3.2 Estimating Decimal

Products and Quotients

Mr. Phillips

Intro to Algebra

Lesson Objectives

By the end of today’s lesson you will be able By the end of today’s lesson you will be able to:to:

1)1)Estimate products using mental math.Estimate products using mental math.

2)2)Estimate quotients using compatible Estimate quotients using compatible numbers.numbers.

Estimating ProductsExample #1 (pg. 132)

Estimate each product.Estimate each product.

1) 7.65 1) 7.65 ×× 3.2 3.2 2) 6.43 2) 6.43 ×× 4.7 4.7

Estimating ProductsOYO #1

Estimate each product.Estimate each product.

3) 4.563) 4.56××7.02 4) 6.37.02 4) 6.3××9.2 5) 3.299.2 5) 3.29××5858

≈ ≈ 3535 ≈ 54≈ 54≈180≈180

Estimating ProductsExample #2 (pg. 132)Josh bought 3 yards of fabric to Josh bought 3 yards of fabric to

make a flag. Fabric costs $5.35 per make a flag. Fabric costs $5.35 per yard. The clerk says his total is yard. The clerk says his total is $14.95 before tax. Did the clerk $14.95 before tax. Did the clerk

make a mistake?make a mistake?

Estimating ProductsOYO #2

You buy 24 donuts from the Donut You buy 24 donuts from the Donut Emporium in Plano. Each donut costs Emporium in Plano. Each donut costs

$.98 . Estimate the cost before tax for 2 $.98 . Estimate the cost before tax for 2 dozen donuts?dozen donuts?

≈ ≈ $24$24

Objective #1

Can you… Can you…

~ estimate products using mental ~ estimate products using mental math?math?

Let’s Check…Let’s Check…

Check for Understanding

Do problems 11, 13, 15 on Practice Do problems 11, 13, 15 on Practice Worksheet 3-2.Worksheet 3-2.

Next, compare answers with a neighbor.Next, compare answers with a neighbor.

11)11)≈≈54 13) ≈600 15) ≈144054 13) ≈600 15) ≈1440

Estimating Quotients

6 ÷ 3 = 26 ÷ 3 = 2

The first number is the The first number is the dividenddividend..

The second number is the The second number is the divisordivisor..

The number after the = sign is the The number after the = sign is the quotientquotient..

Estimating Quotients

Name the following:Name the following:

18 ÷3 = 618 ÷3 = 6

3 is the: 3 is the:

18 is the:18 is the:

6 is the:6 is the:

Estimating Quotients

defdefnn: : compatible numberscompatible numbers: :

-numbers easy to divide mentally-numbers easy to divide mentally

*When dividing, you can use *When dividing, you can use compatible numbers to estimate compatible numbers to estimate quotientsquotients

Estimating Quotients

When you estimate the quotient:When you estimate the quotient:

1)1)Round the Round the divisordivisor..

2)2)Round the Round the dividenddividend to a to a compatible number.compatible number.

Estimating QuotientsExample #3 (pg. 133)

Estimate the quotient using Estimate the quotient using compatible numbers.compatible numbers.

1)1) 14.9 ÷ 2.8 14.9 ÷ 2.8 2) 25.3 2) 25.3 ÷ 4.9÷ 4.9

Estimating QuotientsOYO #3

Estimate the quotient using compatible Estimate the quotient using compatible numbers.numbers.

3) 35.8÷3.8 4) 29.4÷1.8 5) 49.6÷4.43) 35.8÷3.8 4) 29.4÷1.8 5) 49.6÷4.4

≈ ≈ 9 ≈ 15 ≈ 109 ≈ 15 ≈ 10

Estimating QuotientsExample #4 (pg. 133)

The cost to ship 1 yearbook is $3.12. The total The cost to ship 1 yearbook is $3.12. The total cost for a shipment was $62.40. Estimate cost for a shipment was $62.40. Estimate how many books were in the shipment. how many books were in the shipment.

1)1)Round the divisor.Round the divisor.

2)2)Round to a multiple of 3.Round to a multiple of 3.

3)3)Find the quotient.Find the quotient.

Estimating QuotientsExample #5 (pg. 133)

Use estimation. Is each quotient Use estimation. Is each quotient reasonable?reasonable?

1) 17.931÷8.34 =2.151) 17.931÷8.34 =2.15 2) 2) 31.423÷5.94=3.2931.423÷5.94=3.29

Estimating QuotientsOYO #5

Use estimation. Is each quotient reasonable?Use estimation. Is each quotient reasonable?

3) 318.274÷4.07=78.23) 318.274÷4.07=78.2 4) 4) 41.09÷6.88=5.1241.09÷6.88=5.12

Reasonable Not Reasonable Reasonable Not Reasonable

Objective #2

Can you… Can you…

~ estimate quotients using ~ estimate quotients using compatible numbers?compatible numbers?

Let’s Check…Let’s Check…

Check for Understanding

Do problems 18, 19, 21 on Practice Do problems 18, 19, 21 on Practice Worksheet 3-2.Worksheet 3-2.

Next, compare answers with a neighbor.Next, compare answers with a neighbor.

18) ≈5 19) ≈6 21) ≈1518) ≈5 19) ≈6 21) ≈15

3.2 Estimating Decimal Products and Quotients

Ask yourself if you can do the following:Ask yourself if you can do the following:

1)1)Estimate products using mental math.Estimate products using mental math.

2)2)Estimate quotients using compatible Estimate quotients using compatible numbers.numbers.

Homework: 3.2 on the assignment sheetHomework: 3.2 on the assignment sheet