1 - Jefferson School District

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Transcript 1 - Jefferson School District

4-4
Multiplying Fractions and Mixed Numbers
California
Standards
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
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
Example 1: Transportation Application
In 2001, the car toll on the George Washington
Bridge was $6.00. In 1995 the toll was 2 of that toll.
3
What was the toll in 1995?
Think: How much is 2 of 6? Use multiplication to find a
3
fraction of a number.
1 1
1 1
1 1
1
1 1
6  2 = 2+ 2 + 2 + 2 + 2 + 2
+
+
+
+
3 3
3 3
3 3
3
3 3
3
3 3 3 3 3 3
12
= 3
4
= 1
1
3
+
1 1
3 3
1 1 1 1 1 1 1 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3
Simplify
1
1
1
1
= $4.00 Write the fraction as a decimal.
The George Washington Bridge toll for a car was $4.00 in 1995.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Example 2A: Multiplying Fractions
Multiply. Write the answer in simplest form.
12  3
4
12  3 = 12  3 Write 12 as a fraction.
4
1 4
3
12  3 Divide a numerator and
=
1  41 denominator by their GCD, 4.
= 9 = 9 Multiply numerators.
1
Multiply denominators.
Remember!
Simplify.
Use the GCD of a numerator and denominator to simplify
before multiplying.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 2B: Multiplying Fractions
Multiply. Write the answer in simplest form.
31
5 4
3 1 =
5 4
=
Holt CA Course 1
3  1
5 4
3
20
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Example 3A: Multiplying Mixed Numbers
Multiply. Write the answer in simplest form.
2  12
5
3
2 12 = 25
5 3
3
5
Write the mixed number as
an improper fraction.
1 Divide a numerator and
= 2 5
denominator by their GCD, 5.
5 3
1
Multiply numerators.
=2
3
Multiply denominators.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Example 3B: Multiplying Mixed Numbers
Multiply. Write the answer in simplest form.
1
41

2
7
5
41  2 1 = 21  15
5
7
5 7
Write mixed numbers as
improper fractions.
3
3
21  15
Divide numerators and
= 5
denominators by their GCDs, 5
7
1 and 7.
1
or 9
= 9
1
Holt CA Course 1
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 1
In 2002, the fee to park in a parking garage was
3
$4. In 2000 the fee was 4 of the fee in 2002.
What was the fee in 2000?
43 =3 + 3 + 3 +3
4
4
4
4
4
=
12
4
3
= 1
111
444
+
111
444
+
111
444
+
111
444
111111111111
444444444444
1
1
1
= $3.00
The fee to park in the parking garage was $3.00 in 2000.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 2
Multiply. Write the answer in simplest form.
3  1
7 8
3 1= 3  1
7 8
7 8
=
Holt CA Course 1
3
56
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 3
Multiply. Write the answer in simplest form.
3 21
5
3
3 2 1 = 3 7
5 3
3
5
Holt CA Course 1
Write the mixed number as an
improper fraction.
13 7

=
5 31
Divide a numerator and
denominator by the GCD, 3.
= 7 or 12
5
5
Multiply numerators.
Multiply denominators.