Multiplication and Division of Fraction

1. Multiplying and dividing
fraction
Visual model
Muhammad Yusuf
m.yusuf.edu@gmail.com

2. Multiplying Fraction by using model.
Example 1: 4 ×
2
3
Step 1: Draw four bars on the given paper.
Step 2: Look at the denominator of the fraction. Divide bars into three parts.
Step 3: Shade 2/3 on all four bars.
Step 4: collect all the bars together and count. We will find 2 complete bars and one 2/3 in
the third bar. It can be written 2
2
3
Step 6: Write equation 4 ×
2
3
=
8
3
= 2
2
3
1. 5 ×
3
4
2.
2
5
× 3

3. Multiplying Fraction by using model.
Example 2:
1
4
×
2
3
Step 1: Look at denominators of both fractions
Step 2: Draw a rectangle of 4 rows by 3
columns.
Step 3: shade one row for showing ¼
Step 4: Shade 2 columns for showing 2/3.
Step 5: Mark the double shaded boxes. Count
the parts with respect to whole figure 2/12.
Step 6: Write an equation
1
4
×
2
3
=
2
12
=
1
6
Now try yourself.
1.
2
5
×
3
4
2.
4
5
×
2
3

4. Dividing Fraction by using model.
If
1
2
a chocolate bar is divided equally among 4
children, What will each child get?
Step 1: Draw a rectangle. Divide it into two
equal parts.
Step 2: Shade one part to show ½
Step 3: Divide ½ part into 4 equal parts.
Step 4: Read one of the parts with reference
to the whole figure. Your answer will be 1/8
Step 5: Write the equation.
1
2
÷ 4 =
1
8

5. How many children will 4 chocolate bars, if each chocolate bar is divided into ½?
Step 1: Draw 4 bars.
Step 2: Divide each bar into two equal parts.
Step 3: Count all the parts. You get 8.
Step 4: Write the equation.
4÷1/2 = 8

6. Dividing Fraction by using model.
Example 1:
2
5
÷
2
3
The division answers the question: “How many
2
3
𝑠 are there in
2
5
Step 1: Look at the denominator of both fractions. Draw 5
columns by 3 rows rectangle.
Step 2: Shade 2 columns for 2/5.
Step 3: Crile 2 rows for
2/3. You can observe that
4 shaded small boxes are
in the circle and 2 shaded
small boxes are outside
the circle.
Step 4: Bring those two small boxes in the
circle. Consider 2/3 circled area as 1 whole
and write fraction with reference to shaded
small boxes.
6
10
(6 shaded small boxes out
of 10 small boxes)
Step 5: Write the equation.
2
5
÷
2
3
=
6
10
=
3
5

7. 3
4
÷
2
3
The division answers the question: “How many
2
3
𝑠
are there in
3
4
Step 1: Look at the denominator of both fractions.
Draw 4 columns by 3 rows rectangle.
Step 2: Shade 2 columns for 3/4.
Step 3: Crile 2 rows for 2/3.
You can observe that 6 shaded
small boxes are in the circle
and 3 shaded small boxes are
outside the circle.
Step 4: Bring those 3 small boxes in the circle. Consider 2/3
circled area as 1 whole, and you can observe that area 2/3
once and 1 small box out of the next 8. So, the answer is 1
1
8
. (1 complete area and 1 reaming small box.)
Step 5: Write the equation.
3
4
÷
2
3
= 1
1
8
Now, try yourself.
3
5
÷
1
2
5
7
+
1
3

8. You have 2/4 of a pizza and you want to share it equally between 2 people. How much of the pizza does
each person get?
A baker is making cakes for a big party. She uses 1/4 cup of oil for each cake. How many cakes can she
make if she has a bottle of oil that has 6 cups in it?
Erum has
1
3
of a pizza left. She cuts this into two pieces of equal size. Write and explain what fraction
shows the two pieces as part of the whole pizza.
Five-twelfths of the flowers in the box is red. Write an equivalent fraction to show what part of the
flowers in the box is not red.
At the book fair convention, one-fourth of the people are students, one-fourth are teachers, and one-
sixth are authors of books for children. The rest of the people are employees of the convention center. If
there are 348 people at the convention, how many are employees of the center?
Try yourself