Download Reciprocals Division with Fractions

Math 952
3.6 "Division with Fractions"
Objectives:
*
Be able to recognize and …nd the reciprocal of a number or algebraic expression.
*
Know that to divide you multiply by the reciprocal of the divisor.
Preliminaries:
In this section we learn to divide fractions by expressing them as products. The main de…nition we require is the
following.
De…nition:
"Reciprocal"
a
The reciprocal of is
b
The product of a nonzero number and its reciprocal is 1.
:
That is,
:
Question:
NOTE: Here we need a 6= 0 and b 6= 0.
Does 0 have a reciprocal ? Please explain.
Reciprocals
Example 1: (Finding reciprocals)
Find the reciprocal of the following fractions.
11
31a
a)
b)
18
10
c) 3
Division with Fractions
To understand division of fractions consider the following division:
2 5
3 7
Division of Fractions
To divide by any nonzero number, we multiply by its reciprocal. In other words,
:
Question: Is division of fractions a commutative operation? To answer this consider the following situation:
Page: 1
2
3
3 ? 3
=
5
5
2
3
Notes by Bibiana Lopez
Prealgebra by Franklin Wright
3.6
Example 2: (Dividing fractions)
Divide (whenever possible).
4 1
a)
9 2
d)
14
20
( 4)
b)
21
10
0
c) 0
e)
5
8
5
8
f)
21
3
4
5
8
15
Example 3: (Dividing and reducing to lowest terms)
Divide and reduce to lowest terms.
5
25
a)
13y 52y
c)
56b
1
3
b)
d)
Page: 2
19a
24b
26x2
35
5a
8b
39x
40
Notes by Bibiana Lopez
Prealgebra by Franklin Wright
3.6
Now we consider some situations where division can be used to …nd a missing number.
Example 4: (Using division to …nd a missing number)
9
8
The result of multiplying two numbers is
. If one number is
; what is the other number?
10
25
Example 5: (Using division to …nd a missing number)
The product of two numbers is 110.
a) Is 110 a product or a quotient?
2
b) If one of the numbers is , do you expect the other number to be smaller or larger?
3
c) What is the other number?
Example 6: (Word problem)
A truck is towing 3000 pounds. This is
4
of the truck’s towing capacity.
5
a) Can the truck tow 4000 pounds?
4
b) If you were to multiply times 3000, would the product be bigger or smaller than 3000?
5
c) What is the maximum towing capacity of the truck?
Page: 3
Notes by Bibiana Lopez