WORD PROBLEMS INVOLVING OPERATIONS ON FRACTIONS

Problem 1:

Find the sum of 2/3 and 3/4.

Solution:

= 2/3 + 3/4

LCM of 3, 4 is 12.

= (8 + 9) / 12

= 17/12

= 1  5/12

Problem 2:

Find 7/12 of my investment of $180000.

Solution:

= 7/12 × 180000

= $105000

Problem 3:

What number must 3/4 be multiplied by to get an answer of 15?

Solution:

Let x be a number.

x × 3/4 = 15

x = 15 × 4/3

x = 20

Problem 4:

By how much does 4/5 exceed 7/12?

Solution:

x + 7/12 = 4/5

x = 4/5 - 7/12

x = (48 - 35) / 60

x = 13/60

Problem 5:

In a pig pen containing 36 piglets, 16 are female. What fraction are male?

Solution:

Total pig pen = 36

Female pig = 16

Male pig = (36 - 16) / 36

= 20/36

= 5/9

Problem 6:

Which is the better score in a mathematics test, 17 out of 20 or 21 out of 25?

Solution:

17 out of 20:

= 17/20 × 100

 = 85%

21 out of 25:

= 21/25 × 100

 = 84%

So, 17 out of 20 is the best score in mathematics.

Problem 7:

Find 2/5 of $245.

Solution:

= 2/5 × 245

= 49 × 2

= $98

Problem 8:

How many 2 1/3 m lengths of rope can be cut from a rope of length 21m?

Solution:

Total length of rope = 21m

Length of one rope piece = 2 1/3m = 7/3 m

Number of pieces of rope = 21 / (7/3)

= 9 lengths

Problem 9:

Five pieces of material are required to make some curtains, each of length 3 3/4 m. find the total length required.

Solution:

Total pieces = 5

Length of one pieces = 3 3/4m = 15/4m

Total length = 5 × 15/4

= 75/4

Total length = 18 3/4 m

Problem 10:

On consecutive days you eat 1/3, 1/4 and 1/5 of a lasagne.

a. What fraction has been eaten?

b. What fraction remains?

Solution:

a.

= 1/3 + 1/4 + 1/5

LCM of 3, 4 and 5 is 60.

= (20 + 15 + 12) / 60

= 47/60

b.

Remaining lasagne = 1 - 47/60

= 13/60