Learn to multiply fractions, decimals, and mixed numbers'

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Learn to multiply fractions, decimals, and mixed
numbers.
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Kendall invited 36 people to a party. She needs
to triple the recipe for a dip, or multiply the
amount of each ingredient by 3. Remember that
multiplication by a whole number can be written
as repeated addition.
Notice that multiplying a fraction by a whole
number is the same as multiplying the whole
number by just the numerator of the fraction and
keeping the same denominator.
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RULES FOR MULTIPLYING TWO RATIONAL NUMBERS
If the signs of the factors are the same, the
product is positive.
() () () or () () ()
If the signs of the factors are different, the
product is negative.
() () () or () () ()
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Additional Example 1A Multiplying a Fraction and
an Integer
Multiply. Write the answer in simplest form.
6 7
A.
8
Multiply
Simplify
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Additional Example 1B Multiplying a Fraction and
an Integer
Multiply. Write the answer in simplest form.
1 3
2
5
B.
Multiply
Simplify
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Try This Example 1A
Multiply. Write the answer in simplest form.
5 8
3
A.
Multiply
Simplify
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Try This Example 1B
Multiply. Write the answer in simplest form.
2 5
4
9
B.
Multiply
Simplify
8
2 3
3 5
A model of is shown. Notice that to
multiply fractions, you multiply the numerators
and multiply the denominators.

If you place the first rectangle on top of the
second, the number of green squares represents
the numerator, and the number of total squares
represents the denominator.
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To simplify the product, rearrange the six green
squares into the first two columns. You can see
that this is .
2 5
6 15
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Additional Example 2A Multiplying Fractions
Multiply. Write the answer in simplest form.
6 7
1 8
A.
Multiply numerators.
Multiply denominators.
Look for common factors 2.
Simplest form
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Additional Example 2B Multiplying Fractions
Multiply. Write the answer in simplest form.
9 2
2 3
B.

Multiply numerators.
Multiply denominators.
Look for common factors 2, 3.
Simplest form
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Additional Example 2C Multiplying Fractions
Multiply. Write the answer in simplest form.
1 2
3 7
4
C.
Write as an improper fraction.
Multiply numerators. Multiply denominators.
31 14 2 R3
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Try This Example 2A
Multiply. Write the answer in simplest form.
5 8
3 5
A.
Multiply numerators.
Multiply denominators.
Look for common factors 5.
Simplest form
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Try This Example 2B
Multiply. Write the answer in simplest form.
4 7
7 8
B.

Multiply numerators.
Multiply denominators.
Look for common factors 4, 7.
Simplest form
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Try This Example 2C
Multiply. Write the answer in simplest form.
7 9
3 5
C.
2
Write as an improper fraction.
Multiply numerators. Multiply denominators.
91 45 2 R 1
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Additional Example 3 Multiplying Decimals
Multiply.
A.
2(0.51)
Product is negative with 2 decimal places.
2 (0.51) 1.02
(0.4)(3.75)
B.
Product is positive with 3 decimal places.
(0.4) (3.75) 1.500
1.5
00
You can drop the zeros after the decimal point.
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Try This Example 3
Multiply.
A.
3.1 (0.28)
3.1 (0.28) 0.868
Product is positive with 3 decimal places.
(0.4)(2.53)
B.
Product is positive with 3 decimal places.
(0.4) (2.53) 1.012
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Additional Example 4A Evaluating Expressions
with Rational Numbers
A. x 5
Substitute 5 for x.
Write as an improper fraction.
125 8 15 R5
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Additional Example 4B Evaluating Expressions
with Rational Numbers Continued
2
B. x
7
Write as an improper fraction.
1
Look for common factors 2.
4
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Try This Example 4A
67
A.
y
Write as an improper fraction.
4
Look for common factors 7.
1
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Try This Example 4B
B. y 3
Substitute 3 for y.
Write as an improper fraction.
84 5 16 R4
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Lesson Quiz Part 1
Multiply.
1 7
1.
9
5 8
2 3

2.
1.034
3. 0.47(2.2)
1 2
45
4. Evaluate 2 (x) for x .
2
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Lesson Quiz Part 2
5.
Teri is shopping for new shoes. Her mom has
agreed to pay half the cost (and all the sales
tax). The shoes that Teri likes are normally 30
a pair but are on sale for off. How much
money does Teri need to buy the shoes?
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