September 30, 2013
In division, the first number is
the dividend, the second
number is the divisor, and the
answer is the quotient.
September 30, 2013
In division, the first number is
the dividend, the second
number is the divisor, and the
answer is the quotient.
8÷2=4
September 30, 2013
Division is not commutative.
8÷2=4
2÷8=
1
4
September 30, 2013
Division is not commutative.
8÷2=4
2÷8=
1
4
The quotients above, 4 and 1/4,
are reciprocals.
September 30, 2013
When the dividend and the
divisor are reversed in a
division problem, the quotient
is the reciprocal of the quotient
of the original problem.
September 30, 2013
The product of a pair of
reciprocals is one.
September 30, 2013
The product of a pair of
reciprocals is one.
4•
1
4
4
4
= =1
September 30, 2013
The product of a pair of
reciprocals is one.
The reciprocal of a non-zero
number, n, is 1/n.
September 30, 2013
The product of a pair of
reciprocals is one.
The reciprocal of a non-zero
real number, n, is 1/n.
Property of reciprocals:
For any non-zero number, n,
n • 1/n = 1
September 30, 2013
The product of a pair of
reciprocals is one.
4•
1
4
4
4
= =1
September 30, 2013
The product of a pair of
reciprocals is one.
4•
1
4
n•
1
n
4
4
= =1
n
n
= =1
September 30, 2013
The property of reciprocals is
often referred to as the
Multiplicative inverse property.
September 30, 2013
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.
September 30, 2013
The product of a pair of
reciprocals is one.
The number, one, is called the
multiplicative identity,
because when a number is
multiplied by one, the number
retains its identity.
September 30, 2013
Multiplicative identity property:
For any real number, n, n • 1 = n
Some textbooks call this
property
The multiplication property of
one
September 30, 2013
Dividing by a number is the
same as multiplying by its
reciprocal.
12 ÷ 4 = 3
12 •
1
4
=3
September 30, 2013
The rules, then, when negative
numbers are involved in division
are the same as they are for
multiplication.
18 ÷ 6 = 3
18 ÷ -6 = -3
-18 ÷ 6 = -3
-18 ÷ -6 = 3
September 30, 2013
When dividing two non-zero
numbers, the answer is positive if
the signs are the same, and the
answer is negative if the signs are
different. Zero divided by a nonzero is zero, and division by zero
is undefined.
September 30, 2013
Most scientific calculators have a
reciprocal key.
On some models the key is:
x-1
And on other models the key is:
1/x
September 30, 2013
Summary
When dividing two non-zero
numbers, the answer is positive if
the signs are the same, and the
answer is negative if the signs are
different. Zero divided by a nonzero is zero, and division by zero
is undefined.
September 30, 2013
Summary
The reciprocal of a non-zero
number, n, is 1/n.
The product of a pair of
reciprocals is one.
September 30, 2013
Summary
Zero does not have a reciprocal.
Division by zero is undefined.
Zero divided by any non-zero
real number is equal to zero.
September 30, 2013
Summary
Property of reciprocals:
For any non-zero real number, n,
n • 1/n = 1
Multiplicative identity property:
For any real number, n, n • 1 = n
September 30, 2013
September 30, 2013