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

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