Multiplying Rational Numbers

1
Multiplying Rational Numbers

• 3.3

Pre-Algebra
2
Warm up
Write each number as an improper fraction.
1
2
7
1.
3.
2
2.
3
1
3
5
8
2
3
4.
6
5.
5
3
8
3
Learn to multiply fractions, decimals, and mixed
numbers.
4
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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Example Multiplying a Fraction and an Integer
Multiply. Write the answer in simplest form.
6 7
A.
8
Multiply
Simplify
7
Example Multiplying a Fraction and an Integer
Multiply. Write the answer in simplest form.
1 3
2
5
B.
Multiply
Simplify
8
Try This
Multiply. Write the answer in simplest form.
5 8
3
A.
Multiply
Simplify
9
Try This
Multiply. Write the answer in simplest form.
2 5
4
9
B.
Multiply
Simplify
10
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.
11
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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Example 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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Example 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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Example 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
15
Try This
Multiply. Write the answer in simplest form.
5 8
3 5
A.
Multiply numerators.
Multiply denominators.
Look for common factors 5.
Simplest form
16
Try This
Multiply. Write the answer in simplest form.
4 7
7 8
B.

Multiply numerators.
Multiply denominators.
Look for common factors 4, 7.
Simplest form
17
Try This
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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Example 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.
19
Try This
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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Example 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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Example Evaluating Expressions with Rational
Numbers Continued
2
B. x
7
Write as an improper fraction.
1
Look for common factors 2.
4
22
Try This
67
A.
y
Write as an improper fraction.
4
Look for common factors 7.
1
23
Try This
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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