ADDING AND SUBTRACTING MIXED FRACTIONS

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, use 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

Example 7 :

Shannon needs 2  2/5 yards of the solid fabric for the bedspread and 2 7/8 yards of the solid fabric for the curtains. How much solid fabric does Shannon need for this project? 

Solution :

Quantity of fabric needed for bedspread = 2  2/5 yards

Quantity of fabric needed for curtains = 2  7/8 yards

Total quantity of fabric = 2  2/5 + 2  7/8

Adding the whole number and adding the fractions separately.

= (2 + 2) + (2/5 + 7/8)

= 4 + (16 + 35)/40

= 4 + 51/40

= 4 + 1 + 11/40

= 5  11/40

So, the required quantity of fabrics is 5  11/40 yards.

Example 8 :

Shannon needs a total of 6 yards of lining fabric for the curtains. She already has 2 7/12 yards of lining fabric. How much more lining fabric does she need?

Solution :

Let x be the required quantity of fabric.

x + 2  7/12 = 6

x + (24 + 7)/12 = 6

x + 31/12 = 6

x = 6 - (31/12)

x = (72 - 31)/12

x = 41/12

x = 3  5/12 yards

So, the required quantity is 3  5/12 yards.

Example 9 :

Miguel bought 2  1/4 pounds of hamburger, 1  1/5 pounds of sliced turkey, and 2 pounds of cheese. What was the total weight of all of his purchases?

Solution :

Quantity of hamburger = 2  1/4 pounds

Quantity of sliced turkey = 1  1/5 pounds

Quantity of cheese = 2 pounds

Total weight = 2  1/4 + 1  1/5 + 2

= (2 + 1 + 2) + 1/4 + 1/5

= 5 + 9/20

= 5  9/20

So, the total weight is 5  9/20 pounds.

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