holt ca course 1 4-4 multiplying fractions and mixed numbers warm up warm up california standards...
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Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
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California StandardsCalifornia Standards
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Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
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What is of each of the following?
1. 24 2. 16
3. 30 4. 28
12 8
15
12
14
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.Also covered: NS2.4, NS2.2
California Standards
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Recall that multiplication can be written as repeated addition. For example, 3 5 = 5 + 5 + 5 = 15. You can use repeated addition to multiply a whole number by a fraction.
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Additional Example 1: Transportation ApplicationIn 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2
3of that toll.
What was the toll in 1995?
23
6 = 23
+ 23
23
23
23
23
+ + + + +
= 123
=41
= $4.00The George Washington Bridge toll for a car was $4.00 in 1995.
+ + + +13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
1 1 1 1
Think: How much is of 6? Use multiplication to find a fraction of a number.
23
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
In 2002, the fee to park in a parking garage was
$4. In 2000 the fee was of the fee in 2002.
What was the fee in 2000?
Check It Out! Example 1
34
4 = 34
+ 34
34
34
+ +
= 124
=31
= $3.00
The fee to park in the parking garage was $3.00 in 2000.
34
+14
14
14
14
14
14 + +1
414
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
1 1 1
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2A: Multiplying Fractions
12 34
12 34
= 121
34
Write 12 as a fraction.
= 12 31 4
3
1
Divide a numerator and denominator by their GCD, 4.
91
= = 9 Multiply numerators.Multiply denominators.
Use the GCD of a numerator and denominator to simplify before multiplying.
Remember!
Pre-reduce
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2B: Multiplying Fractions
Multiply numerators.Multiply denominators.
413
5
35
14
=35
1 4
= 3 20
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2C: Multiplying Fractions
8
=Divide a numerator and denominator by their GCD, 3.
Multiply numerators.Multiply denominators.
313
1
1
= 18
38
13
13
3 8
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out! Example 2A
16 14
16 14
= 161
14
Write 16 as a fraction.
= 16 11 4
4
1
Divide a numerator and denominator by their GCD, 4.
41
= = 4 Multiply numerators.Multiply denominators.
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out! Example 2B
8
Multiply numerators.Multiply denominators.
137
18
37 =
37
1 8
= 3 56
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out! Example 2C
9
= Divide a numerator and denominator by their GCD, 6.
Multiply numerators.Multiply denominators.
616
1
1
= 19
69
16
16
6 9
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3A: Multiplying Mixed Numbers
IMPORTANT: Write the mixed number as an improper fraction.
Divide a numerator and denominator by their GCD, 5.
Multiply numerators.Multiply denominators.
2
25
1 23 = 2
5 53
= 25
53
1
1
5 1 2
3
= 23
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3B: Multiplying Mixed Numbers
Write mixed numbers as improper fractions.
Divide numerators and denominators by their GCDs, 5 and 7.
4 15 2 1
7
415
17
= 215
157
= 5
71521
1
3
1
3
= 91
or 9 Multiply numerators.Multiply denominators.
2
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3C: Multiplying Mixed Numbers
Multiply numerators.Multiply denominators.
23 4
256
23 4 2
56 = 20
3 22
5
203
225
=4
1
Write mixed numbers as improper fractions.
Divide a numerator and denominator by their GCD, 5.
3= 88 or 291
3
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out! Example 3A
Write the mixed number as an improper fraction.
Divide a numerator and denominator by the GCD, 3.
Multiply numerators.Multiply denominators.
3
35
2 13 = 3
5 73
= 35
73 1
1
5 2 1
3
= or 175
25
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out! Example 3B
Write mixed numbers as improper fractions.
Divide a numerator and denominator by their GCD, 3.
3 35 1 1
3
335
113
= 185
43
= 5
3418
1
6
Multiply numerators.Multiply denominators.= 24
5or 44
5
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Multiply numerators.Multiply denominators.
16 1 1
33
16 1 1
33 = 19
6 4
3
196
43
=3
2
Write mixed numbers as improper fractions.
Divide a numerator and denominator by their GCD, 2.
9= 38 or 4 2
9
Check It Out! Example 3C
Holt CA Course 1
4-4 Multiplying Fractions and Mixed Numbers
Lesson Quiz
Multiply. Write each answer in simplest terms.
1. 2.
3. 4.78
3512
or 1112
2
17 2
12
or 8
548
5. A recipe for clam chowder calls for 2 14 pounds of
butter. If you prepare one-half of the recipe, how
much butter do you need?
118
pounds