10 years from now ?

(A)  25000   (B)  48000    (C)  56000   (D)  30000

(10)  In 2000 the price of a house was $72600. By 2010 the price of the house has increased to 125598.

(A)  70%    (B)  62%    (C)  73%    (D)  90%

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To download a printable version of this game, use the links below. There are three sets - set A is the easiest and set C is the most difficult. If you print double sided, then the cards will have an NRICH logo on the back. Otherwise, you can just print the first page. Set A , Set B , Set C

The aim of this game is to match pairs of cards. 

Click on a card in the interactivity below to turn it over. Then click on another one. If the two cards match, they will stay face-up. If the two cards do not match, they will return to being face-down. 

The game ends when all the cards have been matched in pairs. 

Click on the links below if you would like to try some alternative versions of the Level 1 game:

• Play with face-up cards  - the cards are all face-up at the start so you can focus on the maths rather than the memory aspect of the game. How quickly can you match them all?
• Play with a scoring system  - you start with 100 points, lose 10 points whenever you turn over cards that don't match, and add 50 points whenever they do match.

Once you've mastered Level 1, there are four more levels to try, getting progressively more difficult:

• Level 2     Face-up      Face-down
• Level 3     Face-up      Face-down
• Level 4     Face-up      Face-down
• Level 5     Face-up      Face-down

What strategies did you use to work out that two cards matched? Which pairs did you find easy to match?  Which pairs did you find more difficult to match?

We would love to hear about the strategies you used as you played the game.

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Convert Percent to a Fraction Number Conversion Worksheets Math Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

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Convert Percent to a Fraction Number Conversion Worksheets Math Problems Make learning percentages and decimals engaging with our comprehensive set of worksheets designed to reinforce understanding and mastery of these essential mathematical concepts. Whether you’re a teacher looking for classroom resources or a parent seeking supplementary materials for at-home learning, our worksheets cater to various skill levels and learning styles. Variety of Problems: Each worksheet offers a diverse range of problems, including converting between percentages and decimals, calculating percentages of numbers, and solving word problems involving percentages and decimals. Progressive Difficulty: Worksheets are organized by difficulty level, allowing learners to gradually build their skills from basic to advanced concepts. Answer Keys: Each worksheet comes with an answer key for easy grading and self-assessment, facilitating independent learning. Enhanced Understanding: Through repeated practice, students develop a deeper comprehension of percentages and decimals, paving the way for proficiency in more advanced mathematical concepts. Improved Problem-Solving Skills: By tackling a variety of problems, learners sharpen their analytical and critical-thinking abilities, essential for solving mathematical problems and real-world challenges. Confidence Boost: Success in solving problems boosts students’ confidence and enthusiasm for learning mathematics, fostering a positive attitude towards the subject. Whether you’re introducing percentages and decimals for the first time or reinforcing existing knowledge, our worksheets provide valuable resources to support effective teaching and learning. Empower your students to excel in mathematics with our engaging and comprehensive materials. Worksheets are made in 8.5” x 11” Standard Letter Size. This resource is helpful in students’ assessment, Independent Studies, group activities, practice and homework. This product is available in PDF format and ready to print as well.

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