# Fraction - Techniques with Practice Questions

• Proper
• Improper
• Mixed Fraction
I. Proper Fraction: [when numerator < denominator ]

Eg. 4/5 , 6/8 , 9/

II. Improper Fraction : [when numerator > denominator ]

Eg. 4/2 , 5/3 , 6/

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/

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/

#### # 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 