Page 73 - Algebra 1

To divide signed numbers, use the rules in the table below.
Dividing Signed Numbers
The quotient of two numbers with the same sign is a positive number.
Examples 6 ÷ 3 = 2 -8 ÷ (-2) = 4 __
6 = 2 -8 = 4 3 -2
The quotient of two numbers with opposite signs is a negative number.
Examples 10 ÷ (-5) = -2 -12 ÷ 3 = -4 __
10 =-2 -12=-4 -5 3
Dividing Real Numbers
Simplify each expression. Justify your answer.
Example
3
a. -16 ÷ (-2) SOLUTION
-16 ÷ (-2) = 8
b. 2.8 ÷ (-7) SOLUTION
2.8 ÷ (-7) = -0.4
The quotient of two numbers with the same sign is positive.
The quotient of two numbers with opposite signs is negative.
Dividing by a number a is the same as multiplying by the reciprocal _1 , or a
multiplicative inverse, of the divisor. 12÷2=12·_1 =6
2
The reciprocal of 2 is _1 . Multiplying 12 by _1 is the same as dividing 12 by 2. 22
Dividing Positive and Negative Fractions
Evaluate each expression.
a. -_2÷(-_3) 34
SOLUTION
- _2 ÷ ( - _3 ) 34
Example
4
Hint
The product of a number and its reciprocal is always 1. So, both the number and its reciprocal have the same sign.
2 · _1 = 1 a n d
2 _1
-2 · (- 2 ) = 1
58 Saxon Algebra 1
-_2 · (-_4 ) 334
Multiply by the reciprocal of -_3 .
-_2 · (-_4 )= _8 The product of two fractions with the 3 3 9 same sign is positive.