6 steps to math problem solving

The expand command is used mainly to rewrite polynomials with all brackets and whole number powers multiplied out and all like terms collected together. In the advanced section, you also have the option of expanding trigonometric functions, expanding modulo any integer and leaving certain parts of the expression untouched whilst expanding the rest.

Go to the Expand page

The factor command will try to rewrite an expression as a product of smaller expressions. It takes care of such things as taking out common factors, factoring by pairs, quadratic trinomials, differences of two squares, sums and differences of two cubes, and a whole lot more. The advanced section includes options for factoring trigonometric functions, factoring modulo any integer, factoring over the field of Gaussian integers (just the thing for those tricky sums of squares), and even extending the field over which factoring occurs with your own custom extensions.

Go to the Factor page

Simplifying is perhaps the most difficult of all the commands to describe. The way simplification is performed in QuickMath involves looking at many different combinations of transformations of an expression and choosing the one which has the smallest number of parts. Amongst other things, the Simplify command will take care of canceling common factors from the top and bottom of a fraction and collecting like terms. The advanced options allow you to simplify trigonometric functions or to instruct QuickMath to try harder to find a simplified expression.

Go to the Simplify page

The cancel command allows you to cancel out common factors in the denominator and numerator of any fraction appearing in an expression. This command works by canceling the greatest common divisor of the denominator and numerator.

Go to the Cancel page

Partial Fractions

The partial fractions command allows you to split a rational function into a sum or difference of fractions. A rational function is simply a quotient of two polynomials. Any rational function can be written as a sum of fractions, where the denominators of the fractions are powers of the factors of the denominator of the original expression. This command is especially useful if you need to integrate a rational function. By splitting it into partial fractions first, the integration can often be made much simpler.

Go to the Partial Fractions page

Join Fractions

The join fractions command essentially does the reverse of the partial fractions command. It will rewrite a number of fractions which are added or subtracted as a single fraction. The denominator of this single fraction will usually be the lowest common multiple of the denominators of all the fractions being added or subtracted. Any common factors in the numerator and denominator of the answer will automatically be cancelled out.

Go to the Join Fractions page

Introduction to Algebraic Functions

The notion of correspondence is encountered frequently in everyday life. For example, to each book in a library there corresponds the number of pages in the book. As another example, to each human being there corresponds a birth date. To cite a third example, if the temperature of the air is recorded throughout a day, then at each instant of time there is a corresponding temperature.

The examples of correspondences we have given involve two sets X and Y. In our first example, X denotes the set of books in a library and Y the set of positive integers. For each book x in X there corresponds a positive integer y, namely the number of pages in the book. In the second example, if we let X denote the set of all human beings and Y the set of all possible dates, then to each person x in X there corresponds a birth date y.

We sometimes represent correspondences by diagrams of the type shown in Figure 1.17, where the sets X and Y are represented by points within regions in a plane. The curved arrow indicates that the element y of Y corresponds to the element x of X. We have pictured X and Y as different sets. However, X and Y may have elements in common. As a matter of fact, we often have X = Y.

A function f from a set X to a set Y is a correspondence that assigns to each element x of X a unique element y of Y. The element y is called the image of x under f and is denoted by f(x). The set X is called the domain of the function. The range of the function consists of all images of elements of X.

Earlier, we introduced the notation f(x) for the element of Y which corresponds to x. This is usually read "f of x." We also call f(x) the value of f at x. In terms of the pictorial representation given earlier, we may now sketch a diagram as in Figure 1.18. The curved arrows indicate that the elements f(x), f(w), f(z), and f(a) of Y correspond to the elements x, y, z and a of X. Let us repeat the important fact that to each x in X there is assigned precisely one image f(x) in Y; however, different elements of X such as w and z in Figure 1.18 may have the same image in Y.

Solution As in Example 1, finding images under f is simply a matter of substituting the appropriate number for x in the expression for f(x). Thus:

Many formulas which occur in mathematics and the sciences determine functions. As an illustration, the formula A = pi*r 2 for the area A of a circle of radius r assigns to each positive real number r a unique value of A. This determines a function f, where f(r) = pi*r 2 , and we may write A= f(r). The letter r, which represents an arbitrary number from the domain off, is often called an independent variable. The letter A, which represents a number from the range off, is called a dependent variable, since its value depends on the number assigned tor. When two variables r and A are related in this manner, it is customary to use the phrase A is a function of r. To cite another example, if an automobile travels at a uniform rate of 50 miles per hour, then the distance d (miles) traveled in time t (hours) is given by d = 50t and hence the distance d is a function of time t.

We have seen that different elements in the domain of a function may have the same image. If images are always different, then, as in the next definition, the function is called one-to-one.  

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

Strategies for Solving Math Word Problems

Math word problems can be tricky and often challenging to solve. Employing the SQRQCQ method can make solving math word problems easier and less intimidating.

