ADDING AND SUBTRACTING MIXED FRACTIONS

Adding and subtraction can be done in two different ways.

(i)  By regrouping method

(ii) Converting into improper fractions and simplify.

Regrouping Method

To see problems on converting into mixed fractions and simplify, click the link given below.

Adding and Subtracting Mixed Fractions with Unlike Denominators

Problem 3 :

4  1/3 + 2  1/6

Solution :

=  4 + 1/3 + 2 + 1/6

= (4 + 2) (1/3 + 1/6)

By taking the least common multiple, we get

= 6 + (2 + 1)/6

= 6 + 3/6

= 6 + 1/2

= 6  1/2

Problem 4 :

2  2/3  - 5  5/6

Solution :

= 2 + 2/3 - 5 - 5/6

= (2 - 5) + 2/3 - 5/6

= -3 + [(4 - 5)/6]

= -3 - 1/6

= -3  1/6

Problem 5 :

-2  1/4 + 3  1/8

Solution :

= -2 + 1/4 + 3 + 1/8

=(-2 + 3) (1/4 + 1/8)

By taking the least common multiple, we get

= 1 [1(2) + 1(1)]/8

= 1 (2 + 1)/8

= 1  3/8

Problem 6 :

4  1/5  - 2  1/6

Solution :

=  4 + 1/5 - 2 - 1/6

= (4 – 2) + (1/5 – 1/6)

By taking the least common multiple, we get

= 2 + [1(6) – 1(5)]/30

= 2 + (6 – 5)/30

= 2 + 1/30

= 2  1/30

Problem 7 :

2  1/3 + 1  1/6

Solution :

= 2 + 1/3 + 1 + 1/6

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

By taking the least common multiple, we get

= 3 + [1(2) + 1(1)]/6

= 3 + [(2 + 1)/6]

= 3 + 1/2

= 3  1/2

Problem 8 :

1  1/2 + 4  2/3

Solution :

= 1 + 1/2 + 4 + 2/3

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

By taking the least common multiple, we get

= 5 [1(3) + 2(2)]/6

= 5 (3 + 4)/6

= 5 + 7/6

= 5 + 1 + 1/6

= 6  1/6

Problem 9 :

3  1/3  - 1  1/2

Solution :

= 3 + 1/3  - 1 + 1/2

=  (3 - 1) + (1/3 – 1/2)

By taking the least common multiple, we get

= 2 + [1(2) – 1(3)]/6

= 2 + (2 – 3)/6

= 2 + (-1/6)

= 1 + 1 - 1/6

= 1 + 6/6 - 1/6

= 1 + 5/6

= 1 5/6

Problem 10 :

4  3/7  - 2  1/3

Solution :

= 4 + 3/7  - 2 + 1/3

= (4 – 2) + (3/7 – 1/3)

By taking the least common multiple, we get

= 2 + [3(3) – 1(7)]/21

= 2 + (9 – 7)/21

= 2 + 2/21

= 2  2/21