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3.2 Estimating Decimal
Products and Quotients
Mr. Phillips
Intro to Algebra
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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.
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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
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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
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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?
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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
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Objective #1
Can you… Can you…
~ estimate products using mental ~ estimate products using mental math?math?
Let’s Check…Let’s Check…
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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
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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..
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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:
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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
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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.
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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
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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
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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.
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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
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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
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Objective #2
Can you… Can you…
~ estimate quotients using ~ estimate quotients using compatible numbers?compatible numbers?
Let’s Check…Let’s Check…
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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
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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