example 3 multiplying mixed numbers postcards a designer creates postcards that are inches long and...
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Example 3 Multiplying Mixed Numbers
POSTCARDS
A designer creates postcards that are inches long
and inches wide. Find the area of the postcard.215
433
Write area formula.
SOLUTION
Area Length Width= •
Substitute values.= •215
433
2
11Write as improper fractions.= •
4
15
Example 3 Multiplying Mixed Numbers
Use rule for multiplying fractions.=4•2
15•11
Write as a mixed number.=85
20
The area of a postcard is square inches.
ANSWER
85
20
Multiply.=8
165
You are making costumes for a school play. Each
costume requires yards of fabric. Evaluate
when x 3 to determine how many yards of fabric
you need to make 3 costumes.
Example 4 Using an Algebraic Expression
=92
2
COSTUMES
92
2 •
SOLUTION
Substitute 3 for x.=•922 x •
922 3
Write as improper fractions.9
20= •
1
3
x
Example 4 Using an Algebraic Expression
Use rule for multiplying fractions.=1•9
3•20
Divide out common factors.=1••2013
93
Multiply.=3
20
Write as a mixed number.=326
Example 4 Using an Algebraic Expression
ANSWER
You need yards of fabric to make 3 costumes.32
6
Example 5 Evaluating an Algebraic Expression
Evaluate x 2y
Use rule for multiplying fractions.=• ( )7––( )7– 3•
3•3 4•
Write as a factor 2 times.= –37
43
–37
–37
x 2y =
312–
43
Substitute for x and for y.31
2–43
2
Write as an improper fraction.== –37
43
31
2–2
=43
and y .=31
2–when x
Example 5 Evaluating an Algebraic Expression
Divide out common factors.=• ( )7––( )7– •
31• 4•
13
3
Multiply.=12
49
Write as a mixed number.=121
4
Guided Practice
Find the product. Simplify if possible.
for Examples 3, 4, and 5
5. •52
121
3 ANSWER109
4
6. •21
565
1– ANSWER121
10–
ANSWER2019
14–7. •53
243
5–
8. •31
2– –43
ANSWER43
1
Guided Practice
9. WHAT IF?
for Examples 3, 4, and 5
In Example 4, how many yards of fabric would be needed to make 5 costumes?
ANSWER91
11 yd
Evaluate the expression when x and y .=65
1–43
=
10. x32 ANSWER –
21
11. 2y ANSWER32
3
Guided Practice for Examples 3, 4, and 5
Evaluate the expression when x and y .=65
1–43
=
12. xy
13. xy 2
ANSWER83
1–
ANSWER4825
2–