Simple or Vulgar Fraction
A number expressed with numerator and denominator. Say I have 3 of 10 apples then I will express it as 3/10. The total is written below a horizontal or diagonal line, and the number of parts comprising the fraction (numerator) is written above. Such fractions are called vulgar fractions or simple fractions. Eg:[ 3/4 ]
Decimal Fraction
Expressing the fraction in decimal values (denominator a power of 10) is called decimal fraction. 1/2 is expressed as 0.5 in decimal fraction. Eg:[ 0.45773 ]
Converting a decimal to vulgar fraction:
Step 1: Calculate the total numbers after decimal point.
Step 2: Remove the decimal point from the number.
Step 3: Put 1 under the denominator and annex it with "0" as many as the total in step a.
Step 4: Reduce the fraction to its lowest terms.
Example: Consider 0.44
Example: Consider 0.44
Step 1: Total number after decimal point is 2
Step 2 and 3: 44/100
Step 4: Reducing it to lowest terms : 44/100 = 22/50 = 11/25
Converting a recurring decimal to vulgar fraction
A decimal with recurring value is called recurring decimal.
E.g: 2/9 will give 0.22222222...... where 2 is recurring number.
E.g: 2/9 will give 0.22222222...... where 2 is recurring number.
Method:
Step 1: Separate the recurring number from the decimal fraction.
Step 2: Annex denominator with "9" as many times as the length of the recurring number.
Step 3: Reduce the fraction to its lowest terms.
Example: Consider 0.2323232323
Step 1: The recurring number is 23
Step 2: 23/99 [the number 23 is of length 2 so we have added two nines]
Step 3: Reducing it to lowest terms : 23/99 [it can not be reduced further].
Mixed Recurring to Fractions:
If N= 0.abcbcbc…. Then N = abc - a / 990 = Repeated & non-repeated digits - Non repeated digits / As many 9's as repeated digits followed by as many zero as non - repeated digits
Eg: 0.25757..... = 257 - 2 / 990 = 255 / 990 = 17 / 60.
1. 20.05 + 35.603- …… =43.087
a. 10.263
b. 12.566
c. 15.426
d. 13.286
2. Which of the following fraction is smallest?
a. 23
28
b. 14
15
c. 15
19
d. 21
24
3. 0.585858 is equivalent to the fraction….
a. 58
100
b. 58
99
c. 85
100
d. 85
99
4. The value of 
is
is
a. 47
198
b. 3 4/198
c. 48
98
d. 58
36
5. 0.9*0.007= _________
a. 0.063
b. 0.0063
c.0.63
d. 0.00063
6. 0.0015÷ ? = 0.003
a. 0.05
b. 0.005
c. 0.5
d. 5
7. 0.363*0.522+0.363*0.478 = ?
a.0.522
b. 0.845
c. 0.363
d. 0.985
8. If 7125¸1.25= 5700< the value of 712.5÷12.5 is:
a. 5.7
b. 57
c. 570
d. .57
9. The value of 34.31*0.473*1.567 is close to
0.0673*23.25*7.57
a. 2.0
b. 1.15
c. 2.05
d. 2.15
10. Evaluate (5.68)2 – (4.32)2
5.68- 4.32
a. 8
b. 9
c. 10
d. 12
11. Evaluate 4.3*4.3*4.3+1
4.3*4.3-4.3+1
a. 14.3
b. 52.3
c. 5.3
d. 42.3
13. If 5.51*10k = 0.0551, then the value of k is:
a. –4
b. –3
c. –2
d. –1
14. 25.25 is equal to:
2000
a. 1.012526
b. 0.012625
c. 0.12526
d. 0.12625
15. The value of (2.502+0.064)2 - (2.502-0.064)2
2.502*0.064
a. .25
b. .235
c. 4
d. 3
16. The value of 4.5*1.8+4.5*8.2
1.5*4.5+1.5*5.5
a. 10
b. 8
c. 5
d. 3
17. The value of (.02)2 + (0.52)2 + (0.035)2
(0.002)2 + (0.052)2 + (0.0035)2
a. 100
b. 1000
c. .001
d. .0001
18. Out of 200 donors, ¼ are men and remaining are women. Each male donor donates Rs.3000 per year and each female donor donates ½ of that amount. What is the total yearly collection through donations?
