This document discusses division of real numbers. It defines division as multiplying by the reciprocal. It provides examples of dividing numbers and simplifying expressions using division. It also discusses properties of division including that the quotient of numbers with the same sign is positive and opposite signs is negative. It cannot divide by zero since zero has no reciprocal. An example problem calculates velocity by dividing distance by time.

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?