Fraction - Techniques with Practice Questions

# Types

• Proper
• Improper
• Mixed Fraction

I. Proper Fraction: [when numerator < denominator ]

Eg. ⁴/₅ , ⁶/8 , ⁹/₇ 

II. Improper Fraction : [when numerator > denominator ]

Eg. ⁴/₂ , ⁵/₃ , ⁶/₂ 

III. Mixed Fraction :

• Mixed with Proper Fraction
• Mixed with Improper fraction

a) Mixed with Proper Fraction: When a proper fraction is mixed with a whole number known as mixed with proper fraction.

Eg. 5²/₃ , 6³/₄ , 7¹/₄ 

b) Mixed with Improper Fraction: When a proper fraction is mixed with a whole number known as mixed with Improper fraction.

Eg. 2³/_{2 ,} 4⁴/_{1 ,} 6⁶/₁ 

# Rules

I. 4 + ³/₈ = 4 ³/₈

II. 4+⁸/₃= 4 + 2²/₃
= 6²/₃
III. 4-³/₈=3+(1-³/₈)=3+⁵/₈=3⁵/₈

Q1. Arrange the fractions a=³/5 , b=⁴/7 , c=⁸/9 and d=⁹/11 in their descending order.

a) a,b,c,d

b)c,d,a,c 

b) a,d,c,a,b

d) c,d,a,b

e) None of these

Q2.[ 0.00625 of 23/5 ], when expressed as a vulgar, fraction, equals:

a)23/80 b) 23/8000 c) 23/800 d) 125/23 e) None of these

a)5/6 b) 5/9 c) 15/18 d) 3/18 e) None of these

Q4.If 47.2506 = 4A +7/B+2C +5/D+6E, then the value of 5A + 3B + 6C + D + 3E is:

a) 153.6003 b)53.6003 c) 53.603 d) None of these e) 213.0003

Q5.4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.What is half of that number?

a)215 b) 315 c) 305 d) 325 e)None of these

Q6. Find the value of ¹/_{2 x 3} + ¹/_{3 x 4} + ¹/_{4 x 5} + ¹/_{5 x 6} +............+ ¹/_{9 x 10}

a)⁴/₁₀ b) ²/10  c) ²/5 d) ⁴/₅ e) None of these

Solution

(1)
Sol: Option d
Clearly ³/5=0.6, ⁴/7 = 0.571 , ⁸/9 = 0.88, ⁹/11= 0.818
Now, 0.88 > 0.818 > 0.6 > 0.571

(2)
Sol: Option c
[0.000625 of ²³/5]=[⁶²⁵/100000 * ²³/5]=²³/800

(3)
Sol: Option (a)

(4)
Sol: Option (a)
4A +⁷/B + 2C +⁵/D +6E = 47.2506
4A +⁷/B + ²/C +⁵/D +6E = 40+7+0.2+0.05+0.0006
Comparing the terms on both sides, we get
  4A=40, ⁷/B =7, 2C = 0.2, ⁵/D=0.05, 6E=0.0006
or
a=10, B=1, C=0.1, D = 100, E = 0.0001
5A+3B+6C+D+3E
=(5810)+(3*1)+(6*0.1)+100+(3*0.0001)
=50+3+0.6+100+0.0003=153.6003

(5)
Sol: Option B
Let the number be x. Then,
⁴/₁₅ of ⁵/₇ of x - ⁴/₉ of ²/₅ of x = 8
⁴/₂₁x-⁸/₄₅x=8
[⁴/₂₁-⁸/₄₅]x=8
[^60-56/₃₁₅]x=8
⁴/₃₁₅x=8
x=[^8*315/₄]=630
¹/₂ x = 315

(6)
Sol: Option C
Given expression [¹/₂-¹/₃]+[¹/3-¹/4]+[¹/4-¹/5]+[¹/5-¹/6]+.....................+[¹/9-¹/10]

=[¹/2-¹/10]

=4/10

=2/5