PROBLEMS ON FUNDAMENTAL OPERATIONS WITH FRACTIONS

Problem 1 :

Find the sum of 1/3 and 2/5

Solution :

Given, 1/3 + 2/5

In the given, denominators are not equal.

So we take LCM of 3 and 5 is 15

1/3 + 2/5  =  [(1×5)/15] + [(2×3)/15]

1/3 + 2/5  =  (5+6)/15

=  11/15

So, the answer is 11/15

Problem 2 :

Find the difference between 1/4 and 2/3

Solution :

Equivalent fraction of 1/4 is 3/12

Equivalent fraction of 2/3 is 8/12

Difference between 8/12 and 3/12

=  8/12 - (3/12)

=  5/12

So, the answer is 5/12.

Problem 3 :

Find the number 3 less than 2/3

Solution :

Let x be the number.

Given, x  =  2/3 – 3

Since the denominators are not same, we take least common multiple.

x  =  2/3 – 9/3

x  =  - 7/3

By converting the improper fraction to mixed fraction, we get

x  =  -2  1/3

Problem 4 :

Find the number 2/3 more than 1 1/4

Solution  :

Let x be the number.

Given, x  =  1 1/4 + 2/3

First, we write 1 1/4  =  5/4

Then, x  =  5/4 + 2/3

Least common multiple of 4 and 3 is 12.

x  =  [(5×3)/12] + [(2×4)/12]

x  =  (15+8)/12

x  =  23/12

By changing it as mixed fraction, we get

x  =  1  11/12

Problem 5 :

What must 1/5 be increased by to get 2/3 ?

Solution :

Let x be the unknown,

x+(1/5)  =  2/3

x  =  (2/3) – (1/5)

The least common multiple of 3 and 5 is 15.

2/3 – 1/5  =  [(2×5)/15] – [(1×3)/15]

=  (10–3)/15

=  7/15

So, the answer is 7/15

Problem 6 :

What number is 3/4 less than – 1  1/2 ?

Solution :

Let x be the number.

-1  1/2  =  -3/2

=  (-3/2) - (3/4)

=  (-6-3)/4

=  -9/4

By converting the improper fraction in to mixed fraction, we get

x  =  -2   1/4

Problem 7 :

Find the average of 1/4  and 3/4

Solution :

Given, 1/4 + 3/4

We know that,

Average  =  Sum of all terms/Number of terms

Average  =  (1/4 + 3/4)/2

=  (4/4)/2

=  1/2

So, the answer is 1/2

Problem 8 :

Find the number midway between – 1/2 and 2/3

Solution :

Let x be the number.

Given, x  =   - 1/2 + 2/3

We Know that,

Middle number  =  sum of term/2

=  (-1/2 + 2/3)/2

=  [(- 3+4)/6]/2

=  1/6 × 1/2

=  1/12

So, the number is 1/12

Problem 9 :

Find the average of 1/2, 2/3 and 3/4

Solution :

Given, 1/2 + 2/3 + 3/4

We know that,

Average  =  Sum of all terms / Number of terms

Average  =  (1/2 + 2/3 + 3/4)/3

=  [(6 + 8 + 9)/12]/3

=  (23/12)/3

=  (23/12) × (1/3)

=  23/36

So, the average is 23/36

Problem 10 :

Find the quotient of 1/3 and 3/4

Solution :

Given, 1/3 ÷ 3/4

=  1/3 × 4/3  (the reciprocal of 3/4)

=  4/9

So, the answer is 4/9

Problem 10 :

An empty box weights 2  1/4 pounds. It is then filled with 16  2/3 pounds of fruit. What is the weight of the box when it is full ?

Solution :

Weight of empty box = 2  1/4 pounds

Weight of fruit = 16  2/3 pounds

weight of box with fruit = 2  1/4 + 16  2/3

= (2 + 16) + (1/4 + 2/3)

= 18 + (3 + 8)/12

= 18 + 11/12

= 18   11/12

Problem 11 :

Yanni is making formula for the baby. Each bottle contains 6  2/5 scoops of formula. The formula container holds 320 scoops of formula. How many bottles of formula can Yanni make?

Solution :

Quantity of formula each bottle contains = 6  2/5

Number of containers = 320 scoops of formula

Number of bottles = 320/(6  2/5)

= 320/(32/5)

= 320 x (5/32)

= 10 x 5

= 50

So, number of bottles is 50.

Problem 12 :

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

= 9/4 + 6/5 + 2

LCM = 20

= (45/20) + (24/20) + (40/20)

= (45 + 24 + 40)/20

= 109/20

= 5  9/20

Problem 13 :

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

Solution :

Quantity of fabric she has = 8 yards

Quantity of material used = 2  1/4 yards

Quantity of left = 8 - 2  1/4

= 8 - 9/4

= (32 - 9)/4

= 23/4

Problem 14 :

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? (Hint: You can think of father’s money as one whole.)

Solution :

Amount received by the first child = 1/3

Amount received by the second child = 1/6

Amount received by the third child = 2/5

Amount left for the remaining child

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

LCM (3, 6 and 5) = 30

= 1 - [10/30 + 5/30 + 12/30]

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

= 1 - 27/30

= 1 - 9/10

= 1/10

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