1. Chapter 2 – Properties of
Real Numbers
2.7 – Division of Real Numbers

2. 2.7 – Division of Real Numbers
 Today we will learn how to:
 Divide real numbers
 Use division to simplify algebraic expressions

3. 2.7 – Division of Real Numbers
 Suppose you owe a friend $50.00. You and
your friend decide to come up with a payment
schedule. You decide on 4 equal monthly
payments. We can determine the monthly
payment using division of real numbers.

4. 2.7 – Division of Real Numbers
 Every real number (except zero) has a
RECIPROCAL
 The product of a number and its reciprocal is 1
 Example: 2 · ½ = 1

5. 2.7 – Division of Real Numbers
 The reciprocal of a is 1 , when a ≠ 0
a
1
 Example: -8 and −
8
a b
 The reciprocal of is , when a ≠ 0 and b ≠ 0
b a
2 and 5
 Example:
− −
5 2

6. 2.7 – Division of Real Numbers
 Zero is the only real number that has no
reciprocal. There is no number that when
multiplied by zero gives a product of 1.
Because zero does not have a reciprocal, you
cannot divide by zero.

7. 2.7 – Division of Real Numbers
 You can use a reciprocal to write a division as a
product.
 DIVISION RULE
 To divide a number a by a nonzero number b, multiply a
by the reciprocal of b.
 1
a ÷b = a⋅
b

8. 2.7 – Division of Real Numbers
 Example 1
1. 15 ÷ (−5)
5
2. − 45 ÷
6
1
2
3. 3
−3
−1
4.
2
3

9. 2.7 – Division of Real Numbers
 THE SIGN OF A QUOTIENT
 The quotient of two numbers with the same sign is
positive
 -a  -b = a/b
 -20  (-4) = 5
 The quotient of two numbers with opposite signs is
negative
 -a b = - a/b
 -20  4 = -5

10. 2.7 – Division of Real Numbers
 Example 2
Simplify the expression
9 − 27 x
−3

11. 2.7 – Division of Real Numbers
 Example 3
A mountain climber descends 300 feet in 50 minutes.
What is her velocity per minute?