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Multiplication of Fraction - Multiplication of a Fraction by a Fraction

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  • Multiplication of a fraction by a fraction
  • Value of the Products

notes

Multiplication of a fraction by a fraction:

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

To do this we first learn to find the products like `1/2 xx 1/3`.

We divide the whole into three equal parts. Each of the three parts represents `1/3` of the whole. Take one part of these three parts and shade it.

Divide this one-third `(1/3)` shaded part into two equal parts. Each of these two parts represents `1/2  "of" 1/3  "i.e.," 1/2 xx 1/3`.

Take out 1 part of these two and name it ‘A’. ‘A’ represents `1/2 xx 1/3`.

The whole was divided in 6 = 2 x 3 parts and 1 = 1 x 1 part was taken out of it.

Thus, `1/2 xx 1/3 = 1/6 = (1 xx 1)/(2 xx 3)`

or `1/2 xx 1/3 = (1 xx 1)/(2 xx 3)`

The value of `1/3 xx 1/2` can be found in a similar way. Divide the whole into two equal parts and then divide one of these parts into three equal parts. Take one of these parts. This will represent `1/3 xx 1/2  "i.e.," 1/6`.

Therefore, `1/3 xx 1/2 = 1/6 = (1 xx 1)/(3 xx 2)` as discussed earlier.

Hence, `1/2 xx 1/3 = 1/3 xx 1/2 = 1/6`.

Now,

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 into three equal parts. Further, divide each of these three parts into two equal parts. One part out of it is the shape we considered

It will represent `1/2 xx 1/3 = 1/6`.

The total of such parts would be `5 xx 1/6 = 5/6`.

Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as

`"Product of numerators"/"Product of denominators"`

For example, `2/3 xx 5/7 = (2 xx 5)/(3 xx 7) = 10/21`.

2. 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 = 12 and 12 > 4, 12 > 3.

A) Product of two proper fractions:

When two proper fractions are multiplied, the product is less than each of the fractions. Or, we say the value of the product of two proper fractions is smaller than each of the two fractions.

`2/3 xx 4/5 = 8/15`

`8/15 < 2/3, 8/15 < 4/5`

Product is less than each of the fractions

B) Product of two improper fractions:

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

`7/3 xx 5/2 = 35/6` `35/6 > 7/3, 35/6 > 5/2` Product is greater than each of the fractions

C) Product of improper fractions and proper fractions:

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

`2/3 xx 7/5 = 14/15` `14/15 < 7/5 and 14/15 > 2/3` Product is less than the improper fraction and greater than the proper fraction.

Example

Sulochanabai owns 42 acres of farmland. If she planted wheat on `2/7` of the land, on how many acres has she planted wheat?

We must find out 2 7 of 42 acres

∴ `42/1 xx 2/7 = (42 xx 2)/(1xx 7) = (6 xx 7 xx 2)/7 × × = 12`

Sulochanabai has planted wheat on 12 acres of land.

If you would like to contribute notes or other learning material, please submit them using the button below.

Shaalaa.com | Multiplication of a Proper Fraction by an Improper Fraction

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