How Can I Check My Math Homework: Tips for Working Backward

Have you ever put lots of effort into a math problem on your homework or a test, but when you got it back, you found out that your answer was wrong? You can avoid this by taking a few minutes to check your math problems using a technique called 'working backward.'

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How to Check Your Answers

You can check your answers to math problems by using inverse operations or by plugging your solution back into the original problem and reworking it. To learn how, find the section below that pertains to the type of problem you'd like to check.

Basic Operations

You can check 1-step problems involving basic operations, like addition, subtraction, multiplication and division, by following these steps:

1. Solve the problem. For instance, 24 - 4 = 20.
2. Identify the inverse of the operation you used in the problem. This is the operation you'll use in the next step. Addition and subtraction are inverse operations, and so are multiplication and division. Subtraction was used in the problem above, so you'll use addition in the next step.
3. Add, subtract, multiply or divide the answer by the second number in the original problem. For this example, the operation is 20 + 4 because the original problem was 24 - 4 = 20.
4. If the solution is the first number in the problem, your answer is correct. For example, since 20 + 4 = 24, and the original problem was 24 - 4 = 20, this answer is correct. If your solution is a different number, then you should recheck your original answer.

This technique works with any type of 1-step problem, including those that involve decimals, fractions and percentages. For instance, here's how you'd check the problem 6.28 ÷ 3.14:

1. Arrive at your solution. For instance, let's say your result is 6.28 ÷ 3.14 = 2.
2. Identify the inverse operation you'll be using. Since the original problem uses division, you'll need to use multiplication.
3. Multiply your answer by the second number from the problem, like this: 2 x 3.14 = 6.28.
4. Since this solution matches the first number in the problem (6.28), your answer is correct.

Algebra Equations

You can use a similar technique to check your solutions to algebra equations. For instance, if you're solving the equation 15 + x = 20, and you arrive at the solution x = 5, you can check it by following these steps:

1. Replace the variable in the original equation with the value that you found for it. In this example, you'd replace x with five, like this: 15 + 5 = 20.
2. Simplify the equation, like this: 20 = 20.
3. If the two sides of the equation are equal, then your answer is correct. If they're not equal, then you have not found the correct solution.
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