How to Estimate a Math Problem

Estimation is a great way to check your work and solve math problems quickly. Once you learn to round numbers successfully, you can do much more complex math equations in your head. Here are some tips and tricks for mastering the art of rounding and estimation.

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How to Estimate

Rounding Numbers

Decimals

When you estimate math problems, start by rounding off the numbers. Rounding makes math problems easier to estimate. If you're working with decimals, you might want to round to the nearest whole number. If you have a number with a decimal value of 0.5 or higher, you round up (5.7 rounds to 6, for instance). The opposite is also true - numbers with decimal values lower than 0.5 are rounded down. For instance, 4.3 rounds down to 4.

Whole Numbers

If you're working with whole numbers, you'll probably want to round to the nearest ten or hundred, depending on how close you need your estimation to be. Naturally, close rounding will make your estimation more accurate. For example, if you round 4,557 to 4,560 (the nearest ten), your estimation will be more accurate than if you round to 4,600 (the nearest hundred).

Sample Estimation Question

Once you've rounded the numbers, you can estimate the answer in your head. As an example, we'll estimate the math problem 51 x 69. This would be a hard problem to do mentally, so to make it easier, you'll start by rounding to the nearest ten. You can round 51 to 50 and 69 to 70. Then, in your head, multiply 5 x 7 = 35 and add two zeros to your answer. The final, estimated answer is 50 x 70 = 3,500.

Now you know that 51 x 69 is about 3,500. By checking it on a calculator, you'll see that 51 x 69 = 3,519. That's only 19 off, which isn't bad for a quick estimation!

Practice Problems

Using the skills you've learned, try to estimate the following math problems. You can start by rounding to the nearest whole number that is easy enough to work with (for instance, 20 instead of 19 and 50 instead of 48).

  1. 49 + 99
  2. 153 - 33
  3. 56 x 81
  4. 67 x 42
  5. 78 ÷ 41

Answers

Although there are really no 'wrong' answers to these problems, since you're estimating, the answers below are the ones you should have if you've followed the steps explained above. The important thing is that your estimated answers are in the ballpark of the correct answers, which you can find using a calculator. It's also important that you can explain how you arrived at your estimated answers.

  1. If you round 49 to 50 and 99 to 100, you'll get an estimated answer of 150.
  2. Start by rounding 153 to 150 and 33 to 30. After you subtract, you should get an estimated answer of 120.
  3. Round 56 to 60 and 81 to 80, and then multiply. Your estimated answer will be 4,800.
  4. After you've rounded 67 to 70 and 42 to 40, you'll multiply to get the estimated answer of 2,800.
  5. Begin by rounding 78 to 80 and 41 to 40. Then, divide to get an estimated answer of 2.
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