**Example 1 :**

Find the sum of 1/3 and 2/5

**Solution :**

Given, 1/3 + 2/5

In the given, denominators are not equal.

So we take LCM of 3 and 5 is 15

1/3 + 2/5 = [(1×5)/15] + [(2×3)/15]

1/3 + 2/5 = (5+6)/15

= 11/15

So, the answer is 11/15

**Example 2 :**

Find the difference between 1/4 and 2/3

**Solution :**

Equivalent fraction of 1/4 is 3/12

Equivalent fraction of 2/3 is 8/12

Difference between 8/12 and 3/12

= 8/12 - (3/12)

= 5/12

So, the answer is 5/12.

**Example 3 :**

Find the number 3 less than 2/3

**Solution :**

Let x be the number.

Given, x = 2/3 – 3

Since the denominators are not same, we take least common multiple.

x = 2/3 – 9/3

x = - 7/3

By converting the improper fraction to mixed fraction, we get

x = -2 1/3

**Example 4 :**

Find the number 2/3 more than 1 1/4

**Solution :**

Let x be the number.

Given, x = 1 1/4 + 2/3

First, we write 1 1/4 = 5/4

Then, x = 5/4 + 2/3

Least common multiple of 4 and 3 is 12.

x = [(5×3)/12] + [(2×4)/12]

x = (15+8)/12

x = 23/12

By changing it as mixed fraction, we get

x = 1 11/12

**Example 5 :**

What must 1/5 be increased by to get 2/3 ?

**Solution :**

Let x be the unknown,.

x+(1/5) = 2/3

x = (2/3) – (1/5)

The least common multiple of 3 and 5 is 15.

2/3 – 1/5 = [(2×5)/15] – [(1×3)/15]

= (10–3)/15

= 7/15

So, the answer is 7/15

**Example 6 :**

What number is 3/4 less than – 1 1/2 ?

**Solution :**

Let x be the number.

-1 1/2 = -3/2

= (-3/2) - (3/4)

= (-6-3)/4

= -9/4

By converting the improper fraction in to mixed fraction, we get

x = -2 1/4

**Example 7 :**

Find the average of 1/4 and 3/4

**Solution :**

Given, 1/4 + 3/4

We know that,

Average = Sum of all terms/Number of terms

Average = (1/4 + 3/4)/2

= (4/4)/2

= 1/2

So, the answer is 1/2

**Example 8 :**

Find the number midway between – 1/2 and 2/3

**Solution :**

Let x be the number.

Given, x = - 1/2 + 2/3

We Know that,

Middle number = sum of term/2

= (-1/2 + 2/3)/2

= [(- 3+4)/6]/2

= 1/6 × 1/2

= 1/12

So, the number is 1/12

**Example 9 :**

Find the average of 1/2, 2/3 and 3/4

**Solution :**

Given, 1/2 + 2/3 + 3/4

We know that,

Average = Sum of all terms / Number of terms

Average = (1/2 + 2/3 + 3/4)/3

= [(6 + 8 + 9)/12]/3

= (23/12)/3

= (23/12) × (1/3)

= 23/36

So, the average is 23/36

**Example 10 :**

Find the quotient of 1/3 and 3/4

**Solution :**

Given, 1/3 ÷ 3/4

= 1/3 × 4/3 (the reciprocal of 3/4)

= 4/9

So, the answer is 4/9

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