Math Core

Sometimes you don't need an exact answer. You just need to know "about how many." And even when you do need the exact answer, a quick estimate tells you whether your answer makes sense. To estimate a product, round the numbers first, then multiply.

Round, then multiply

Rounded numbers end in zeros, so they are easy to multiply in your head.

To estimate $7 \times 382$ , round 382 to the nearest hundred. 382 is closer to 400 than to 300.

382 is between 300 and 400, and it is closer to 400.

Now multiply the rounded number: $7 \times 400 = 2{,}800$ . So $7 \times 382$ is about 2,800. (The exact product is 2,674, which is close.)

Estimating a product

Round each number to a friendly number, such as the nearest ten, hundred or thousand. (Leave a one-digit number as it is.)
Multiply the rounded numbers.
The result is an estimate. It is close to the exact product, but usually not equal to it.

Worked example: Two two-digit numbers

Estimate $48 \times 31$ .

Round each number to the nearest ten: 48 rounds to 50, and 31 rounds to 30.

50 \times 30 = 1{,}500

So $48 \times 31$ is about 1,500. (The exact product is 1,488.)

Common mistake

Round before you multiply, not after. Estimating is supposed to be quick. If you work out the exact product first and then round it, you have done the hard work for nothing, and you have no check on your answer.

Is my answer reasonable?

An estimate is a great way to catch mistakes. If your exact answer is far from your estimate, check your work.

Worked example: Catching a mistake

Mia found $27 \times 34$ and got 6,318. Is her answer reasonable?

Round both numbers to the nearest ten: $30 \times 30 = 900$ .

Mia's answer, 6,318, is much too big. It is not reasonable. When she multiplies again, she finds $27 \times 34 = 918$ , which is close to 900.

Is there enough?

Estimates also help you make decisions. Pay attention to whether you rounded up or down.

Worked example: Enough money?

A class wants to buy 6 tickets that cost $18 each. The class has $150. Is that enough?

Round $18 up to $20. Then $6 \times 20 = 120$ , so the tickets cost about $120.

Even at $20 each, the tickets cost only $120, which is less than $150. The real price, $18, is lower than $20, so the real total is even less. Yes, the class has enough money. (The exact cost is $6 \times 18 = 108$ , or $108.)

Tip

If you round every number up, your estimate is bigger than the exact answer. If you round every number down, your estimate is smaller. Knowing which way you rounded tells you whether the real answer is above or below your estimate.

Practice

Practice 1

Estimate $4 \times 289$ by rounding 289 to the nearest hundred.

Type a number.

Practice 2

Estimate $6 \times 712$ by rounding 712 to the nearest hundred.

Type a number.

Practice 3

Estimate $38 \times 52$ by rounding each number to the nearest ten.

Type a number.

Practice 4

Estimate $73 \times 18$ by rounding each number to the nearest ten.

Type a number.

Practice 5

Estimate $5 \times 4{,}186$ by rounding 4,186 to the nearest thousand.

Type a number.

Practice 6

Which is the exact product $61 \times 29$ ? Use an estimate to decide.

Practice 7

Each bus holds 52 students. A school has 9 buses and 420 students going on a trip. Round 52 to the nearest ten to decide: can all the students ride?

Practice 8

Estimate $8 \times 395$ by rounding 395 to the nearest hundred. The exact product is 3,160. How far is your estimate from the exact product?

Type a number.