Estimate Quotients with Two-Digit Divisors

Students use compatible numbers and place value reasoning to estimate quotients when dividing by two-digit divisors. Estimation helps students check the reasonableness of computed answers and determine the approximate size of each quotient digit.

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Grade 5 · Whole Number Division with Multi-Digit Dividends · question 1 of 3

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Hana has 716 carrots to feed to 39 rabbits at the zoo over a month. Use 800 for 716 and 40 for 39 to estimate. About how many carrots does each rabbit get?

How it is taught

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An estimate uses nearby numbers that divide easily.

Compatible numbers tell about how large the quotient is.

Read it: Estimating with compatible numbers

3612 ÷ 41: round the divisor to a ten, 41 ≈ 40. Then change 3612 to a nearby number that 40 divides with a fact: 36 ÷ 4 = 9, so use 3600. 3600 ÷ 40 = 90, so 3612 ÷ 41 is about 90.

Round the divisor to the nearest ten.
Look at the first digits of the dividend and find the nearest multiple of the divisor's tens digit: that is the fact.
Write the dividend with that fact and 0s, and divide: the answer is the estimate.

Compatible numbers are close to the real ones, so their quotient is close to the real quotient.

3600 ÷ 40 is 360 ÷ 4, and 36 ÷ 4 = 9, so it is 90.

An estimate tells you how big the answer should be, so you can check an exact answer.

Round the divisor to a ten, change the dividend so a fact fits, then divide.

Dropping a 0: 3600 ÷ 40 = 9.

36 ÷ 4 = 9, so 360 ÷ 40 = 9 and 3600 ÷ 40 = 90.

Estimate with compatible numbers: 1795 ÷ 28 ≈ ___ — 60. 28 is about 30, and 1795 is about 1800: 1800 ÷ 30 = 60.

367 ÷ 53

Three hundred sixty-seven cookies, fifty-three friends. About how many cookies does each friend get?

Solving this exactly is hard. Let's estimate first to get a quick, reasonable answer.

Step one: round the divisor. Fifty-three is close to fifty, and fifty is much friendlier to divide by.

Step two: find a number near three hundred sixty-seven that pairs nicely with fifty. Three hundred fifty works — its digits are basic-fact friends with five.

We already know thirty-five divided by five is seven.

So three hundred fifty divided by fifty is also seven — the place values cancel out, leaving the same answer.

Grade 5 · Use compatible numbers to estimate

That tells us three hundred sixty-seven divided by fifty-three is about seven.

Each friend gets about seven cookies. Estimation done!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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