A pair of numbers that have a
product of one are called
reciprocals.
A pair of numbers that have a
product of one are called
reciprocals.
For any pair of real numbers,
a and b, if ab = 1, then a and b
are reciprocals.
A pair of numbers that have a
product of one are called
reciprocals.
For any pair of real numbers,
a and b, if ab = 1, then a and b
are reciprocals.
The product of a pair of
reciprocals is one.
The product of a pair of
reciprocals is one.
1
4• 4
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
4
4 • 3
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n• n
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n
n• n = n
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n
n• n = n=1
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n
n• n = n=1
a
b
b • a
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n
n• n = n=1
a
b
ab
b • a = ab
The product of a pair of
reciprocals is one.
1
4
4• 4 = 4=1
3
12
4
4 • 3 = 12 = 1
1
n
n• n = n=1
a
b
ab
b • a = ab = 1
Property of Reciprocals
For any nonzero real number, n,
n and 1 are reciprocals. 1 • 1 = 1
n
n
For any nonzero real numbers,
a and b, a and b are reciprocals.
a
b
a • b =1
b a
The property of reciprocals is
often referred to as the
Multiplicative inverse property.
The property of reciprocals is
often referred to as the
Multiplicative inverse property.
The reciprocal of a positive number
is another positive number. The
reciprocal of a negative number is
another negative number.
Zero has no reciprocal, because if
it did, the number would be 1/0,
and division by zero is undefined.
Zero has no reciprocal, because if
it did, the number would be 1/0,
and division by zero is undefined.
Another way to show why zero
has no reciprocal is because a pair
of reciprocals must have a product
of one, and zero times any number
is equal to zero.
Most scientific calculators have a
reciprocal key.
On some models the key is:
x-1
And on other models the key is:
1/x
Find the reciprocal:
42
Find the reciprocal:
42
1
42
Find the reciprocal:
42
1
42
42
42 = 1
Find the reciprocal:
42
1
42
42
42 = 1
1
42
Find the reciprocal:
42
1
42
42
42 = 1
1
42
Find the reciprocal:
3
5
Find the reciprocal:
3
5
5
3
Find the reciprocal:
3
5
5
3
Find the reciprocal:
3
5
1
3
5
5
3
Find the reciprocal:
3
5
1
3 =1÷
5
5
3
3
5
=
Find the reciprocal:
3
5
1
3 =1÷
5
5
3
3
5
=1 •
5
3
Find the reciprocal:
3
5
1
3 =1÷
5
5
3
3
5
=1 •
5
= 3
5
3
Find the reciprocal:
3
5
1
3 =1÷
5
5
3
3
5
=1 •
5
= 3
5
3
Find the reciprocal:
0.75
Find the reciprocal:
3
0.75 = 4
Find the reciprocal:
3
0.75 = 4
4
3
Find the reciprocal:
3
0.75 = 4
4
3
Find the reciprocal:
3
0.75 = 4
1
7
8
4
3
Find the reciprocal:
3
0.75 = 4
15
1 = 8
7
8
4
3
Find the reciprocal:
3
0.75 = 4
15
1 = 8
7
8
4
3
8
15
Find the reciprocal:
3
0.75 = 4
15
1 = 8
7
8
4
3
8
15
Find the reciprocal:
7.5
65%
Find the reciprocal:
7.5 = 7
65%
1
2
Find the reciprocal:
7.5 = 7
65%
1
2
15
= 2
Find the reciprocal:
7.5 = 7
65%
1
2
15
= 2
2
15
Find the reciprocal:
7.5 = 7
65%
1
2
15
= 2
2
15
Find the reciprocal:
7.5 = 7
1
2
15
= 2
65
65% = 100
2
15
Find the reciprocal:
7.5 = 7
1
2
15
= 2
65 13
65% = 100 = 20
2
15
Find the reciprocal:
7.5 = 7
1
2
15
= 2
65 13
65% = 100 = 20
2
15
20
13
Find the reciprocal:
7.5 = 7
1
2
15
= 2
65 13
65% = 100 = 20
2
15
20
13
A pair of numbers that have a product
of one are called reciprocals.
For any pair of real numbers,
a and b, if ab = 1, then a and b are
reciprocals.
The product of a pair of
reciprocals is one.
Property of Reciprocals
For any nonzero real number, n,
n and 1 are reciprocals. 1 • 1 = 1
n
n
For any nonzero real numbers,
a and b, a and b are reciprocals.
a
b
a • b =1
b a
Zero is the only real
number that does not
have a reciprocal.