PRACTICE PROBLEMS WITH FRACTIONS

(1)  Find

(i)  -1/2 + 5/2

(ii) -1/4 + 3/4 - 2

(iii)  7/9 - 2/3

(2)  Find 

(i)  3/4 - 1  1/2

(ii)  1 2/3 + 3  1/4

(iii)  -2  1/4 + 3  1/8

(3)  The sum of 1/3 and 2/5

(4)  The difference between 1/4 and 2/3

(5)  The number 3 less than 2/3.

(6)  The number 2/3 more than 1  1/4.

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

(8)  What number is 3/4 less than -1  1/2 ?

(9)  Find the product of 2/7 x 1  2/5.

(10)  Find 1  1/3 ÷ 3  1/2

(11)  What number must be added to both numerator and denominator of the fraction 1/3 to get the fraction 7/8 ?

(12)  What number must be added to both numerator and denominator of the fraction 2/5 to get the fraction 7/8 ?

(13)  If a = -1, b = 4 and c = -6, find the value of (2b + 3c)/2a

Detailed answers

Question 1 :

(i)  -1/2 + 5/2

Solution :

Since the denominators are same, we can write one denominator commonly and simplify the numerator.

So, we get

=  (-1+5)/2

=  4/2

=  2

So, the answer is 2.

(ii) -1/4 + 3/4 - 2

Solution :

=  -1/4 + 3/4 - 2/1

=  (-1+3-8)/4

=  (-9+3)/4

=  -6/4

=  -3/2

So, the answer is -3/2

(iii)  7/9 - 2/3

Solution :

=  7/9 - 2/3

=  (7-6)/9

=  1/9

So, the answer is 1/9.

Question 2 :

(i)  3/4 - 1  1/2

Solution :

Changing the mixed fraction as improper fraction, we get

=  3/4 - 3/2

=  (3-6)/4

=   -3/4

(ii)  1 2/3 + 3  1/4

Solution :

Adding the whole part, we get

=  4  2/3 + 1/4

=  4  (8+3)/12

=  4  11/12

(iii)  -2  1/4 + 3  1/8

Solution :

By combing the whole parts, we get

=  (-2+3)   1/4 + 1/8

=  1  (2+1)/8

=  1  3/8

Question 3 :

The sum of 1/3 and 2/5

Solution :

=  1/3 + 2/5

=  (5+6)/15

=  11/15

Question 4 :

The difference between 1/4 and 2/3

Solution :

=  1/4 - 2/3

=  (3-8)/12

=  -5/12

Question 5 :

The number 3 less than 2/3.

Solution :

=  3-2/3

=  (9-2)/3

=  7/3

Question 6 :

The number 2/3 more than 1  1/4.

Solution :

=  2/3 + 1  1/4

Converting the mixed fraction as improper fraction, we get

=  2/3 + 5/4

=  (8+15)/12

=  23/12

=  1  11/12

So, the answer is 1  11/12.

Question 7 :

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

Solution :

=  1/5 + 2/3

=  (3+10)/15

=  13/15

Question 8 :

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

Solution :

=  3/4 - (-1  1/2)

=  3/4  +  1  1/2

=  3/4 + 3/2

=  (3+6)/4

=  9/4

=  2  1/4

So, the answer is 2  1/4.

Question 9 :

Find the product of 2/7 x 1  2/5.

Solution :

Converting the given mixed fraction as improper fraction, we get

  =  2/7 x 7/5

=  2/5

So, the answer is 2/5.

Question 10 :

Find 1  1/3 ÷ 3  1/2

Solution :

1  1/3 ÷ 3  1/2

Converting the mixed fraction into improper fraction, we get

=  4/3 ÷ 7/2

=  (4/3) ⋅ (2/7)

=  8/21

Question 11 :

What number must be added to both numerator and denominator of the fraction 1/3 to get the fraction 7/8 ?

Solution :

Let x be the number to be added in both numerator and denominator.

In the fraction (1/3), 1 should be added with x and 3 should also be added with x.

(1 + x)/(3 + x) = 7/8

Since we have fractions on both sides of the equal sign, we can do the cross multiplication.

8(1 + x) = 7(3 + x)

8 + 8x = 21 + 7x

Subtracting 7x and subtracting 8 on both sides, we get

8x - 7x = 21 - 8

x = 13

So, the required number to be added to both numerator and denominator is 13.

Question 12 :

What number must be added to both numerator and denominator of the fraction 2/5 to get the fraction 7/8 ?

Solution :

Let x be the number to be added in both numerator and denominator.

In the fraction (2/5), 2 should be added with x and 5 should also be added with x.

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

Since we have fractions on both sides of the equal sign, we can do the cross multiplication.

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

16 + 8x = 35 + 7x

Subtracting 7x and subtracting 16 on both sides, we get

8x - 7x = 35 - 16

x = 19

So, the required number to be added to both numerator and denominator is 19.

Question 13 :

If a = -1, b = 4 and c = -6, find the value of (2b + 3c)/2a

Solution :

Given that, a = -1, b = 4 and c = -6.

Applying all the values in the given expression, we get

= (2b + 3c)/2a

= [2(4) + 3(-6)]/2(-1)

= (8 - 18)/(-2)

= -10/(-2)

= 5

So, the answer is 5.

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