ADDING FRACTIONS WITH WHOLE NUMBERS

We can follow the steps given below to add a fraction and a whole number.

Step 1 :

Multiply the denominator and whole number.

Step 2 :

After having multiplied the denominator and the whole number, take the denominator as a common denominator. 

Step 3 : 

Now, simplify the numbers in numerator. 

It has been illustrated in the picture shown below.  

Example 1 :

Find the value of :

1/2 + 1

Solution :

Multiply the denominator 2 and the whole number 1. 

That is, 

2 ⋅ 1 = 2

Now, take the denominator 2 as a common denominator for the sum (1 + 2).

(1 + 2)/2 = 3/2

Therefore,

1/2 + 1 = 3/2

Example 2 : 

Find the value of :

3/2 + 10

Solution :

Multiply the denominator 2 and whole number 10. 

That is, 

2 ⋅ 10 = 20

Now, take the denominator 2 as a common denominator for the sum (3 + 20).

(3 + 20)/2 = 23/2

Therefore,

3/2 + 10 = 23/10

Example 3 : 

Find the value of :

5 + 2/3

Solution :

Multiply the denominator 3 and the whole number 5. 

That is, 

3 ⋅ 5 = 15

Now, take the denominator 2 as a common denominator for the sum (15 + 2).

(15 + 2)/3 = 17/3

There fore,

5 + 2/3 = 17/3

Example 4 : 

Find the value of :

7/8 + 9

Solution :

Multiply the denominator 8 and the whole number 9. 

That is, 

8 ⋅ 9 = 72

Now, take the denominator 8 as a common denominator for the sum (7 + 72).

(7 + 72)/8 = 79/3

There fore,

7/8 + 9 = 79/3

Example 5 : 

Find the value of :

7 + 5/8

Solution :

Multiply the denominator 8 and the whole number 7. 

That is, 

8 ⋅ 7 = 56

Now, take the denominator 8 as a common denominator for the sum (56 + 5).

(56 + 5)/8 = 61/8

There fore,

7 + 5/8 = 61/8

Example 6 :

Find the value of :

1/5 + 2/5 + 7

Solution :

1/5 + 2/5 + 7

The two fractions above have the same denominator. That is 5.

So, take the denominator once and add the numerators. 

= (1 + 2)/5 + 7

= 3/5 + 7

Multiply the denominator 5 and the whole number 7. 

That is, 

5 ⋅ 7 = 35

Now, take the denominator 5 as a common denominator for the sum (3 + 35).

(3 + 35)/5 = 38/5

There fore,

1/5 + 2/5 + 7 = 38/5

Example 7 :

Find the value of :

3/4 + 5/6 + 2

Solution :

3/4 + 5/6 + 2

The two fractions above have different denominators.

Least common multiple of the denominators (4, 6) = 12.

In the two fractions 3/4 and 5/6, make each denominator as 12.

= 9/12 + 10/12 + 2

So, take the denominator once and add the numerators. 

= (9 + 10)/12 + 2

= 19/12 + 7

Multiply the denominator 12 and the whole number 7. 

That is, 

12 ⋅ 7 = 84

Now, take the denominator 12 as a common denominator for the sum (19 + 84).

(19 + 84)/12 = 103/12

There fore,

3/4 + 5/6 + 2 = 103/12

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