Estimate quotients using multiples

When we estimate quotients using multiples, we are not looking for an exact answer. Instead, as it says, we are looking for an estimate, or a number that is close to the real answer.

Examples showing how to estimate quotients using multiples

Example #1

Find two numbers the quotient of 50 ÷ 7 is between. Then estimate the quotient.

Step 1

Ask yourself, " what number multiplied by 7 is about 50? " 

Instead of guessing, you can just make a table showing some possibilities. Keep in mind that the product of any counting number multiplied by 7 is a multiple.

Therefore, the table will show multiples of 7. 

Counting number	1	2	3	4	5	6	7	8
Multiples of 7	7	14	21	28	35	42	49	56

Step 2

Use the table to find multiples of 7 closest to 50.

7 × 7 = 49

7 × 8 = 56

50 is between 49 and 56, so the answer is either 7 or 8.

50 is closest to 49, so 50 ÷ 7 is about 7.

Trick to estimate quotients using multiples when the quotient is big.

Example #2

Find two numbers the quotient of 152 ÷ 6 is between. Then estimate the quotient.

Step 1

Ask yourself, " what number multiplied by 6 is about 152? " 

Once again, instead of guessing, you can just make a table showing some possibilities. This time though, we need to play strategically and here is the reason why.

Notice that 6 × 10 = 60. This means that if we had made a table with just the first 10 counting numbers, we would still be very far away from 152. If we put counting numbers 1, 2, 3, 4, 5, and so forth, this will make the table way too big!

Therefore, instead of using counting numbers 1, 2, 3, 4, 5, and so forth, we should use 10, 15, 20, 25, 30, and so forth to keep the table small.

Counting number	10	15	20	25	30
Multiples of 6	60	90	120	150	180

Step 2

Use the table to find multiples of 6 closest to 152.

6 × 25 = 150

6 × 30 = 180

152 is between 150 and 180, so the answer is either 25 or 30.

152 is closest to 150, so 152 ÷ 6 is about 25.

This figure summarizes the process of estimating quotients using multiples