Grade 4 Long Division: Estimating Quotients

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Use compatible numbers to estimate 377 ÷ 2: round 377 to the closest multiple of 200 (2 × 100, 2 × 200, 2 × 300, …) and divide. What is your estimate?

   1. To estimate, swap 377 for a compatible number: a multiple of 200 that is close to 377 and easy to divide by 2.
   2. 377 is between 200 and 400. It is closer to 400 (377 − 200 = 177, 400 − 377 = 23).
   3. Use a basic fact: 4 ÷ 2 = 2, so 400 ÷ 2 = 200 (put back the 2 zeros).
   4. So the estimate is about 200.

   Answer: 200

2. Example 2

   Estimate 315 ÷ 4. Replace 315 with the closest multiple of 40 (4 × 10, 4 × 20, 4 × 30, …), then divide. What is your estimate?

   1. To estimate, swap 315 for a compatible number: a multiple of 40 that is close to 315 and easy to divide by 4.
   2. 315 is between 280 and 320. It is closer to 320 (315 − 280 = 35, 320 − 315 = 5).
   3. Use a basic fact: 32 ÷ 4 = 8, so 320 ÷ 4 = 80 (put back the zero).
   4. So the estimate is about 80.

   Answer: 80

3. Example 3

   284 people ride a train with 9 cars, the same number in each car. About how many people are in each car? Estimate: use the closest multiple of 90 (9 × 10, 9 × 20, 9 × 30, …) in place of 284, then divide.

   1. To estimate, swap 284 for a compatible number: a multiple of 90 that is close to 284 and easy to divide by 9.
   2. 284 is between 270 and 360. It is closer to 270 (284 − 270 = 14, 360 − 284 = 76).
   3. Use a basic fact: 27 ÷ 9 = 3, so 270 ÷ 9 = 30 (put back the zero).
   4. So the estimate is about 30 people.

   Answer: 30