a. Rs.1, 50,000
b. Rs.3, 75,000
c. Rs.1, 40,300
d. Rs.2, 25,000
19. One-fifth of Ramu’s expenditure is equal to one-half of his savings. If his monthly income is Rs.6300 how much amount does he save?
a. Rs.1550
b. Rs.1800
c. Rs.2000
d. Rs.2350
20. The width of a rectangular hall is ½ of its length. If the area of the hall is 450 sq.m, what is the difference between its length and breadth?
a. 8m
b. 10m
c. 12m
d. 15m
Answer & Explanations
1. Exp: 20.05 + 35.603- 43.087 = 55.653- 43.087= 12.566
2. Exp: 23 =0.821
28
14 = 0.933
15
15 = 0.7894
19
21 = 0.875
24
So, 15 = 0.7894 is smallest.
19
5. Exp: 9*7=63
Sum of decimal places= 4
So, 0.9*0.007= 0.0063
6. Exp: Let 0.0015 = 0.003
X
X= 0.0015 = 0.5
0.003
7. Exp: Given Expression= 0.363*(0.522+0.478)= 0.363*1= 0.363
8. Exp: Given 7125 = 5700
1.25
1.25
712.5 =71.25 = 7125*1 = 5700 = 57
12.5 1.25 1.25*100 100
9. Exp: 34.31*0.473*1.567 = 25.4303 = 2.15
0.0673*23.25*7.57 11.845
10. Exp. Given Expression = a2-b2 = (a+b) (a-b) = (a+b)
a-b a-b
(5.68)2 – (4.32)2 = (5.68+ 4.32) = 10
5.68- 4.32
11. Exp: Given Expression = a3+b3 =(a+b)
a2-ab+b2
= (4.3+1)= 5.3
13. Exp: 10k = 0.0551 = 5.51 = 5.51* 102 = 1 = 10-2
5.51 551 551* 102 102
14. Exp: 25.25 = 2525 = 0.012625
2000 200000
15. Exp: (2.502+0.064)2 - (2.502-0.064)2 = (a+b)2 - (a-b)2 = 4ab = 4
2.502*0.064 ab ab
16. Exp: 4.5*1.8+4.5*8.2 = 4.5 (1.8+8.2) = 4.5*10 = 45 =3
1.5*4.5+1.5*5.5 1.5 (4.5+5.5) 1.5*10 15
17. Exp: (.02)2 + (0.52)2 + (0.035)2 = a2+b2+c2
(0.002)2 + (0.052)2 + (0.0035)2 ( a /10) 2+ ( b/10) 2 + ( c/10) 2 ,
where a= .02, b= .52, c= .035
= 100(a2+b2+c2) = 100
a2+b2+c2
18. Exp: Number of men donors= 200*1/4 =50
Number of women donors=200-50=150
1 man donor donates = Rs.3000
Therefore, 50 men donor donates = 3000* 50= Rs.1,50,000
1 woman donor donates= 3000*1/2 = Rs.1500
Therefore, 150 women donor donates = 1500* 150= Rs.2,25,000
Hence total amount collected = 1,50,000+ 2,25,000
= Rs.3,75,000
19. Let the saving be Rs. x
Therefore, Expenditure = Rs. (6300-x)
then, (6300-x)* 1 = x* 1
5 2
=> 1260- x = x
5 2
=> 1260= x + x
2 5
=> 7x = 1260
10
x= 1800
20. Exp: Let the length of the hall be x m
Breadth of the hall = 1x m
2
Area of the hall = Length * Breadth
450 = x * 1x
2
x² = 900
x =30
Difference between the length and breadth of the hall = x - 1x = x/2
2
30 = 15m
2
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