Download Two numbers are of each other if their product is 1. Every number

Two numbers are reciprocals of each other if their product is 1. Every number
except 0 has a reciprocal.
1
5
1
5
5 ª ᎏᎏ = 1, so 5 and ᎏᎏ are reciprocals.
2
3
2
3
ᎏᎏ ª ᎏᎏ = 1, so ᎏᎏ and ᎏᎏ are reciprocals.
3
2
3
2
1
4
4
5
5 4
4 5
1
4
4
5
1ᎏᎏ ª ᎏᎏ = ᎏᎏ • ᎏᎏ = 1, so 1ᎏᎏ and ᎏᎏ are reciprocals.
To find the reciprocal of a number, write the number as a fraction. Then
interchange the numerator and the denominator.
1
4
Find the reciprocal of 3ᎏᎏ.
EXAMPLE
1
4
13
4
Write 3} } as a fraction.
4
ᎏᎏ
13
13
ᎏ
4
䉴
1
4
3ᎏᎏ = ᎏᎏ
SOLUTION
Interchange numerator and denominator.
4
13
1
4
The reciprocal of 3ᎏᎏ is ᎏᎏ.
✓CHECK
4
13
1
4
4
13
13
4
13 ª 4
4 ª 13
3ᎏᎏ ª ᎏᎏ = ᎏᎏ ª ᎏᎏ = ᎏᎏ = 1
To divide by a fraction, multiply by its reciprocal.
EXAMPLE
3
5
3
6
ᎏᎏ ÷ ᎏᎏ = ᎏᎏ ª ᎏᎏ
4
6
4
5
3ª6
= ᎏᎏ
4ª5
2•9
2 • 10
Factor numerator and denominator.
9
10
Simplify fraction to lowest terms.
= ᎏᎏ
1
6
5
25
2
6
5
6
= ᎏ ᎏ ª ᎏᎏ
2
25
2ᎏᎏ ÷ 4ᎏᎏ = ᎏᎏ ÷ ᎏᎏ
Write mixed numbers as fractions.
25
6
6
25
The reciprocal of } } is } } .
5ª6
2 ª 25
Multiply numerators and denominators.
30
50
Simplify.
3 ª 10
5 ª 10
Factor numerators and denominators.
3
5
Simplify fraction to lowest terms.
= ᎏᎏ
= ᎏᎏ
= ᎏᎏ
= ᎏᎏ
782
Multiply numerators and denominators.
Simplify.
= ᎏᎏ
1
2
6
5
18
20
= ᎏᎏ
EXAMPLE
5
6
The reciprocal of } } is } } .
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