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To help you out we have covered every minute detail in the Worksheet for Subtraction of Rational Numbers and you can get a good hold of the concepts. The Questions over here include Subtracting Rational Numbers with both the Same and Different Denominators.

1. Evaluate each of the following

(i) 2/4 – 3/2

(ii) -4/5 – 2/(-3)

(iii) 7/3 – (-5)/(-7)

**Solution:**

(i) 2/4 – 3/2

Since the Denominators aren’t the same firstly find the LCM to rewrite them into Equivalent Rational Numbers

LCM(4, 2) = 4

Rewriting the Rational Numbers as Equivalent Rational Numbers using the LCM obtained.

2/4 = 2*1/4*1 = 2/4

3/2 =3*2/2*2 = 6/4

2/4-6/4 = (2-6)/4

= -4/4

= -1/1

(ii) -4/5 – 2/(-3)

Rearrange the Rational Numbers to obtain the positive denominator.

2/-3 = 2*(-1)/-3*(-1) = -2/3

Since the Denominators aren’t the same firstly find the LCM to rewrite them into Equivalent Rational Numbers.

LCM(5,3) = 15

-4/5 = -4*3/5*3 = -12/15

(-2/3) = -2*5/3*5 = -10/15

= -12/15-(-10/15)

= 2/15

(iii) 7/3 – (-5)/(-7)

(-5)/(-7) = 5/7

LCM(3, 7) = 21

7/3 = 7*7/3*7 = 49/ 21

5/7 = 5*3/7*3 = 35/21

= 49/21-35/21

= 14/21

= 2/3

2. Subtract the first rational number from the second one in the following

(i) 3/8, 6/8

(ii) -5/9, 3/9

(iii) -2/10, -9/10

(iv) 11/15, -4/15

**Solution:**

(i) 6/8 – 3/8 = 3/8

(ii) 3/9 -(-5/9) = 8/9

(iii) -9/10-(-2/10) = -7/10

(iv) -4/15-11/15 = -15/15 = -1

3. The Sum of Two Numbers is 4/9. If one of it is 1/3 find the other.

**Solution:**

Let the number to be found as x

From the given data we get the equation as follows

x+1/3 = 4/9

x = 4/9 – 1/3

= (4-3)/9

= 1/9

1/9 should be added to 1/3 to get the resultant sum 4/9.

4. What number should be subtracted from 4/7 to get 5/4?

**Solution:**

From the given at we have

4/7 – x = 5/4

x= 4/7-5/4

= (16-35)/28

= -19/28

-19/28 should be subtracted from 4/7 to get 5/4.

5. Simplify (8/5 -1/5) – 2/5?

**Solution:**

Given (8/5 -1/5) – 2/5

= 7/5 – 2/5

= 5/5

= 1

6. Simplify the following and write your answer as a proper fraction or as a whole or mixed number?

12/5 – 4/5

**Solution:**

Since the Denominators are the Same we can write the expression with a common denominator and then combine the numerators

= (12-4)/5

= 8/5

7. Simplify the following and write your answer as a proper fraction or as a whole or mixed number?

5/4 – 3/5

**Solution:**

Since the Denominators aren’t the same find the LCM of Denominators of given rational numbers.

LCM(4, 5) = 20

Writing the given Rational Numbers as Equivalent Rational Numbers

5/4 = 5*5/4*5 = 25/20

3/5 = 3*4/5*4 = 12/20

= 25/20 -12/20

= 13/20

8. Fill in the Blanks

(i) -3/11 – (-4)/11 = ……

(ii) (-7)/13 + …… = -1

**Solution:**

(i) -3/11 – (-4)/11

= -3/11 – (-4)/11

= -3/11+4/11

= 1/11

(ii) (-7)/13 + …… = -1

Consider the number to be found as x

-7/13+x = -1

x = -1-(-7/13)

= -1+7/13

= (-13+7)/13

= -6/13