1-1 Estimating with Whole Numbers

Learn to estimate with whole numbers.

1-1 Estimating with Whole Numbers

Vocabulary

estimate

compatible numberunderestimateoverestimate

1-1 Estimating with Whole Numbers

Sometimes in math you do not need an exact answer. Instead, you can use an estimate. Estimates are close to the exact answer but are usually easier and faster to find.

When estimating, you can round the numbers in the problem to compatible numbers. Compatible numbers are close to the numbers in the problem, and they can help you do math mentally.

1-1 Estimating with Whole Numbers

When rounding, look at the digit to the right of the place to which you are rounding.

• If that digit is 5 or greater, round up.

• If that digit is less than 5, round down.

Remember!

1-1 Estimating with Whole Numbers

Additional Example 1A: Estimating a Sum or Difference by Rounding

Estimate the sum by rounding to the place value indicated.

12,345 + 62,167; ten thousands

10,000 Round 12,345 down.

Round 62,167 down.+ 60,000__________

The sum is about 70,000.

70,000

1-1 Estimating with Whole Numbers

Additional Example 1B: Estimating a Sum or Difference by Rounding

Estimate the difference by rounding to the place value indicated.

4,983 – 2,447; thousands

5,000 Round 4,983 up.

Round 2,447 down. – 2,000__________

The difference is about 3,000.

3,000

1-1 Estimating with Whole Numbers

Check It Out: Example 1A

Estimate the sum by rounding to the place value indicated.

13,235 + 41,139; ten thousands

10,000 Round 13,235 down.

Round 41,139 down.+ 40,000__________

The sum is about 50,000.

50,000

1-1 Estimating with Whole Numbers

Check It Out: Example 1B

Estimate the difference by rounding to the place value indicated.

5,723 – 1,393; thousands

6,000 Round 5,723 up.

Round 1,393 down. – 1,000__________

The difference is about 5,000.

5,000

1-1 Estimating with Whole Numbers

An estimate that is less than the exact answer is an underestimate.

An estimate that is greater than the exact answer is an overestimate.

1-1 Estimating with Whole Numbers

Additional Example 2: Estimating a Product by Rounding

Chelsea is planning the annual softball banquet for the 8 teams in the region. Each team has 18 members. Estimate how many plates she will need to buy if all the members attend.

8 18 8 20 Overestimate the number of softball members.

The actual number of softball members is less than 160.

8 20 = 160

Chelsea should buy about 160 plates.

Find the number of softball members.

1-1 Estimating with Whole Numbers

Additional Example 2 Continued

Another method

8 18 10 18 Overestimate the number of teams.

The actual number of softball members is less than 180.

10 18 = 180

Chelsea should buy about 180 plates.

Find the number of softball members.

1-1 Estimating with Whole Numbers

Check It Out: Example 2

Ms. Oliver wants to buy the entire seventh-grade new pencils. There are 5 seventh-grade homeroom classes of 28 students. Estimate how many pencils Ms. Oliver needs to buy for all of the students.

5 28 5 30 Overestimate the number of students.

The actual number of students is less than 150.

5 30 = 150

Ms. Oliver should buy about 150 pencils.

Find the number of students in the seventh grade.

1-1 Estimating with Whole Numbers

Additional Example 3: Estimating a Quotient Using Compatible Numbers

Mr. Dehmel will drive 243 miles to the fair at 65 mi/h. About how long will his trip take?

243 ÷ 65 240 ÷ 60240 and 60 are compatible numbers. Underestimate the speed.

Because he underestimated the speed, the actual time will be less than 4 hours.

240 ÷ 60 = 4

The trip will take about 4 hours.

1-1 Estimating with Whole Numbers

Check It Out: Example 3

Mrs. Blair will drive 103 miles to the airport at 55 mi/h. About how long will her trip take?

103 ÷ 55 100 ÷ 50100 and 50 are compatible numbers. Underestimate the speed.

Because she underestimated the speed, the actual time will be less than 2 hours.

100 ÷ 50 = 2

The trip will take about 2 hours.