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3-4 Multiplying Decimals
Estimating & Multiplying Decimals
3-4 Multiplying Decimals
MA.6.A.1.2 Multiply…decimals efficiently.
MA.6.A.1.3 Solve real-world problems involving multiplication…of…decimals.
Also MA.6.A.1.1
Sunshine State Standards
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3 three tenths
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3 three tenths
0.27
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3 three tenths
0.27 twenty-seven hundredths
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3 three tenths
0.27 twenty-seven hundredths
5.238
3-4 Multiplying Decimals
Reading Decimal Place Value
How would you say the following decimals?
0.3 three tenths
0.27 twenty-seven hundredths
5.238 five and two hundred
thirty-eight thousandths
3-4 Multiplying Decimals
How do you determine place value for decimals?
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
decimal.
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
decimal.
0.375
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
decimal.
0.375
1
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
decimal.
0.375
1000
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
decimal.
0.375
1000
Read the whole number on top and the
number you see on the bottom as a “spit
number”
3-4 Multiplying Decimals
How do you determine place value for decimals?
When in doubt, place a one under the
decimal and a zero for each digit past the
Decimal. 0.375
1000
Read the whole number on top and the
number you see on the bottom as a “spit
number” –
three hundred seventy-five thousandths
3-4 Multiplying Decimals
How do you read the following decimals?
3.78
3-4 Multiplying Decimals
How do you read the following decimals?
3.78 three and seventy-eight
hundredths
3-4 Multiplying Decimals
How do you read the following decimals?
3.78 three and seventy-eight
hundredths
2.003
3-4 Multiplying Decimals
How do you read the following decimals?
3.78 three and seventy-eight
hundredths
2.003 two and three thousandths
3-4 Multiplying Decimals
Model the following decimals:
0.18
3-4 Multiplying Decimals
Model the following decimals:
0.18
3-4 Multiplying Decimals
Model the following decimals:
0.18 · 3
3-4 Multiplying Decimals
Model the following decimals:
0.18 · 3
3-4 Multiplying Decimals
Model the following decimals:
0.18 · 3 = 0.54
3-4 Multiplying Decimals
Model the following decimal
0.3
3-4 Multiplying Decimals
Model the following decimal
0.3
3-4 Multiplying Decimals
Model the following decimals
0.3 · 0.70
3-4 Multiplying Decimals
Model the following decimals
0.3 · 0.70
3-4 Multiplying Decimals
Model the following decimals
0.3 · 0.70 = 0.21
3-4 Multiplying Decimals
Additional Example 1: Science Application
Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon?
Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.
17 4
68
Multiply as you would with whole numbers.
4 0.17
3-4 Multiplying Decimals
Additional Example 1 Continued
Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon?
0.17 40.68
Place the decimal point by adding the number of decimal places in the numbers multiplied.
A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.
2 decimal places+ 0 decimal places
2 decimal places
3-4 Multiplying Decimals
Check It Out: Example 1
Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?
Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.
17 7119
Multiply as you would with whole numbers.
7 0.17
3-4 Multiplying Decimals
Check It Out: Example 1 Continued
Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?
0.17 71.19
Place the decimal point by adding the number of decimal places in the numbers multiplied.
A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.
2 decimal places+ 0 decimal places
2 decimal places
3-4 Multiplying Decimals
Additional Example 2A: Multiplying a Decimal by a Decimal
Find the product.
0.3 0.4
Multiply. Then place the decimal point.
0.3
0.4
1 decimal place
+ 1 decimal place
2 decimal places 0.12
3-4 Multiplying Decimals
Estimating Decimals
3-4 Multiplying Decimals
Estimating Decimals
3-4 Multiplying Decimals
ClusteringWhat is clustering?
When would you use clustering to estimate the solution to a problem involving decimals?
3-4 Multiplying Decimals
ClusteringNancy wants to cycle, ice skate, and water ski for
30 minutes each. About how many calories will
she burn in all? (Cycling – 165.5 calories, ice
skating – 177.5 calories, and water skiing – 171.5
calories.)
In this example , why would each of the three
addends (numbers being added) be rounded to
170? What operation could you use rather than
adding 170 plus 170 plus 170?
3-4 Multiplying Decimals
RoundingWhen rounding a decimal, how do you know
which digit to look at?
Explain the rules for rounding a decimal.
If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?
3-4 Multiplying Decimals
Compatible NumbersWhat is a compatible number?
Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain.
Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26?
