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

Problem 11 :

A gingerbread cookie recipe calls for 3/4 cup of sugar, 2 cups of flour, 1/3 cup of dark molasses, 1/2 cup of water and 2/3 cup of shortening. Determine the combined amount, in cups, of these ingredients.

Express your answer as a mixed number.

Solution :

Quantity of sugar = 3/4 cups

Quantity of flour = 2 cups

Quantity of dark molasses = 1/3 cups

Quantity of water = 1/2 cups

Quantity of shortening = 2/3 cups

Quantity of these ingredients = 3/4 + 2 + 1/3 + 1/2 + 2/3

LCM of (2, 3, 4) = 12

= 2 + (9 + 4 + 6 + 8) / 12

= 2 + 27/12

= (24 + 27)/12

= 51/12

= 4  3/4 cups

Problem 12 :

On a steel-string acoustic guitar, the material that supports the strings at the end closest to the headstock is called the nut. The width of the nut typically ranges between 11 1/16 inches and 1  3/4 inches. Determine the difference between these two nut widths.

Solution :

The width of the nut typically ranges between 11 1/16 inches and 1  3/4 inches

Difference = 11 1/16 - 1  3/4

= (11 - 3) + (1/16 - 3/4)

= 8 + (1 - 12)/16

= 8 + (-11/16)

= 7 + 1 - 11/16

= 7 + (16 - 11)/16

= 7  5/16 

So, the required difference is 7  5/16 inches.