Math Help: Estimating Division Problems

Help Estimating Division Problems

Estimating means making an educated guess at the answer to a math problem. You'll likely encounter math problems where you're specifically asked to estimate, or where you can save time by estimating. Here are a few general tips you can use to estimate effectively:

1. Round. It could be quite a task to divide 321 by 22 in your head, but 320 ÷ 20 is a bit more doable.

2. Find a range. It can be helpful to know that your answer is between 2 numbers. For example, if you're dividing 500 by 13, you can estimate that the answer is between 20 and 50 by solving 500 ÷ 10 and 500 ÷ 25 in your head.

3. Improve your mental math skills. The better you are at doing math in your head, the less actual estimation you'll have to do, and the more precise your estimation can be. Memorize your multiplication and division facts, including the ones through twelves and the tens, fifteens and twenties.

Estimating and Long Division

Because long division involves trial and error, it naturally requires you to estimate. For example, imagine you're dividing 1,234 by 15. You know that 15 can't go into 12, but it can definitely go into 123.

To complete the next step in the problem, you need to estimate how many times 15 goes into 123. Then, you'll multiply that estimate by 15 and try to subtract the answer from 123. If 15 or more is left over, you guessed too low, but if your answer is larger than 123, you guessed too high.

Using the rounding strategy explained earlier, you can round 15 up to 20 and 123 down to 120. Since 120 ÷ 20 = 6, you'll try multiplying 15 x 6. The answer is only 90, though, so you've guessed too low. You can figure out how much you need to add to 6 by subtracting 90 from 123. The answer is 33, and you know that 30 ÷ 15 = 2, so add 2 + 6 and try 8. Since 15 x 8 = 120, this means 8 is the solution to this step of the division problem.

Estimation and Problem Solving

Some word problems specifically ask you to estimate an answer. Select one of the strategies described earlier and explain your reasoning in solving the problem, if asked.

Estimation can also be helpful for solving math problems that have multiple-choice answers. For instance, you might be asked to find the area of a garden that's 13 feet by 7 feet. Imagine the 3 answers provided are 2 1/7 feet, 20 feet and 91 feet. You find area by multiplying the 2 side lengths together, so you can round 13 down to 10 and estimate that the answer must be larger than 70, since 10 x 7 = 70. Based on this estimation, you can select the third answer, 91 feet.