What would you use?
3-4 Multiplying Decimals
Estimating Decimals
3-4 Multiplying Decimals
Additional Example 2B: Multiplying a Decimal by a Decimal
0.07 0.8
Multiply. Then place the decimal point.
0.07 0.8
2 decimal places + 1 decimal place3 decimal places; use a placeholder zero
0.056
Estimate the product. 0.8 is close to 1.
0.07 1 = 0.07
0.056 is close to the estimate of 0.07. The answer is reasonable.
3-4 Multiplying Decimals
Additional Example 2C: Multiplying a Decimal by a Decimal
1.34 2.5
Multiply. Then place the decimal point.
1.34
2.52 decimal places
+ 1 decimal place
3 decimal places
670
Estimate the product. Round each factor to the nearest whole number.
1 3 = 3
3.350 is close to the estimate of 3. The answer is reasonable.
26803.350
3-4 Multiplying Decimals
Check It Out: Example 2A
Find the product.
0.5 0.2
Multiply. Then place the decimal point.
0.5
0.21 decimal place
+ 1 decimal place
2 decimal places 0.10
3-4 Multiplying Decimals
Check It Out: Example 2B
0.03 0.9
Multiply. Then place the decimal point.
0.03
0.92 decimal places
+ 1 decimal place3 decimal places; use a placeholder zero
0.027
Estimate the product. 0.9 is close to 1.
0.03 1 = 0.03
0.027 is close to the estimate of 0.03. The answer is reasonable.
3-4 Multiplying Decimals
Check It Out: Example 2C
3.80 3.3
Multiply. Then place the decimal point.
3.80
3.32 decimal places
+ 1 decimal places
3 decimal places
1140
Estimate the product. Round each factor to the nearest whole number.
4 3 = 12
12.54 is close to the estimate of 12. The answer is reasonable.
1140012.540
3-4 Multiplying Decimals
Additional Example 3A: Evaluating Decimal Expressions
Evaluate 5x for the value of x.
x = 3.062
3.062
53 decimal places
+ 0 decimal places
3 decimal places15.310
Substitute 3.062 for x. 5x = 5(3.062)
These notations all mean multiply 3 times x.
3 • x 3x 3(x)
Remember!
3-4 Multiplying Decimals
Additional Example 3B: Evaluating Decimal Expressions
Evaluate 5x for the value of x.
x = 4.79
4.79
52 decimal places
+ 0 decimal places
2 decimal places 23.95
Substitute 4.79 for x. 5x = 5(4.79)
3-4 Multiplying Decimals
Check It Out: Example 3A
Evaluate 5x for the value of x.
x = 2.012
2.012
53 decimal places
+ 0 decimal places
3 decimal places 10.060
Substitute 2.012 for x. 5x = 5(2.012)
3-4 Multiplying Decimals
Check It Out: Example 3B
Evaluate 5x for the value of x.
x = 6.22
6.22
52 decimal places
+ 0 decimal places
2 decimal places 31.10
Substitute 6.22 for x. 5x = 5(6.22)
3-4 Multiplying Decimals
Lesson Quiz
Find each product.
1. 0.8 0.07
2. 0.006 0.07
Evaluate 8x for each value of x.
0.00042
0.056
21.64 6.432
$87.40
3. x = 2.705 4. x = 0.804
5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged?
3-4 Multiplying Decimals
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
3-4 Multiplying Decimals
1. Identify the product.
0.29 0.01
A. 0.29
B. 0.029
C. 0.0029
D. 0.00029
Lesson Quiz for Student Response Systems
3-4 Multiplying Decimals
2. Identify the product.
0.052 0.03
A. 1.0056
B. 0.1056
C. 0.0156
D. 0.00156
Lesson Quiz for Student Response Systems
3-4 Multiplying Decimals
3. Evaluate 4x for x = 5.325.
A. 21
B. 21.2
C. 21.28
D. 21.3
Lesson Quiz for Student Response Systems
3-4 Multiplying Decimals
4. Evaluate 9x for x = 0.012.
A. 10.8
B. 1.08
C. 0.108
D. 0.0108
Lesson Quiz for Student Response Systems
3-4 Multiplying Decimals
5. Strawberry lemonade costs $0.89 per packet. Karen bought 58 packets of strawberry lemonade for a picnic. How much did she pay for it?
A. $51.62
B. $51.86
C. $52.54
D. $52.93
Lesson Quiz for Student Response Systems