The SQRQCQ method is particularly useful for children with learning disabilities and can be used effectively in special education programs. SQRQCQ is an abbreviation for Survey, Question, Read, Question, Compute, and Question.

Step 1 – SURVEY the Math Problem

The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem. The idea here is to get a general understanding.

Step 2 – QUESTION

Once you have an idea of what you’re attempting to solve, you need to determine what formulas, steps, or equations should be utilized in order to find the correct answer. It is impossible to find an answer if you can’t determine what needs to be solved. Basically, what are the questions being asked by the problem?

Step 3 – REREAD

Now that you’ve determined what needs to be solved, reread the problem and pay close attention to specific details. Determine which aspects of the problem are interrelated. Identify all relevant facts and information needed to solve the problem. As you do, write them down.

Step 4 – QUESTION

Now that you’re familiar with specific details and how different facts and information within the problem are interrelated, determine what formulas or equations must be used to set up and solve the problem. Be sure to write down what steps or operations you will use for easy reference.

Step 5 – COMPUTE

Use the formulas and/or equations identified in the previous step to complete the calculations. Be sure to follow the steps you outlined while setting up an equation or using a formula. As you complete each step, check it off your list.

Step 6 – QUESTION

Once you’ve completed the calculations, review the final answer and make sure it is correct and accurate. If it does not appear logical, review the steps you took to find the answer and look for calculation or set-up errors. Recalculate the numbers or make other changes until you get an answer that makes sense.

How does SQRQCQ help students with learning disabilities?

Math word problems tend to be especially challenging for Learning Disabled (LD) students. LD students often lack “Concept Imagery”, or the ability to visualize the whole problem by creating a complete mental image. They often jump right into calculations and computations without understanding what the problem is asking or what they’re looking for.

LD students may also struggle to understand the words or wording within math word problems correctly. The inability to correctly interpret and understand wording greatly impacts their math reasoning skills and often leads them to making the wrong calculations and arriving incorrect conclusions.

Remembering and manipulating information and details in their working memory is another challenge some LD students face as they try to see the whole picture. Slow processing of information, followed by frustration and anxiety, will often lead LD students to try and get through math word problems as quickly as possible – which is why they often jump straight into computations in their attempt to make it to the finish line as quickly as possible.

SQRQCQ is a metacognitive guide that provides LD students with a logical order for solving math word problems. It provides just enough direction to guide them through the reasoning process without overwhelming them. SQRQCQ is also a mnemonic that is easy for students to remember and which they can fall back on when completing homework or taking tests.

Read also: – A Guide for St u dying Math

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Best iPad Math Notes Like Calculator Apps for Android

Ipados math notes calculator's feature is an old trick in android's book.

The recently concluded Apple’s WWDC 2024 event grabbed eyeballs worldwide. While iOS 18 has been the talk of the town with features like the ability to move app icons anywhere on the iPhone’s home screen, the ability to apply light/dark or tint to the app icons, the fully customizable Control Center, the option to change the focus of the flashlight , etc., one app also managed to grab headlines, called the Calculator app introduced for iPadOS 18.

However, the newly introduced iPad Calculator app isn’t just any other calculator app. The Math Notes is the main highlighting feature of the iPadOS 18 Calculator app, which auto-completes the calculation as soon as you write the equals sign after your equation. In this guide, we will show you the best iPad Math Notes calculator alternatives for Android. Of course, if it’s there for iOS, Android users may want it for themselves. Let’s jump right into it.

Table of Contents

What’s so good about the iPad Calculator?

So, iPads debuted back in 2010, and ever since their debut, they have been calculator-less. Thankfully, the iPadOS 18 update, announced at WWDC 2024 , added the Calculator app, and not just a simple calculation app; it does more than that. The iPad Calculator app has an interface similar to that of calculator apps across Apple platforms.

The app boasts round buttons in black and orange and features an improved unit conversion system, a history tape sidebar, and the most talked about Math Notes feature. The iPad Math Notes feature can be accessed from the Calculator app by using the dedicated button in the bottom left corner of the app screen.

Once you are in, simply write the equation, and as soon as you write equals to the (=) sign, the iPad Math Notes feature will automatically solve the problem for you. The iPad Math Notes feature in the Calculator app supports graphical expressions and gets answers by inputting various values into variables. The Math Notes are automatically stored in the new Math Notes folder.

If you loved the new iPad Math Notes and other features of the Calculator app for the iPad, let us take a look at the iPad Math Notes calculator app’s Android alternatives that offer a similar experience.

4 Best iPad Math Notes Calculator App Alternatives for Android

Microsoft Maths Solver – Offers step-by-step explanation

One of the best, or it is safe to say, advanced calculator apps that can easily be a great alternative to the iPadOS 18’s Calculator app is Microsoft Maths Solver. The app offers various similar features to the iPad Math Notes feature. You can easily handwrite your math problem or equations on the screen by tapping Send, and then the Microsoft Maths Solver will automatically solve the problem for you.

