ADDING AND SUBTRACTING MIXED FRACTIONS

We can add or subtract mixed fractions using the steps explained below.

Step 1 :

To add and subtract mixed fractions, first convert the mixed fractions to improper fractions.

Step 2 :

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

If the denominators are different, we can make the denominators same using least common multiple.

Step 3 :

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

Example 1 :

Add 3 1/5 and 4 4/5.

Solution :

Convert the mixed fractions to improper fractions.

3 1/5 = 16/5

4 4/5 = 24/5

3 1/5 + 4 4/5 :

= 16/5 + 24/5

The fractions 16/5 and 24/5 have the same denominator. So, take the denominator once and combine the numerators.

= (16 + 24)/5

= 40/5

= 8

Example 2 :

Subtract 3 1/5 from 4 4/5.

Solution :

Convert the mixed fractions to improper fractions.

4 4/5 = 24/5

3 1/5 = 16/5

4 4/5 - 3 1/5 :

= 24/5 - 16/5

= (24 - 16)/5

= 8/5

= 1 3/5

Example 3 :

Add 2 1/5 and 1 3/4.

Solution :

Convert the mixed fractions to improper fractions.

2 1/5 = 11/5

1 3/4 = 7/4

The denominators of the fractions 11/5 and 7/4 are different.

Least common multiple of (5, 4) = 20.

To make the denominator as 20, 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

2 1/5 + 1 3/4 :

= 11/5 + 7/4

= 44/20 + 35/20

= (44 + 35)/20

= 79/20

= 3 19/20

Example 4 :

Subtract 1 2/3 from 1 10/11.

Solution :

Convert the mixed fractions into improper fractions.

1 10/11 = 21/11

1 2/3 = 5/3

The denominators of the fractions 21/11 and 5/3 are different.

Least common multiple of (11, 3) = 33

To make the denominator as 33, 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

5/3 = (5 ⋅ 11)/(3 ⋅ 11) = 55/33

1 10/11 - 1 2/3 :

= 21/11 - 5/3

= 63/33 - 55/33

= (63 - 55)/33

= 8/33

Example 5 :

Add 1 10/11 and 1 2/3.

Solution :

Convert the mixed fractions into improper fractions.

1 10/11 = 21/11

1 2/3 = 5/3

The denominators of the fractions 21/11 and 5/3 are different.

Least common multiple of (11, 3) = 33

To make the denominator as 33, 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

5/3 = (5 ⋅ 11)/(3 ⋅ 11) = 55/33

1 10/11 + 1 2/3 :

= 21/11 + 5/3

= 63/33 + 55/33

= (63 + 55)/33

= 118/33

= 3 19/33

Example 6 :

Add 2 3/4 and 1 1/5.

Solution :

Convert the mixed fractions into improper fractions.

2 3/4 = 11/4

1 1/5 = 6/5

The denominators of the fractions 11/4 and 6/5 are different.

Least common multiple of (4, 5) = 20

To make the denominator as 20, 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

2 3/4 + 1 1/5 :

= 11/4 + 6/5

= 55/20 + 24/20

= (55 + 24)/20

= 79/20

= 3 19/20

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