Transcript Document

PRE-ALGEBRA
Lesson 5-4 Warm-Up
Use the cards 1, 4, 2, and 3 to find each sum in exercises 1 – 4. Each card can only be
used once.
Use the cards 6, 2, 5, and 8 to find each sum in exercises 1 – 4. Each card can only be
used once.
PRE-ALGEBRA
Multiplying and Dividing
Fractions (5-4)
How do you
multiply
fractions?
To multiply fractions together, multiply the numerators and denominators
together separately. If the numerator and denominator have common factors,
you can simplify them before multiplying.
Example:
 Multiply the numerators and denominators
together separately. Since 2 and 8 have a GCF, 2,
simplify by dividing by 2
 Multiply the numerator.
 Multiply the denominatos.
How do you
model the
multiplication of
fractions?
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
Find 2 • 5 .
3
2
5
2•5
•
=
3
7
3•7
=
10
21
7
Multiply the numerators.
Multiply the denominators.
Simplify.
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
a. Find 3 • 2 .
4
3
3 2
3 12
• =
•
4 3 24 13
1
=
1
2
Divide the common factors.
Multiply.
5 3w
• .
w 17
5 • 3w = 5 • 3w 1
w 17
17
1w
b. Find
=
15
17
Divide the common factors.
Multiply.
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
1
1
Keesha’s desktop is a rectangle 3 2 ft long and 1 ft
2
wide. What is the area of her desktop?
A =3
1
1
•1
2
2
Area of a rectangle = length • width.
1
1
7
3
and 1 as improper fractions, and .
2
2
2
2
=7• 3
Write 3
21
4
Multiply.
2
=
2
1
= 54
Write as a mixed number.
The area of Keesha’s desk is 5 1 ft2.
4
PRE-ALGEBRA
Multiplying and Dividing
Fractions (5-4)
What are
“reciprocals”?
Reciprocals: two numbers whose product is 1 – The reciprocal of a is b ,
b
a
since a • b = 1.
b a
How do you find
the reciprocal of
a number?
To find the reciprocal of a number, simply switch the numerator and denominator
around. In the case of a whole number, make it a fraction by putting it over 1 first
(so, the reciprocal of a whole number will always be 1 over the number)
Example: What is the reciprocal of 9?
=
9
1
 Make the whole number into a fraction by
9 = 1
1
9
 Turn the fraction over so that the numerator
1
Check : 1 • 9 = 1 = 1
1
91 1
 Check using rule of reciprocals (a number times
putting it over 1.
and denominatorare switched
its reciprocal equals 1)
PRE-ALGEBRA
Multiplying and Dividing
Fractions (5-4)
How do you
divide by a
fraction?
To divide by a fraction, multiply by its reciprocal.
c
a
Rule: a 
=
•
d
b
b
ad
, where b, c, and d do not equal 0.
bc
d
=
c
Example: What is the 1  1 ?
2
8
How do you
model the
division of
fractions?
1  1 = 1 • 8
2
8
2 1
 To divide by a fraction, multiply by its
1 • 8 = 1•8
1
2
2•1
= 8 =4
2
 Multiply the numerators and denominators
reciprocal
separately.
 The fraction bar means divide, so divide the
numebrator into the denominator to simplify.
1
4
 2 = 8 , so there are 4 one-eighth parts in onehalf.
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
3
7
a. Find ÷
.
5 10
3
7
3
10
÷
=
•
5 10
5
7
Multiply by the reciprocal of the divisor.
2
3
10
=
•
7
15
Divide the common factors.
= 6
Simplify.
7
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
(continued)
b. Find 27 ÷ 9 .
8q
4q
27
÷ 9 = 27 • 4q
4q
9
8q
8q
3
1
Multiply by the reciprocal of the divisor.
1
27
=
• 4q
91
2 8q 1
Divide the common factors.
= 3
Simplify.
2
= 11
2
Write as a mixed number.
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Additional Examples
(continued)
c. Find 4 1 ÷ (–3 3 ).
2
8
4 1 ÷ (–3 3 ) = 9 ÷ (– 27 )
2
8
2
8
9
8
• (– )
2
27
=
Change to improper fractions.
Multiply by –
8
27
, the reciprocal of – .
27
8
4
1
9
8
=
• –
273
12
4
3
= – , or –1
Divide the common factors.
1
3
Simplify.
PRE-ALGEBRA
Multiplying and Dividing Fractions
LESSON 5-4
Lesson Quiz
Simplify each expression.
1. –
3
7
•
8
12
– 7
3z
5z
÷
4
7
21
1
,
or
1
20
20
32
12g
2.
5
3. 25 •
2g
4. 5 5 ÷ 1 11
8
16
6
1
,
or
1
5
5
10
1
,
or
3
3
3
PRE-ALGEBRA