How to add Mixed Fractions?

In this article, we space going to learn on exactly how to add of mixed fractions or blended numbers. There are two approaches to add the blended fractions.

You are watching: Two mixed numbers with a sum of 3

Method 1

In this method, whole numbers independently added. The fractional components are also included separately. If the fractions have different denominators, then uncover their L.C.M. And change the fractions into like fractions. The sum of whole numbers and fractions is climate calculated.

Example 1

Add: 2 3/5 + 1 3/10

Solution

2 3/5 + 1 3/10 = (2 + 1) + (3/5 + 3/10)

= 3 + (3/5 + 3/10)

The L.C.M. The 5 and 10 = 10

= 3 + (3 × 2/5 × 5 + 3 × 1/10 × 1,

= 3 + 6/10 + 3/10

= 3 + 9/10

= 3 9/10

 

Example 2

Add the following portion together: 1 1/6, 2 1/8 and 3 ¼

Solution

1 1/6 + 2 1/8 + 3 ¼

= (1 + 2 + 3) + (1/6 + 1/8 + ¼)

= 6 + 1/6 + 1/8 + ¼

L.C.M that 6, 8 and 4 = 24

= 6 + 1 × 4/6 × 4 + 1 × 3/8 × 3 + 1 × 6 /4 × 6

= 6 + 4/24 + 3/24 + 6/24

= 6 + (4 + 3 + 6)/24

= 6 + 13/24

= 6 13/24

 

Example 3

Add these fractions together: 5 1/9, 2 1/ 12 and ¾

Solution

5 1/9, 2 1/ 12 and ¾

= (5 + 2 +0) + (1/9 + 1/12 + ¾)

= 7 + 1/9 + 1/12 + ¾

L.C.M = 36

= 7 + 1 × 4/9 × 4 + 1 × 3/12 × 3 + 3 × 9/4 × 9

= 7 + 4/36 + 3/36 + 27/36

= 7 + (4 + 3 + 27)/36

= 7 + 34/36

= 7 + 17/18,

= 7 17/18.

 

Example 4

Solve:

5/6 + 2 ½ + 3 ¼

Solution

5/6 + 2 ½ + 3 ¼

= (0 + 2 + 3) + (5/6 + ½ + ¼)

= 5 + 5/6 + ½ + ¼

Since the L.C.M =12

= 5 + 5 × 2/6 × 2 + 1 × 6/2 × 6 + 1 × 3/4 × 3

= 5 + 10/12 + 6/12 + 3/12

= 5 + (10 + 6 +3)/12

= 5 + 19/12

The portion 19/12 deserve to be converted right into a combined fraction.

= 5 + 17/12

= (5 + 1)+ 7/12

= 6 7/12

 

Method 2

In the second method, the adhering to steps space followed:

Convert the mixed number into improper fraction.Find the L.C.M and also convert the fractions right into like fractions.Find the amount of the fractions and express the last answer in its easiest form.

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Example 5

Add: 2 3/5 + 1 3/10

Solution

2 3/5 = (5 × 2) + 3/5=13/5

1 3/10 = (1 x 10) + 3 = 13/10

= 13/5 + 13/10

L.C.M = 10

= 13 × 2/5 × 2 + 13 × 1/10 × 1

= 26/10 + 13/10

= 26 + 13/10

= 39/10

= 3 9/10

 

Example 6

Work out: 2 3/9 + 1 1/6 + 2 2/3

Solution

2 3/9 + 1 1/6 + 2 2/3

= (9 × 2) + 3/9 + (6 × 1) + 1/6 + (3 × 2) + 2/3

L.C.M of 9, 6 and 3 is 18, therefore,

= 21/9 + 7/6 + 8/3

= 21 × 2/9 × 2 + 7 × 3/6 × 3 + 8 × 6/3 × 6

= 42/18 + 21/18 + 48/18

= 42 + 21 + 48/18

= 111/18

= 37/6

= 6 1/6

 

Example 7

Work out: 2 ½ + 3 1/3 + 4 ¼

Solution

2 ½ + 3 1/3 + 4 ¼

= (2 × 2) + 1}/2 + (3 × 3) + 1/3 + (4 × 4) + 1/4

L.C.M. The 2, 3 and also 4 is 12

= 5/2 + 10/3 + 17/4,

= 5 × 6/2 × 6 + 10 × 4/3 × 4 + 17 × 3/4 × 3

= 30/12 + 40/12 + 51/12

= 30 + 40 + 51/12

= 121/12

= 10 1/12

 

How to add mixed numbers through unlike denominators?

Let’s find out this scenario through the aid of examples.