How to Check Math Homework

Step-by-Step Guide

1. 1

   Step 1: Estimate.

   If you have an general idea of what your answer should be, you can compare the estimate with your solution to verify that it makes sense.
   
   Estimating usually involves rounding to place values that make the number you are working with easy to calculate in your head.For example, you might need to calculate 824+288{\displaystyle 824+288}.
   
   Round each number to the nearest hundred. 824 rounds down to 800 and 288 rounds up to
   300.
   
   Add together your estimated numbers: 800+300=1,100{\displaystyle 800+300=1,100}.
   
   You can estimate before you start the actual calculation, or after.
   
   Once you complete the actual calculation, compare it with the estimate to check for reasonableness.
   
   For example, if you calculated 824+288=1,812{\displaystyle 824+288=1,812}, you know your answer may not be correct because 1,812 is much larger than the estimate of 1,100.
   
   If you calculated 824+288=1,112{\displaystyle 824+288=1,112}, you can assume that your answer is correct, because 1,112 is close to the estimate 1,100.
2. 2

   Step 2: Use inverse operations.

   Inverse operations are operations that undo each other.
   
   You can think of them as opposites.
   
   Addition and subtraction are inverse operations.
   
   Multiplication and division are inverse operations, too.If you do a problem with any one of these operations, you can use its inverse operation to see whether your calculations make sense.
   
   For example, you might need to calculate 48÷6{\displaystyle 48\div 6}.
   
   In division, when you multiply the quotient (the answer) and the divisor (the number you are dividing by), your product will be the dividend (the number being divided into).
   
   So, if you calculate 48÷6=8{\displaystyle 48\div 6=8}, you know that your answer is correct, since 8×6=48{\displaystyle 8\times 6=48}.
   
   You might need to calculate 7×9{\displaystyle 7\times 9}.
   
   In multiplication when you divide the product (the answer) by either factor, the quotient is the other factor.
   
   So, if you calculate 7×9=56{\displaystyle 7\times 9=56}, you know your answer is incorrect, because 56÷9{\displaystyle 56\div 9} does not equal
   7.
   
   The answer is 63, because 63÷9=7{\displaystyle 63\div 9=7}. , In algebra it is easy to check your solution by plugging the value you found for the variable back into the original equation.
   
   When working the equation, make sure you use the correct order of operations to solve.
   
   For example, if you are solving the equation 4(x−3)=28{\displaystyle 4(x-3)=28}, and you find that x=10{\displaystyle x=10}, plug in 10 for x{\displaystyle x} in the original equation to see if that makes the equation true.
   
   So, you would calculate:4(x−3)=28{\displaystyle 4(x-3)=28}4(10−3)=28{\displaystyle 4(10-3)=28}4(7)=28{\displaystyle 4(7)=28}28=28{\displaystyle 28=28}Since this equation is true, you know that your solution x=10{\displaystyle x=10} is correct. , Often there is more than one way to solve a problem.
   
   In school, your teacher often wants you to use a particular strategy.
   
   That doesn’t mean, however, that you can’t check your work using a different strategy.
   
   For example, if you are trying to find the area of a rectangle that is 4 units long and 5 units wide using the formula Area=length×width{\displaystyle {\text{Area}}={\text{length}}\times {\text{width}}}, you can check your work by drawing an array.
   
   If you are doing multiplication, you can check your work by doing repeated addition.
3. 3

   Step 3: Plug solutions back into equations.

4. 4

   Step 4: Solve using a different strategy.

Detailed Guide

About the Author