**What are the Operations on Fractions**

Now, we have to learn, how to add and subtract the fractions. Certain methods are to be followed for doing these operations.

**Addition and subtraction of like fractions**

For adding and subtracting like fractions, we follow these steps:

Step 1. Add/subtract the numerators with common denominator.

Step 2. Reduce the fraction to its lowest term.

Step 3. If the result is an improper fraction, convert it into a mixed fraction.

**Read More:**

- Comparing and Ordering of Fractions
- Conversion of Decimal into Fraction
- RS Aggarwal Class 6 Solutions Fractions
- RS Aggarwal Class 7 Solutions Fractions

**Example 1:** Find the sum of

**Solution:**

**Example 2: **Subtract

**Solution:**

**Addition and subtraction of unlike fractions**

For adding/subtracting unlike fractions, we follow these steps:

1. Find the LCM of denominators of the given fractions.

2. Convert unlike fractions into like fractions by making LCM as its denominator.

3. Add/ subtract the like fractions.

**Example 3: **Add \(\frac{9}{5}\) and \(\frac{5}{6}\)

**Solution: **LCM of 10 and 6 = 30

**Example 4:**

**Solution:**

**Example 5: **Find \(\frac{13}{5}\) – \(\frac{4}{5}\)

**Solution: **LCM of 15 and 5 = 15

**Example 6: **Simplify \(6\frac { 1 }{ 2 }\) + \(2\frac{2}{3}\) – \(\frac{1}{4}\)

**Solution: **\(6\frac { 1 }{ 2 }\) + \(2\frac{2}{3}\) – \(\frac{1}{4}\)

### Multiplication of Fractions

**Rule:**

(i) Whole number by a fraction

(ii) Fraction by a fraction

(iii) Whole number by a mixed fraction

(iv) Multiplication of two mixed fractions

**Whole number by a fraction:**

To multiply a whole number by a fraction, we simply multiply the numerator of the fraction by the whole number, keeping the denominator same.

**Example 1: **Find the product

**Solution:**

**Example 2: **Show \(3\times \frac { 1 }{ 5 }\) by picture.

**Solution:**

Note : Multiplication is commutative i.e. ab = ba

**Fraction by a fraction :**

**Example 3:** Find the product

**Solution:**

**Whole Number by a Mixed Fraction :**

To multiply a whole number by a mixed fraction, we follow the following steps:

- Convert the mixed fraction into an improper fraction.
- Multiply the numerator by the whole number keeping the denominator same.
- After multiplication, the fraction should be converted in its lowest form.
- Convert the improper fraction (product so obtained) into a mixed numeral.

**Example 4:** Find \(8\times 5\frac { 1 }{ 6 }\)

**Solution:**

**Example 5:** Find \(6\times 3\frac { 1 }{ 2 }\)

**Solution:**

**Multiplication of two Mixed Fractions:**

- To multiply two or more mixed numerals, we follow the following steps :
- Convert the mixed fractions into improper fractions.
- Multiply the improper fractions.
- Reduce to lowest form.
- If the product is an improper fraction, convert it into mixed fraction.

**Example 6:** Find the product of

**Solution:**

**Facts:**

- It is not necessary first to multiply the fractions and then simplify. We may simplify first then multiply. For example,

- Cancellation could use only for fractions are multiplied and could not use for addition & subtraction of fractions.
- Double of 3 or half of 7 can be written as 2 × 3 and 1/2 × 7 respectively.

If word ‘OF’ is in between two fractions then multiply those fractions. - Product of two proper fractions < Each proper fraction.

- Product of two improper fractions > Each improper fraction.

; - Proper fraction < Product of proper and improper fraction < Improper fraction

- When the product of two fractional numbers or a fractional number and a whole number is 1, then either of them is the multiplicative inverse (or reciprocal) of the other. So the reciprocal of a fraction (or a whole number) is obtained by interchanging its numerator and denominator.

Note : Reciprocal of zero (0) is not possible.

### Division of Fractional Numbers

∵ We know Division = Dividend ÷ Divisor

When a fraction number (or whole no.) divide by fractional number (or whole no.) then we multiply dividend to reciprocal of divisor.

**Example 1:** Find the value of

**Solution:**

**Facts:**

- (Fractional number) ÷ 1 = same fractional number

- 0 ÷ Fractional number = 0 (always)
- non zero fractional number ÷ same number = 1 (always)

- ‘0’ cannot be a divisor (∵ reciprocal of zero is not possible)

**Example 2:**

**Solution:**

**Example 3:**

**Solution:**

### Simplifying brackets in fractions

**Example 1:**

**Solution:**

**Example 2:**

**Solution:**