Math Connect Answers with steps
Answers with steps to Math Connect Edition 5 Questions
1. 3/9=7/X
X= (9 x 7)/3 = 21
2. X% of 60 = 300
(X/100) x 60 = 300
X = (300 x 100)/60 = 500%
3. (99+98)(99-98) = 197
4. (A+B+C ) One day's work = 1/15
(A+C) One day's work= 1/20
B's one day work = (1/15)-(1/20)
=(20-15)/300
= 1/60
Number of days needed by B alone to complete
the work is 60 days
5. CP=X, SP=60
P=(X/100) x X
= X²/100
P= SP - CP
X²/100=60-X
X² = 6000 - 100X
X² + 100X - 6000 = 0
Using quadratic formula,
X = (-100 +√34000)/2, (Neglect the negative value)
X = (-100+184.4)/2
X = 84.4/2
X = 42.2
Rs.42.20
6. 3¹¹ x 3¹¹x 2¹¹x 2¹¹
= 3²² x 2²² = 6²²
7. (1/a) + (1/b)
= (b+a)/ab
= 10/20
= 1/2
8. (3+6+......+ 45)/15
= 3(1+2+.....15)/15
= (3 x 15 x 16)/ (15 x 2) (
Sum of n consecutive natural numbers is n(n+1)/2
= (3 x 16)/2
= 24
9. 80% of 60 = X % of 96
(80/100) x 60 = (X/100) x 96
80 x 60 = X x 96
X = (80 x 60)/96
X = 50
50%
10. 2/3, 10/9, 14/27, 16/81.
HCF (2,10,14,16) = 2
LCM (3,9,27,81) = 81
Therefore HCF of 2/3, 10/9, 14/27, 16/81 is 2/81
Answers to Edition 4 Questions
1. 6=x% of 1 kg= (x/100) of 1000 g
x= 6/10=0.6
2. Total number of terms
=((Last term - First term)/Common Difference) + 1
= ((53-31)/2 )+ 1= (22/2) + 1 = 12
Sum of 12 terms= (12/2)(31+53)
= 6 x 84 = 504
3. Sum of two squares is zero, then
both should be equal to zero
a-5=0 ,a=5
b-2=0, b=2
Therefore (5+2)³=7³= 343
4. 3/4 x 6/5 x 1/5 of a number X = 216
X=(216x5x5x4)/(3x6)
X= 1200
5. The pattern is
5
5x1=5
5x2=10
10x3=30
30x4=120
So, the next two numbers must be
120x5=600
600x6=3600
6. 5/66=(1/6)-(1/11)
5/176=(1/11)-(1/16)
Adding the above, we get
5/48
Now 5(1/48+1/376)
=(5/8)(1/6+1/47)
=(5/8)(53/282)
=265/2256
7. 24⁵=8⁵x3⁵=2¹⁵x3⁵
32⁴=(2⁵)⁴=2²⁰==2¹⁵x2⁵
Comparing both, we find
24⁵ is greater
8. Sum of n consecutive natural numbers
=n(n+1)/2
=300(301)/2
=150x301
=45150
9. 2.754006 x 10⁶ = 2754006.000000
0.002754006 x 10⁹ = 2754006.000000000
Yes, both are equal
10. (25x9x5x120)+(225x400)
=(225x600)+(225x400)
=225(600+400)
=225(1000)
=225000
Answers to Edition 3 Questions
1. 5√2 + ( √16 x√2 ) + (√9 x√2)
= 5√2+4√2+3√2
=12√2
2. ((7x/y) + 2) / ((7x/y) - 2)
= (7(4/7) + 2) / ((7(4/7)-2)
=(4+2)/(4-2)
=6/2=3
3. 33+5^2
=33+25=58
58+6^2
=58+36=94
4. 1/(2x5) + 1/(5x8) + 1/(8x11) +1/(11x14)
=(1/3)((1/2) - (1/5) + (1/5) - (1/8) + (1/8) - (1/11) + (1/11) - (1/14))
=(1/3)((1/2) - (1/14))
= (1/3)(7-1)/14
=(1/3)( 6/14 )= 2/14 = 1/7
5. Let x=√3√3√3√3...
x= √(3x)
x^2=3x
x(x-3)=0
x=3
6. √3√3√3√3
=3^1/2 x 3^1/4 x3^1/8x 3^1/16
=3^(1/2 + 1/4 + 1/8 + 1/16)
=3^(15/16)
7. 1+1+1+1=4
8. 1/2³ = 1/8=9/72
1/3² = 1/9=8/72
2⁻³ is greater
9. 1234500 x (1000-1)
=1234500000-1234500
=1233265500
10. 33075=3 x 3 x 3 x 5 x 5 x 7 x 7
(Prime factorisation)
a=3 : b=5 : c=7
ANSWERS With Steps to Edition 2 Questions
1. 3²⁹ (1+1+1) = 3²⁹. 3
= 3²⁹⁺¹
= 3³⁰
2. 5³³ x 2⁴⁴ = (5³)¹¹ x (2⁴)¹¹
= (5³ x 2⁴ )¹¹
= (125 x 16 ) ¹¹
= (2000)¹¹
3. (125 x 125 x 125 - 25 x 25 x 25)/(125 x 125 + 125 x 25 + 25 x 25).
= (125³ - 25³ )/(125x125 + 125x25 + 25x25)
= [(125 - 25 ) (125² + 125 x 25 + 25²)]/(125² +125x25 + 25²)
= 125 - 25
= 100
4. (5⁵)¹⁰, (6⁴)¹⁰, (7²)¹⁰, (8³)¹⁰
(3125)¹⁰, (1296)¹⁰, (49)¹⁰, (512)¹⁰
5⁵⁰ is the greatest
5. (yz+zx+xy)/xyz =6
yz+zzx+xy = 6xyz = 6(5) = 30
xy²z² + x²yz² + x²y²z
= xyz(yz+zx+xy)
= 5(30)
= 150
6. 64 days = 63 + 1
= 9 weeks + 1
Therefore the answer is Friday.
7 . (√2 + 2√2 + 3√2 ) /√18
=6√2 / √(9x2)
= 6√2 / 3√2
= 2
8. 15, 47, 128, 192, ---, ---
47 - 15 = 32 = 2⁵
128 - 47 = 81 = 3⁴
192 - 128 = 64 = 4³
Next two terms are
192 + 5² = 217
217 + 6¹ = 223
9. √36 + √0.36 + √0.0036 + √0.000036
= 6 + 0.6 + 0.06 + 0.006
= 6.666
10. ( 9² x 18⁴ )/3¹⁶
= (9² x (9x2)⁴/ (3²)⁸
= (9² x 9⁴ x 2⁴) / 9⁸
= (9²⁺⁴ x 2⁴ ) /9⁸
= (9⁶ x 2⁴ ) /9⁸
= 2⁴ / 9⁸⁻⁶
= 2⁴ / 9²
=16/81
Comments
Post a Comment