Math 8 Unit 3: Operations with Fractions.
Name:_________________
Date:________________
Block:__________
Lesson Notes: 3.6: Dividing Fractions.
We have done the division of a whole number by a fraction and a
fraction divided by a whole number.
Today, we shall take a look at other types of “Fraction divisions”.
i) a mixed number divided by a fraction.
ii) a fraction divided by a mixed number.
iii) a mixed number divided by a mixed number.
We have discovered that the easiest and most effective way of calculating the
quotient of fraction division is to multiply by the reciprocal of the divisor.
Can we use this method on today’s problems? If we can, how do we
do it?
Example 1)
1
1
1
÷
2
4
=
=
= ____
Remember the question: How many equal shares of _______ in ______?
Answer:_________
Sometimes the answers may not turn out to be whole numbers. Let us
take a look at another example.
Example 2) 1
2
2
÷
3
3
=
=
= ____
How many equal shares of ______ in _______?
Answer: _________
Example 3) 4
2
7
÷
3
9
=
=
= ____
How many equal shares of ______ in _______?
Answer: _________
Rule:
OK, we just did the mixed number divided by a fraction, how about fractions
divided by mixed numbers, Let us take a look at the following examples.
Example 4)
If 1
1 1
1
2 2
=
= ____
1
is needed to complete an order (1 order = 1 paper bag)
2
How many order ( a paper bag) is filled with a
1
?
2
Answer: ___________
Not all problems can be simplified by using a diagram or a model, so if we
use the more direct mathematical approach: multiply by the reciprocal of the
divisor, the quotient can be determined easily.
Example 5) 7
1 2
 =
3 5
More Practice.
Example 6)
5 23
3 
=
6 24
1
4
1
8
Example 7) 11  1  1
Example 8)
3
=
7
28 7 4
3
  3 =
33 11 9
5
1 8 1
 
3 9 2
Example 9) What number makes this equation true? 5 
Example 10) Replace each
□ with a fraction to make each equation true. Show how you get the
answer.
a)
5

7
□=
3
5

b)
4
1 
7
□

2
3
Extra Exploration.
Replace each
□ with a number
A) 18 ÷
□=
3
B)
72 ÷
□=
8
C)
60 ÷
□=
5
D)
279 ÷
□=
9
E)
65 ÷
□=
13
to make each equation true. Show how you get the answer.