Estimating Quotient

Estimating Quotient

​Mr. Emel Escobido
Mathematics Teacher

How can you estimate a quotient?

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Use compatible numbers! Compatible numbers are pairs of numbers you can add, subtract, multiply, or divide easily in your head.

Let's estimate the quotient of 461 ÷ 9.

Round 461 to the closest number that is a multiple of 9. Some basic multiples of 9 are 36, 45, and 54.

461 is close to 450.

The numbers 450 and 9 are compatible numbers because you can divide with no remainder.

450 ÷ 9 = 50

So,

461 ÷ 9 is about 50.

Drag and Drop

Pick the expression with the better compatible numbers to estimate 2,066 ÷ 7.

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Placeholder

Drag these tiles and drop them in the correct blank above

2,100 ÷ 7

2,000 ÷ 7

Fill in the Blanks

Now, use the expression you picked to estimate the quotient.

2,100 ÷ 7

Drag and Drop

Pick the expression with the better compatible numbers to estimate 2,761 ÷ 9.

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Placeholder

Drag these tiles and drop them in the correct blank above

2,800 ÷ 9

2,700 ÷ 9

Fill in the Blanks

Now, use the expression you picked to estimate the quotient.

2,700 ÷ 9

Estimating Larger Quotient

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Sometimes you need to change both numbers to find compatible numbers.

Let's estimate 5,487 ÷ 77.

First round 77 to the nearest ten.

5,487 ÷ 77

5,487 ÷ 80

Next, round 5,487 to the closest number that is a multiple of 80. Think about basic facts. Some multiples of 8 are 48, 56, 64, and 72.

5,487 is close to 5,600.

The numbers 5,600 and 80 are compatible numbers.

5,487 ÷ 80

5,600 ÷ 80

Now divide.

5,600 ÷ 80 = 70

The quotient of 5,487 ÷ 77 is about 70.

Multiple Choice

Which estimated quotient is most reasonable?

• 3,627 ÷ 6 ≈ 600

• 582 ÷ 3 ≈ 20

• 639 ÷ 6 ≈ 1,000

Multiple Choice

Estimate

5,572 ÷ 8 ≈ ?

• 70

• 700

• 7

Multiple Choice

Estimate

476 ÷ 3 ≈ ?

• 16

• 160

• 1,600

Multiple Select

Which estimated quotients are most reasonable?

• 323 ÷ 8 ≈ 4

• 7,721 ÷ 7 ≈ 1,100

• 198 ÷ 4 ≈ 50

Open Ended

Learners' Takeaways:

Which strategy do you find easy to perform? In what situations can you use division?

What values did you learn from the lesson?