How to Estimate Multiplication Problems

How to Estimate with Multiplication

Decimals

Rounding makes math problems easier to estimate. For example, let's estimate the answer to the problem 3.4 x 8.8. Start by rounding the decimals to the nearest whole number. Numbers with a decimal value of 0.5 or higher are rounded up, and numbers with a decimal value of 0.4 or lower are rounded down. If we follow this rule, 3.4 can be rounded down to 3, and 8.8 can be rounded up to 9.

Next, you'll simply multiply the two resulting numbers together. Since 3 x 9 = 27, that's your estimated answer. Compared to the exact answer, 29.92, the estimate was fairly close.

Whole Numbers

When you're estimating multiplication problems with whole numbers, round each number in the problem to another whole number that's easier to multiply mentally. For example, if you have the problem 54 x 97, you can round the 54 down to 50 the 97 up to 100. This gives you 50 x 100, which you can solve in your head.

Since 10 x 10 = 100, then 50 x 100 = 50 x 10 x 10. You can find the product of any number and 10 by simply adding a 0 to the other number, so 50 x 10 = 500 and 500 x 10 = 5,000. This means the estimated answer is 5,000. If you check this answer using a calculator, you'll find that 54 x 97 = 5,238, so this estimate is fairly close.

Mixed Problems

Let's look at the problem 3.4 x 89. The first thing we need to do is round 3.4 to the nearest whole number, which is 3. Next, we'll round 89 to the nearest ten, which gives us 90. Since 9 x 10 = 90, you can turn this problem into 3 x 9 x 10. You already know that 3 x 9 = 27, and you can find the answer to 27 x 10 by adding a 0 to get 270. Then, check your answer using a calculator. You'll see that the exact answer is 302.6, which is reasonably close to 270.

Summing Up

These examples give you a sense of how rounding and using mental math can be great tools for quickly estimating answers; however, estimation won't produce exact solutions. Remember that estimating with numbers that are as close as possible to the original numbers in the problem will give you the best possible result. It's also helpful to keep in mind that if you round both numbers in the multiplication problem up, the estimate will be high, and if you round them both down, it will be low.