Download Multiplying Fractions by Whole Numbers

5-5 Multiplying Fractions by Whole Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-5 Multiplying Fractions by Whole Numbers
Warm Up
Multiply.
1. 15  2
30
2. 12  8
96
3. 9  16
144
4. 6  11
66
5. 8  15
120
5-5 Multiplying Fractions by Whole Numbers
Problem of the Day
The length of three dowels are 13 inches,
27 inches, and 19 inches. How can you
use the three dowels to mark off a length
of 5 inches?
13 + 19 – 27
5-5 Multiplying Fractions by Whole Numbers
Sunshine State Standards
MA.6.A.1.2 Multiply and divide
fractions…efficiently.
Also MA.6.A.1.3
5-5 Multiplying Fractions by Whole Numbers
Recall that multiplication by a whole number can
be represented as repeated addition. For
example, 4 • 5 = 5 + 5 + 5 + 5. You can
multiply a whole number by a fraction using the
same method.
1
1
__
__
3•
=
4
4
+
+
1
__
4
+
+
1
__
4
=
=
3
__
4
5-5 Multiplying Fractions by Whole Numbers
There is another way to multiply with fractions.
Remember that a whole number can be written as
an improper fraction with 1 in the denominator.
3.
So 3 = __
1
__
3
3•1
3
__
1 = ______
__
•
=
1
1•4
4
4
Multiply numerators
Multiply denominators
Notice that when you multiply a proper fraction and
a number greater than 1, the product is between
the factors.
5-5 Multiplying Fractions by Whole Numbers
Additional Example 1A: Multiplying Fractions
and Whole Numbers
Multiply. Write each answer in simplest form.
Method 1: Use repeated addition.
7
•
1
__
9
1
__
1
1 __
1 __
1 __
1 __
1 __
1 __
1
__
__
Write
7
•
as addition.
7•
+
+
+
+
+ +
=
9
9
9
9
9
9 9
9
9
Add the numerators.
=
7
__
9
5-5 Multiplying Fractions by Whole Numbers
Additional Example 1B: Multiplying Fractions
and Whole Numbers
Multiply. Write each answer in simplest form.
Method 1: Use repeated addition.
6
•
1
__
8
1
1 __
1 __
1 __
1 __
1 __
1
__
__
6•
+
+
+
+
+
=
8
8
8
8
8
8 8
=
6
__
8
=
3
__
4
1
Write 6 • __
as addition.
8
Add the numerators.
Write your answer in simplest form.
5-5 Multiplying Fractions by Whole Numbers
Additional Example 1C: Multiplying Fractions
and Whole Numbers
Multiply. Write each answer in simplest form.
Method 2: Multiply.
8
•
2
__
3
8
2
16
__
__
___
•
=
1
3
3
= 5
1
__
3
Multiply.
Write your answer in simplest form.
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 1A
Multiply. Write each answer in simplest form.
3
__
9•
4
27
__
4
or
3
6 __
4
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Additional Example 1B
Multiply. Write each answer in simplest form.
2
__
4•
5
__
8
5
or
1
__
3
5
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Additional Example 1C
Multiply. Write each answer in simplest form.
5
__
5•
6
25
__
6
or
1
4 __
6
5-5 Multiplying Fractions by Whole Numbers
Additional Example 2A: Evaluating Fraction
Expressions
Evaluate 4x for each value of x. Write each answer in
simplest form.
x
1
= ___
10
4x
1
4 • ___
10
4
4
1
__
• ___ = ___
1
10
10
2
__
=
5
Write the expression.
Substitute
1
___
for x.
10
Multiply.
Write your answer in simplest form.
5-5 Multiplying Fractions by Whole Numbers
Additional Example 2B: Evaluating Fraction
Expressions
Evaluate 4x for each value of x. Write each answer in
simplest form.
x
3
8
= __
Write the expression.
4x
3
4 • __
8
4 __
3
__
•
1
8
Substitute
3
__
for x.
8
12
___
Multiply.
8
3
1
__
__
=
Write your answer in simplest form.
,or 1
2
2
=
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 2A
Evaluate 3x for each value of x. Write each
answer in simplest form.
x
1
= __
9
1
3 • __ =
9
1
__
3
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 2B
Evaluate 3x for each value of x. Write each
answer in simplest form.
x
2
= __
5
2
6 or
3 • __ = __
5
5
1
1 __
5
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 2C
Evaluate 3x for each value of x. Write each
answer in simplest form.
x
5
= __
6
1
5
15 or 2 __
__
3 • __
=
2
6
6
5-5 Multiplying Fractions by Whole Numbers
Sometimes the denominator of an improper
fraction will divide into the numerator without
a remainder. When this happens, the improper
fraction is equivalent to a whole number, not a
mixed number.
12
___
=4
3
Remember!
12 means 12 ÷ 3.
3
5-5 Multiplying Fractions by Whole Numbers
Additional Example 3: Music Application
There are 25 students in the music club. Of those
3
__
students, 5 are also in the band. How many music
club students are in the band?
3 of 25, multiply.
To find __
5
3 ___
25
3
__
__
•
• 25 =
5
1
5
=
75
___
5
Divide 75 by 5 and write your
answer in simplest form.
= 15
There are 15 music club students in the band.
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 3A
There are 50 people on the football team. Of
1 are also on the basketball
those people, __
5
team. How many people on the football team
are also on the basketball team?
1 = 10
50 • __
5
5-5 Multiplying Fractions by Whole Numbers
Check It Out: Example 3B
There are 16 players on the baseball team. Of
_
1
these players, 4 are girls. How many girls play
on the baseball team?
1 =4
16 • __
4