# 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,

## 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.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6