ADDING AND SUBTRACTING MIXED FRACTIONS WORKSHEET

Adding and Subtracting Mixed Fractions Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on adding and subtracting mixed fractions. 

Before look at the worksheet, if you would like ton learn, how to add and subtract mixed fractions, 

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Adding and Subtracting Mixed Fractions Worksheet - Problems

Problem 1 : 

Find the value of : 

Problem 2 : 

Find the value of : 

Problem 3 : 

Find the value of : 

Problem 4 : 

Find the value of : 

Problem 5 : 

Find the value of : 

Problem 6 : 

Find the value of : 

Adding and Subtracting Mixed Fractions Worksheet - Solutions

Problem 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

Problem 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

Problem 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. 

Problem 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

Problem 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. 

Problem 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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