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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