Division of Fractions
- Dividing Two Proper or Improper Fractions
To divide two proper or improper fractions we turn the
problem into a multiplication problem by multiplying by the reciprocal
Example
3
2
3 5
15
÷
=
x
=
4
5
4 2
8
Example
2
4
12
515
5
÷
=
x
=
9
15 39
24
6
Exercises
Divide
- 4
7
÷
5
11
Hold mouse over the yellow rectangle for the
solution
- 25
15
÷
16
56
Hold mouse over the yellow rectangle for the
solution
-
6 2
÷
9
3
Hold mouse over the yellow rectangle for the
solution
- Division of a Whole Number By a Fraction
In a division problem, when one of the numbers
is a fraction and one a whole number, we can always write the whole number
as a fraction with denominator 1.
Example
Divide
4
3 4
3
3 ÷
=
÷
We write 3 =
7
1 7
1
3 7
21
=
x
=
1 4
4
Example
4
4 2
2
÷ 2 =
÷
We write 2 =
5
5 1
1
24
1
2
=
x
=
5 12
5
Exercise
Divide
- 9
÷ 6
7
Hold mouse over the yellow rectangle for the
solution
-
20
15 ÷
3
Hold mouse over the yellow rectangle for the
solution
- Dividing Mixed Numbers
Recall that when we multiplied mixed numbers we first needed to
convert the mixed numbers into improper fractions. Then we can
multiply. We use the same technique for division
To divide mixed numbers, first convert to
improper fractions then do the division
Example
1 2
5 x 2 + 1 3 x 3 + 2 11
11 Convert
5
÷ 3
=
÷
= ÷
to
2
3
2
3
2 3
improper fractions
111
3
3
1
=
x
= =
1
2 111
2
2
Exercises
Divide
-
3 4
6
÷ 1
4
5
Hold mouse over the yellow rectangle for the
solution
-
2 8
2
÷
7 9
Hold mouse over the yellow rectangle for the
solution
- Application
Example
You have 12 1/2 cups of flower left in the cupboard. A batch of
cookies requires 1 2/3 cups of flower. How many batches of cookies can
you make?
Solution
This is the division problem
1 2
12 x 2 + 1
1 x 3 + 2
25 5
12
÷ 1 =
÷
=
÷
2
3
2
3
2 3
525
3 15
1
=
x
= =
7
2 15
2
2
You can make 7 1/2 batches of cookies.
Exercise
You have decided to build a 100 yard boat dock and divide the dock up
into slots for boats. If each slot requires 3 1/4 yards of space how
many slots can you construct?
Hold mouse over the yellow rectangle for the solution
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