ADDING AND SUBTRACTING MIXED FRACTIONS WORKSHEET

1. Add 3 1/5 and 4 4/5.

2. Subtract 3 1/5 from 4 4/5.

3. Add 2 1/5 and 1 3/4.

4. Subtract 1 2/3 from 1 10/11.

5. Add 1 10/11 and 1 2/3.

6. Add 2 3/4 and 1 1/5.

7.  Sheila had 8 yards of fabric. She used 2  1/4 yards to make a dress. How much fabric does she have left?

8.  Find the total perimeter (sum of the sides) of an equilateral triangle, (triangle with equal sides), if each side measures 2  1/4 inches.

9.  Calculate the area and perimeter of a rectangle of length 4  2/5 cm and width 2  1/4 cm.

10.  A father leaves his money to his four children. The first received 1/3 , the second received 1/6, and the third received 2/5. How much did the remaining child receive?

1. Answer :

3 1/5 + 4 4/5

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

2. Answer :

4 4/5 - 3 1/5

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

3. Answer :

2 1/5 + 1 3/4

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

4. Answer :

1 10/11 - 1 2/3

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

5. Answer :

1 10/11 + 1 2/3

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

6. Answer :

2 3/4 + 1 1/5

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

7. Answer :

Quantity of fabric she has = 8 yards

Quantity of fabric used = 2   1/4 yards

Quantity of fabric left = 8 - 2  1/4

= 7 + 1 - 2 - 1/4

= (7 - 2) + (1 - 1/4)

= 5 + 3/4

= 5  3/4

Quantity of fabric left is 5  3/4 yards.

8. Answer :

Side length of equilateral triangle = 2  1/4 inches

Converting into improper fraction, we get

= 9/4

Perimeter of equilateral triangle = 3(side length)

= 3(9/4)

= 27/4

Converting into mixed fraction, we get

= 6 3/4 inches

So, the perimeter of equilateral triangle is 6  3/4 inches.

9. Answer :

Lenght = 4  2/5 cm

Width = 2  1/4 cm

Perimeter of rectangle = 2(length + width)

= 2 (4  2/5 + 2  1/4)

= 2(6 + 2/5 + 1/4)

= 2(6 + 13/20)

= 2 (120 + 13)/20

= 133/10

= 13  3/10 inches

So, the perimeter of the rectangle is 13  3/10 inches.

10. Answer :

Number of children to be shared = 4

Amount recieved by the first = 1/3

Amount recieved by the second = 1/6

Amount recieved by third = 2/5

Remaining amount = 1 - (1/3 + 1/6 + 2/5)

= 1 - (10+5+12)/30

= 1 - 27/30

= 1 - 9/10

= 1/10

So, the remaining amount is 1/10 part of money.

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