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Students will understand decimals by being able to do the following:
• Learn to write, compare, and order decimals using place value and number lines (3-1)
• Learn to estimate decimal sums, differences, products, and quotients (3-2)
• Learn to add and subtract decimals (3-3)• Learn to multiply and divide decimals by powers of ten and to
convert metric measurements (3-4)• Learn to write large numbers in scientific notation (3-5)
•Learn to multiply decimals by whole numbers and by decimals (3-6)
Today’s Learning Goal Assignment
Learn to multiply decimals by whole numbers and by decimals. Course 1
3-6 Multiplying Decimals
3-6 Multiplying Decimals
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpMultiply.
27,840
754,400
38,060
Course 1
3-6 Multiplying Decimals
120,700
14,112
62,760
1. 87 320
2. 943 800
3. 3,806 10
4. 1,207 100
5. 72 196
6. 120 523
Problem of the Day
Carmen and Rita sold homemade oatmeal cookies. After 8 days, they had sales totaling $70. Each day, their sales were $0.50 higher than the previous day. What were their sales on the first day?
$7.00
Course 1
3-6 Multiplying Decimals
Today’s Learning Goal Assignment
Learn to multiply decimals by whole numbers and by decimals. Course 1
3-6 Multiplying Decimals
Course 1
3-6 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?
4 0.17
0.17You can think of multiplication by a whole number as a repeated addition. 0.17
0.170.17+ _____0.68
Course 1
3-6 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?
You can also multiply as you would with whole numbers. Place the decimal point by adding the number of decimal places in the numbers multiplied.
0.17 4 _____0.68
2 decimal places + 0 decimal places
2 decimal places
A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.
Course 1
3-6 Multiplying Decimals
Try This: 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?
7 0.170.17 You can think of multiplication by a
whole number as a repeated addition.
0.170.170.17
+ _____1.19
0.170.17
0.17
Course 1
3-6 Multiplying Decimals
Try This: 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?
You can also multiply as you would with whole numbers. Place the decimal point by adding the number of decimal places in the numbers multiplied.
0.17 7 _____1.19
2 decimal places + 0 decimal places
2 decimal places
A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.
Course 1
3-6 Multiplying Decimals
Additional Example 2A: Multiplying a Decimal by a Decimal
Find the product.
A. 0.3 0.4Multiply. Then place the decimal point.
0.3
0.4
1 decimal place
+ 1 decimal place
2 decimal places 0.12
Course 1
3-6 Multiplying Decimals
Additional Example 2B: Multiplying a Decimal by a Decimal
B. 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.
Course 1
3-6 Multiplying Decimals
Additional Example 2C: Multiplying a Decimal by a Decimal
C. 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
Course 1
3-6 Multiplying Decimals
Try This: Example 2A
Find each product.
A. 0.5 0.2
Multiply. Then place the decimal point.
0.5
0.21 decimal place
+ 1 decimal place
2 decimal places 0.10
Course 1
3-6 Multiplying Decimals
Try This: Example 2B
B. 0.03 0.9
Multiply. Then place the decimal point.
0.03
0.9
2 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.
Course 1
3-6 Multiplying Decimals
Try This: Example 2C
C. 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
Course 1
3-6 Multiplying Decimals
Additional Example 3A: Evaluating Decimal Expressions
Evaluate 5x for each value of x.
A. 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!
Course 1
3-6 Multiplying Decimals
Additional Example 3B: Evaluating Decimal Expressions
B. x = 4.79
4.79
5
2 decimal places
+ 0 decimal places
2 decimal places 23.95
Substitute 4.79 for x. 5x = 5(4.79)
Course 1
3-6 Multiplying Decimals
Try This: Example 3A
Evaluate 5x for each value of x.
A. x = 2.012
2.012
5
3 decimal places
+ 0 decimal places
3 decimal places 10.060
Substitute 2.012 for x. 5x = 5(2.012)
Course 1
3-6 Multiplying Decimals
Try This: Example 3B
B. 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)
Lesson QuizFind each product.
1. 0.8
2. 0.006 0.07
Evaluate 8x for each value of x.
0.000420.056
Insert Lesson Title Here
21.64 6.432
Course 1
3-6 Multiplying Decimals
0.07
$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?