ADDING AND SUBTRACTING MIXED FRACTIONS

Adding and Subtracting Mixed Fractions :

In this section, you will learn, how to add and subtract mixed fractions.

Adding and Subtracting Mixed Fractions - Steps

Step 1 :

To add and subtract mixed fractions, first we have to convert the mixed fractions into improper fraction. 

Step 2 :

After converting the mixed fraction into an improper fraction, if the denominators are same, we have to take the denominator once and combine the numerators.

If the denominators are not same, we have to use the method of LCM to add or subtract the two fractions. 

Step 3 : 

If the result of step 3 is an improper fraction, then convert it into a mixed fraction. 

Adding and Subtracting Mixed Fractions - Examples

Example 1 : 

Find the value of : 

Solution : 

Convert the mixed fractions into improper fractions. 

3 1/5  =  16/5

4 4/5  =  24/5

Now, we have

3 1/5 + 4 4/5  =  16/5 + 24/5

The fractions 16/5 and 24/5 have the same denominator. That is 5. 

So, take the denominator once and combine the numerators. 

3 1/5 + 4 4/5  =  (16 + 24)/5

3 1/5 + 4 4/5  =  40/5

3 1/5 + 4 4/5  =  8

Example 2 : 

Find the value of : 

Solution : 

Convert the mixed fractions into improper fractions. 

4 4/5  =  24/5

3 1/5  =  16/5

Now, we have

4 4/5 - 3 1/5  =  24/5 - 16/5

The fractions 24/5 and 16/5 have the same denominator. That is 5. 

So, take the denominator once and combine the numerators. 

4 4/5 - 3 1/5  =  (24 - 16)/5

4 4/5 - 3 1/5  =  8/5

4 4/5 - 3 1/5  =  1 3/5

Example 3 :

Find the value of :

Solution :

Convert the mixed fractions into improper fractions. 

2 1/5  =  11/5

1 3/4  =  7/4

Because the denominators of the fractions 11/5 and 7/4 are not same, make the denominators same using LCM of (5, 4). 

LCM of (5, 4)  =  20

To make the denominator as 20, we have to multiply both numerator and denominator of the first fraction by 4 and the second fraction by 5.

11 / 5  =  (11 ⋅ 4) / (5 ⋅ 4)  =  44 / 20

7 / 4  =  (7 ⋅ 5) / (4 ⋅ 5)  =  35 / 20

Now , we have 

2 1/5 + 1 3/4  =  11/5 + 7/4

2 1/5 + 1 3/4  =  44/20 + 35/20

2 1/5 + 1 3/4  =  (44 + 35)/20

2 1/5 + 1 3/4  =  79/20

79/20 is an improper fraction and it can be converted into a mixed fraction as shown below. 

Example 4 :

Find the value of :

Solution :

Convert the mixed fractions into improper fractions. 

1 10/11  = 21/11

1 1/3  =  4/3

Because the denominators of the fractions 21/5 and 4/3 are not same, make the denominators same using LCM of (11, 3). 

LCM of (11, 3)  =  33

To make the denominator as 33, we have to multiply both numerator and denominator of the first fraction by 3 and the second fraction by 11.

21 / 11  =  (21 ⋅ 3) / (11 ⋅ 3)  =  63 / 33

4 / 3  =  (4 ⋅ 11) / (3 ⋅ 11)  =  44 / 33

Now , we have 

1 10/11 - 1 1/3  =  21/11 - 4/3

1 10/11 - 1 1/3  =  63/33 - 44/33

1 10/11 - 1 1/3  =  (63 - 44) / 33

1 10/11 - 1 1/3  =  19 / 33

Example 5 :

Find the value of :

Solution :

Convert the mixed fractions into improper fractions. 

1 10/11  = 21/11

1 1/3  =  4/3

Because the denominators of the fractions 21/5 and 4/3 are not same, make the denominators same using LCM of (11, 3). 

LCM of (11, 3)  =  33

To make the denominator as 33, we have to multiply both numerator and denominator of the first fraction by 3 and the second fraction by 11.

21 / 11  =  (21 ⋅ 3) / (11 ⋅ 3)  =  63 / 33

4 / 3  =  (4 ⋅ 11) / (3 ⋅ 11)  =  44 / 33

Now , we have 

1 10/11 + 1 1/3  =  21/11 + 4/3

1 10/11 + 1 1/3  =  63/33 + 44/33

1 10/11 + 1 1/3  =  (63 + 44) / 33

1 10/11 + 1 1/3  =  107 / 33

107/33 is an improper fraction and it can be converted into a mixed fraction as shown below. 

Example 6 :

Find the value of :

Solution :

Convert the mixed fractions into improper fractions. 

2 3/4  =  11/4

1 1/5  =  6/5

Because the denominators of the fractions 11/4 and 6/5 are not same, make the denominators same using LCM of (4, 5). 

LCM of (4, 5)  =  20

To make the denominator as 20, we have to multiply both numerator and denominator of the first fraction by 5 and the second fraction by 4.

11 / 4  =  (11 ⋅ 5) / (4 ⋅ 5)  =  55 / 20

6 / 5  =  (6 ⋅ 4) / (5 ⋅ 4)  =  24 / 20

Now , we have 

2 3/4 + 1 1/5  =  11/4 + 6/5

2 3/4 + 1 1/5  =  55/20 + 24/20

2 3/4 + 1 1/5  =  (55 + 24) / 20

2 3/4 + 1 1/5  =  79 / 20

79/20 is an improper fraction and it can be converted into a mixed fraction as shown below. 

After having gone through the stuff given above, we hope that the students would have understood, how to add and subtract mixed fractions. 

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