It can solve a variety of math problems, including arithmetic, algebra, trigonometry, calculus, statistics, and other topics, and makes use of AI to provide you with solutions. One of the best features of this app that I liked was the option to “Scan and Solve.” Notably, the feature lets you scan a math problem using your device’s camera to snap a photo and helps you solve it with step-by-step instructions. The feature also provides interactive graphs for a proper explanation.

The Microsoft Math Solver comes with support for advanced scientific math calculators, scanning and solving math problems in multiple worksheets, searching the web for similar problems or video lectures, supporting linear and non-linear functions, and also the ability to solve math problems in your language, including Chinese, French, German, Hindi, Italian, Japanese, Portuguese, Russian, Spanish, and many more.

• It supports advanced math problems, including elementary, pre-algebra, basic calculus, statistics, and more.
• Gives answers in multiple languages
• Support for linear/non-linear functions
• Lets you scan and solve a math problem
• The step-by-step solutions provided are not in real-time

Download Microsoft Math Solver

MyScript Calculator 2 – Solves multi-step problems quickly

Another popular iPad Math Notes Calculator alternative for Android is the MyScript Calculator 2. It is a paid app, but it is very close to how the iPad’s calculator app works. When you open the app, it turns into a virtual paper, where all you need to do is write down your equation and get the answers in real-time.

You can easily scratch and rewrite the correct equation as you would on an actual piece of paper. You can write down equations and problems, extending to several lines. One of the best parts about the MyScript Calculator 2 is that you can mix calculations, i.e., your equations or problems can include multiplication, division, subtraction, etc.

It also supports dragging and dropping numbers and equations; multi-step problems can be rearranged, and you can choose how your answers are displayed: as decimals, fractions, or mixed numbers. The app supports problem-solving related to logs, Trigonometry, inverse trigonometry, power, roots, exponentials, and much more.

• Lets you write or scratch equations or numbers on the screen
• Provides instant solutions to your problems
• Support solving complex multi-step calculations
• Keeps your calculation history
• Doesn’t support graphs
• There is no option for variables

Download MyScript Calculator 2

Maple Calculator – Visualize your problems and solutions in 2D and 3D

The Maple Calculator is an all-in-one calculator app that can help you visualize your problems and solutions in 2D and 3D. This app goes beyond being a simple calculator that solves your equations. You can write your equations on the screen, and the app, using the world’s most powerful math engine, Maple, will recognize your handwriting and give you step-by-step solutions.

The app provides 2D and 3D graphs just like iPad Math Notes, and you can see the graph change as the expressions are changed in real-time. You can also take a picture of your problem and upload it to the Maple Calculator to see the final answer or get a step-by-step solution.

It supports multiple languages and helps solve complex math disciplines such as algebra, calculus, trigonometry, linear algebra, differential equations, etc.

• Lets you visualize your problems and solutions in 2D and 3D
• Gives you step-by-step solutions to your written problems or captured problems
• Support complex math disciplines to be solved
• Step-by-step solutions may not be generated for most of the questions

Download Maple Calculator

Photomath – Google’s answer to Apple

Photomath from Google lets you scan any problem using the camera on your phone. The solutions are teacher-approved, and Photomath breaks your problem into step-by-step explanations to help you understand the solution better. Photomath supports solving problems from elementary arithmetic to advanced geometry, even to advanced calculus.

This calculator app can help you solve any handwritten or textbook-based problems. The animated steps negate the need for guessing to understand how the solution was achieved. There is a 24/7 virtual tutor as well, whom you can reach and get solutions to your questions. The app can even solve word problems and offer solutions in graphs. The app offers multiple solutions for a problem as well.

Google has included step-by-step explanations in the free version itself, and you can ask questions from various math disciplines, including numbers and quantity, algebra, functions, trigonometry and angles, sequences, geometry, and calculus. The app also explains the formulas and equations that have been applied to solve the problem with proper definitions.

• Lets you solve equations and word problems
• Animated step-by-step answers, even in the free version
• Interactive graphs and video learning
• Supports solving advanced math problems
• Scanning of problems may not always be accurate

Download Photomath

Make your Android do the math

The above apps are some of the best iPad Calculator app alternatives for Android that have features similar to Math Notes. Some of them even have more features than the iPad’s calculator app. If you are a Motorola user, then here’s a bonus tip: you can use the Handwriting Calculator app. It was introduced for the Moto G Stylus phone, but you can grab the APK from APKMirror and install it on any Motorola phone. You need to install it and create a home screen shortcut using the Activity Launcher app, and that’s it.

Since iPadOS 18 is expected to roll out to the public this fall, you can take a look at some of the best iPad calculator apps for the time being.

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