Subject: Compulsory Maths

A fraction is a number which is usually expressed in the form of \(\frac{a}{b}\). For examples ( \(\frac{3}{4}\), \(\frac{5}{3}\), \(\frac{9}{7}\), etc.)

**Comparison of fraction**

A fraction can be compared to their likes and unlike terms. We can compare like fractions by comparing their numerators and to compare unlike fractions, we should convert them into like fractions. By comparing those like fractions, as a result, we can find greater and the smaller fraction. For example, Let's compare \(\frac{5}{3}\) and \(\frac{7}{4}\)

Here, the L.C.M of denominators 3 and 4 = 3×4 = 12

Now, \(\frac{5}{3}\) = \(\frac{5×4}{3×4}\) = \(\frac{20}{12}\)

And, \(\frac{7×3}{4×3}\) = \(\frac{21}{12}\)

Here, \(\frac{21}{12}\) > \(\frac{20}{12}\), So, \(\frac{7}{3}\) > \(\frac{4}{3}\)

**Addition and Substraction of Fraction**

If the like fraction is given, we can add or substract them just by adding or substracting their numenator. For example, \(\frac{5}{6}\) + \(\frac{7}{6}\) = \(\frac{12}{6}\) = 2

\(\frac{10}{7}\) - \(\frac{9}{7}\) = \(\frac{10 - 9}{7}\) = \(\frac{1}{7}\) ans.

In case of unlike fraction, at first we should convert them into like fractions with the least common denominator, then we add or substract their numenator. For example,

or,\(\frac{4}{5}\) - \(\frac{3}{7}\) = \(\frac{4 × 7}{5 × 7}\) - \(\frac{3 × 5}{7 × 5}\)

= \(\frac{21}{35}\) - \(\frac{15}{35}\)

= \(\frac{21 -15}{35}\)

= \(\frac{6}{35}\) ans.

**Multiplication of fraction**

Multiplication of fraction can be done by the product of a whole number and a fraction as well as product of a two fraction. For example 3× \(\frac{4}{3}\)

\(\frac{3}{1}\) × \(\frac{4}{3}\) = \(\frac{12}{3}\) =4

\(\frac{1}{3}\) × \(\frac{6}{5}\) = \(\frac{1×6}{3×5}\) = \(\frac{6}{15}\) = \(\frac{2}{5}\) ans.

**Division of fraction**

To divide a whole number by a fraction, we should multiply the whole number by the reciprocal of the fraction. For example,

4÷ \(\frac{1}{6}\) = 4× \(\frac{1}{6}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\) ans.

- To divide a whole number by a fraction, we should multiply the whole number by the reciprocal of the fraction.
- By comparing those like fractions, as a result, we can find greater and the smaller fraction.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Simplify : 2\(\frac{3}{4}\)+1\(\frac{5}{8}\)-3\(\frac{1}{3}\).

sol^{n:}

2\(\frac{3}{4}\)+1\(\frac{5}{8}\)-3\(\frac{1}{3}\)

= \(\frac{11}{4}\)+\(\frac{13}{8}\)-\(\frac{10}{3}\)

=\(\frac{11\times6+13\times3-10\times8}{24}\)

=\(\frac{66+39-80}{24}\)

=\(\frac{105-80}{24}\)

=\(\frac{25}{24}\)

=1\(\frac{1}{24}\)

Add : \(\frac{2}{9}\)+\(\frac{4}{9}\)

\(\frac{2}{9}\)+\(\frac{4}{9}\)

=\(\frac{2+4}{9}\)

=\(\frac{6}{9}\)

=\(\frac{2}{3}\)

Subtraction : \(\frac{3}{5}\)-\(\frac{2}{7}\)

sol^{n:}

\(\frac{3}{5}\)-\(\frac{2}{7}\)

=\(\frac{3\times7-2\times5}{35}\)

=\(\frac{21-10}{35}\)

=\(\frac{11}{35}\)

Addation ; \(\frac{3}{5}\) -\(\frac{2}{7}\)

Sol^{n}:

\(\frac{3}{5}\)-\(\frac{2}{7}\)

=\(\frac{3\times7}{5\times7}\) -\(\frac{2\times5}{7\times5}\)

=\(\frac{21}{35}\) - \(\frac{10}{35}\)

=\(\frac{21-10}{35}\)

=\(\frac{11}{35}\)

Find the value of \(\frac{3}{5}\) of Rs 750.

Sol^{n}:

\(\frac{3}{5}\) of Rs 750=\(\frac{3}{5}\) x Rs 750

=Rs450.

If \(\frac{2}{7}\) of a sum is Rs. 120, find the sum.

Solution:

Let the required sum be x.

Now, \(\frac{2}{7}\) of x = Rs. 120

or, \(\frac{2}{7}\) × x = Rs. 120

or, 2x = 7 × Rs. 120

or, x = \(\frac{7 × Rs. 120}{2}\)

= Rs. 420

So the required sum is Rs. 420.

A man had some milk. When he sold \(\frac{3}{4}\) parts of the quantity of milk, 15 *l* was left. How much milk did he have in the beginning?

Solution:

Let, he had x *l* of milk in the begining.

Remaining parts of the quantity of milk = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\) part.

Now, \(\frac{1}{4}\) of x = 15 *l*

or, \(\frac{1}{4}\) × x = 15 *l*

or, x = 4 × 15 *l* = 60 *l*

So, he had 60 *l* of milk in the begining.

Kamala can do \(\frac{1}{12}\) part a piece of work in 1 day. She worked for 3 days and left. The remaining parts of the work is done by Reeta. How much work is done by Reeta?

Solution:

In 1 day, Kamala can do \(\frac{1}{12}\) part of a piece of work.

In 3 days, Kamala can do 3 × \(\frac{1}{12}\) part of work = \(\frac{1}{4}\) parts of a piece of work

Now, the remaining parts of the work done by Reeta = (1-\(\frac{1}{4}\)) = \(\frac{3}{4}\) parts.

So, \(\frac{3}{4}\) parts of the work is done by Reeta.

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