Math Connect Answers with steps

1ANSWERS TO MATH CONNECT, ENGLISH CONNECT, தமிழ் கனெக்ட் EDITION 14

. Find 79² - 21² without full calculation.

(79+21)(79-21)=(100)(58)=5800

 2. Simplify (225 x 5³ x 2² x 4³)/(3² x 10⁴)

     using exponent laws.

=5²x 3² x 5³ x 2² x 2⁶)/(3² x 5²x 2²)

=5³ x 2⁶=8000

 3. Find n if √(512) = n√2

√(256x2)=n√2

16√2=n√2

n=16

 4. Simplify 3√2 - 2√3 + 5√2 - 3√3

8√2-5√3

 5. Simplify (3x-24)(x²- x - 12)/(x² -5x-24)

3(x-8)(x-4)(x+3)/(x-8)(x+3)

=3(x-4)

 6. Find (4 x 10⁰ ) + 0.002 + (2 x 10⁻³) +

     (40x10⁻³) + (400x10⁻³)

4+.002 + .002 + .04 + 0.4

= 4.444

 7. If A:B = 3:5 and B:C = 25:9 then find A:C

A/C= (A/B)(B/C)=(3/5)(25/9)=5/3

 8. If A:B = 2:7 and C:B =8:3 then find A:B:C

 A:B = 2:7 and B:C =3:8

A:B = 2x3 :7x3 and B:C =3x7 : 8x7

A:B:C = 6:21:56

 9. Simplify 3a - (2a +3 - 3b) - (4b - 3c +3a) + 5a +12 and find the value of the expression at a=1, b=2and c = -3.

 3a - 2a +3 - 3b- 4b - 3c +3a+ 5a +12 

Rearranging,we get

3a-2a+3a+5a-3b-4b-3c+3+12

=9a-7b-3c+15

=9(1)-7(2)-3(-3)+15

9-14+9+15=19

10. Find x+y if x:y=7:4 and x-y=27

Let x=7k and y=4k

7k - 4k = 27

3k=27

k=9

x+y=7k+4k=11k=11(9)=99

1. HAPPINESS 

2. PERSONALITY 

3. CHALLENGE 

4. EMINENT 

5. LEADERSHIP 

1. ஆராய்ச்சியாளர்

2. ஊக்கமுடைமை

3. வகுப்பறை 

4. கருத்தரங்கம் 

5. விளையாட்டு 

Answers with steps to Math Connect Edition 13 Questions 

1. Find the missing numbers 

5, 7, 13, 25, ___, ___

7-5=2=1x2

13-7=6= 2x3

25-13=12=3x4

So, 4x5=20

Next number is 25+20=45

5x6=30

Next number is 45+30=75

2. Find x if x-3√2=√18

x=√18+3√2

=√(9X2)+3√2

=3√2+3√2

=6√2

3. If 306.02÷2=153.01 then find 30.602÷2

  and .0030602÷2 without actual division.

30.602÷2=15.301

.0030602÷2=.0015301

4. Find √(3²+3²+3²+3²)

=√(4(3²))=√36=6

5. Evaluate (2/3) + (2/15) + (2//35) + (2/63)

(2/(1x3)) + (2/(3x5)) + (2/(5x7)) + (2/(7x9))

= 1-(1/3) + (1/3) - (1/5) + (1/5) - (1/7) + (1/7) - (1/9)

= 1-(1/9)

=(9-1)/9=8/9

6. Find x if √x + √7 = √112

√x+√7=√(16x7)

√x+√7=4√7

√x=4√7-√7

√x=3√7

x=(3√7)²=63

7. Find 12³ + 13³ + (-25)³ - 3(12)(13)(-25)

without calculating the cubes.

Since 12+13+(-25)=0, we can write

12³ + 13³ + (-25)³= 3(12)(13)(-25)=-11700

Therefore 

12³ + 13³ + (-25)³ - 3(12)(13)(-25)

=-11700+11700=0

8. Simplify √576/2.56

√576/2.56=24/2.56=2400/256=9.375

9. Fill in the blanks 

24, 72, 36, 108, _____, _____

24x3=72

72÷2=36

36X3=108

108÷2=54

54X3=162

The numbers are 54,162

10. Find 112.34 + (1123.4/10) + (11234/100) + 

(112340/1000)

112.34+112.34+112.34+112.34

=4(112.34)=449.36

Last week (Edition 13) answers 

ENGLISH CONNECT 

1. EDUCATION 

2. INITIATIVE

3. ENCOURAGEMENT 

4. KNOWLEDGE 

5. INSPIRATION 

தமிழ் கனெக்ட் 

1. நுண்ணறிவு 

2. பதக்கங்கள் 

3. பாடசாலை 

4. விடாமுயற்சி 

5. பள்ளிக்கூடம் 

Math Connect answers 

1. 45, 75

2. 6√2

3. 15.301, 0.0015301

4. 6

5. 8/9

6. 63

7. 0 (zero)

8. 9.375

9. 54, 162

10. 449.36

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