# Multiplication of Fractions

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You know how to find the area of a rectangle. It is equal to length × breadth. If the length and breadth of a rectangle are 7 cm and 4 cm respectively, then what will be its area? Its area would be 7 × 4 =

What will be the area of the rectangle if its length and breadth are 7

7

The numbers

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## Multiplication of a Fraction by a Whole Number

Consider the below pictures. The first grid has a shaded portion of

What part of the grid does the shaded portion now cover? It represents

Look at the figures below. Drag all of them unto one and solve the below.

How many green-coloured grids do we have?

What fraction was shaded in each grid?

So we have

**(i)Let us find now 3 x **

- We can re-write 3 as a fraction i.e.
- Multiplying the numerators and denominators, we get
- Another method that we can use is
- Adding the individual numbers
- We have found the answer.

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The fractions that we considered till now, i.e.,

For improper fractions also we have

Thus, to multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same.

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## Try these

**Find if the fraction is proper or mixed fraction.**

(i)

- Finding the product of
x 6, we get9 7 - Now we have an
fraction in our hand. - Converting it into a mixed fraction: re-write the numerator as a sum consisting the nearest multiple + remainder.
- Individually dividing the terms
- Hence the mixed fraction is
- We have found the answer.

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(ii)

- The product is
x 3 is:2 7 - Multiplying we get a
fraction - Thus, we have found our answer.

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To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply. For example,

## Try these

**Find .**

(i) 5 x 2

- Converting the mixed fraction to improper, we get
- Finding the product we get:
- We get an
fraction. - Dividing individually
- Converting to mixed fraction:
- We have found the answer

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## Represent pictorially : 2 · 2 5 = 4 5 .

Click on rectangle and draw a rectangle below.

Click on line and divide the rectangle into 5 equal parts by drawing vertical lines in the rectangle(approximately is fine).

Click on move. Drag and select the drawn rectangles and lines. Once the rectangle is selected, click on copy and then paste. You get a similar rectangle divided into 5 parts. Move it to a different location.

Click on paint and color the left two parts of the first rectange. This represents

Color the right two parts for the second rectangle. This represents the next

Click on move, drag and select the second rectangle and move it over the first rectangle.

This shows

* Rectangle* * Line* * Paint* * Move* * Copy* * Paste*

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## Fraction as an operator ‘of’

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Also, look at these similar squares

So we see that **‘of’ represents multiplication.**

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## Try these

**In a class of 40 students 1/5 of the total number of students like to study English, 2/5 of the total number like to study Mathematics and the remaining students like to study Science.**

**EXAMPLE 1**

**In a class of 40 students 1/5 of the total number of studetns like to study English, 2/5 of the total number like to study Mathematics and the remaining students like to study Science.**

**(i) How many students like to study English?**

Total number of students in the class =

Thus, the number of students who like to study English =

**(ii)What fraction of the total number of students like to study Science?**

The number of students who like English and Mathematics = 8 + 16 =

Thus, the required fraction is

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## Multiplication of a Fraction by a Fraction

Dana had a 9 cm long strip of ribbon. She cut this strip into four equal parts. How did she do it? She folded the strip twice. What fraction of the total length will each part represent?

Each part will be

It will represent

Let us now see how to find the product of two fractions like

To do this we first learn to find the products like

How do we find

Now we need to find

Now move one grid over the other. This image captures a grid divided in 3 parts and each of the 3 parts divided into 2 parts. How many equal parts do we have? We have

How many parts are intersecting? We have

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**Answer the below questions**

**Exercise**

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**Try these**

(i)

(ii)

(iii)

(iv)

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## Example 2 :

**Sushant reads **

- From the problem, we can see that we need to find the
of and - Finding the product, we get:
- Converting the mixed fraction into improper
- Further simplifying it
- Hence, Sushant read
of the book in the given time.11 15

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So,

Also,

This is also shown by the figures drawn below. Each of these five equal shapes are parts of five similar circles. Take one such shape. To obtain this shape we first divide a circle in three equal parts. Further divide each of these three parts in two equal parts. One part out of it is the shape we considered. What will it represent?

It will represent

The total of such parts would be 5

So, we find that we multiply two fractions as

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## Value of the Products

You have seen that the product of two whole numbers is bigger than each of the two whole numbers. For example, 3 × 4 =

Size (in inches) | Number of Shirts Sold | Total |
---|---|---|

Product is less than each of the fractions | ||

Product is less than each of the fractions | ||

| Product is less than each of the fractions | |

| Product is less than each of the fractions |

We find that the product of two improper fractions is

Or, the value of the product of two improper fractions is more than each of the two fractions.

The product obtained is less than the improper fraction and greater than the proper fraction involved in the multiplication.