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S.chand Class 8 Maths Solution Chapter 7 Linear Equations Exercise 7 A

Exercise 7 A

Solve the following equations and check your answer:

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Question 1

(i) $10 p-(3 p-4)=4(p+1)+9$

(ii) $7+2(a+1)-3 a=5 a$

(iii) $4(x+3)-2(x-1)=3 x+3$

Sol :

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Question 2

(i) $\frac{x}{3}-5=8$

(ii) $\frac{t+8}{3}=t$

Sol :

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Question 3

(i) $4 y+\frac{y}{5}=21$

(ii) $\frac{2 m}{3}+\frac{3 m}{4}=17$

Sol :

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Question 4

$\frac{2}{3}\left(x+\frac{3}{5}\right)=\frac{7}{2}$

Sol :

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Question 5

$\frac{x+3}{7}-\frac{2 x-5}{3}=\frac{3 x-5}{5}-25$

Sol :

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Question 6

$\frac{3 x-2}{10}-\frac{x+3}{7}+\frac{4 x-7}{3}=x-1$

Sol :

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Question 7

$2.8 v=54+v$

Sol :

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Question 8

$0.26 x+0.09 x=8-0.45 x$

Sol :

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Question 9

$\frac{1}{6}(4 y+5)-\frac{2}{3}(2 y+7)=\frac{3}{2}$

Sol :

Solve the following equations :

Question 10

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$\frac{3}{x+1}=\frac{5}{2 x}$

Sol :

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Question 11

$\frac{6}{3 m+1}=\frac{9}{5 m-3}$

Sol :

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Question 12

$\frac{2 x+3}{5}=\frac{4 x+9}{11}$

Sol :

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Question 13

$\frac{5 x-7}{3 x}=2$

Sol :

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Question 14

$\frac{0.4 z-3}{1.5 z+9}=\frac{7}{5}$

Sol :

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Question 15

$\frac{x-2}{x-4}=\frac{x+4}{x-2}$

Sol :

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Question 16

$\frac{y-2}{y-5}=\frac{y+3}{y+5}$

Sol :

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Question 17

$\frac{2 y-4}{3 y+2}=-\frac{2}{3}\left(\right.$ Hint. Write $-\frac{2}{3}$ as $\left.\frac{-2}{3}\right)$

Sol :

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Question 18

$\frac{\frac{x}{4}-\frac{3}{5}}{\frac{4}{3}-7 x}=-\frac{3}{20}$

Sol :

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Question 19

$\frac{(2 x+3)-(5 x-7)}{6 x+11}=\frac{-8}{3}$

Sol :

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Question 20

$\frac{17(2-x)-5(x+12)}{1-7 x}=8$

Sol :

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Question 21

$\frac{(4+x)(5-x)}{(2+x)(7-x)}=1$

Sol :

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Question 22

$\frac{x^{2}-(x+1)(x+2)}{5 x+1}=6$

Sol :

Multiple Choice Questions (MCQs)

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Question 23

If $\frac{x+3}{2}-\frac{3 x+1}{4}=\frac{2(x-2)}{3}-2$, then the value of $x$ is

(a) $\frac{61}{11}$

(b) 5

(c) $-5$

(d) $-\frac{61}{11}$

Sol :

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Question 24

The solution of $\frac{2 x+3}{2 x-1}=\frac{3 x-1}{3 x+1}$ is

(a) $\frac{1}{8}$

(b) $-\frac{1}{8}$

(c) $\frac{8}{3}$

(d) $\frac{-8}{3}$

Sol :

High Order Thinking Skills (HOTS)

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Question 25

Solve and give the positive value of $x$ which satisfies the given equation :

$(2 x+4)^{2}-(x-5)^{2}=26 x$

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 G

Exercise 6 G

Factorise:

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Question 1

$4 x^{2}+5 x+1$

Sol :

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Question 2

$2 x^{2}+11 x+14$

Sol :

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Question 3

$2 x^{2}+11 x+12$

Sol :

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Question 4

$3 x^{2}+13 x+4$

Sol :

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Question 5

$2 x^{2}-5 x-12$

Sol :

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Question 6

$4 x^{2}+8 x-5$

Sol :

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Question 7

$13 x^{2}+37 x-6$

Sol :

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Question 8

$40 n^{2}+n-6$

Sol :

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Question 9

$4 z^{2}-16 z+15$

Sol :

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Question 10

$6-9 c-27 c^{2}$

Sol :

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Question 11

$1-t-6 t^{2}$

Sol :

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Question 12

$2 a^{2}+7 a b-15 b^{2}$

Sol :

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Question 13

$4 x^{2}+24 x+20$

Sol :

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Question 14

$12 a^{2}+2 a-4$

Sol :

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Question 15

$12 m^{3}+6 m^{2}-6 m$

Sol :

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Question 16

$6 x^{5}-22 x^{3}-8 x$

Sol :

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Question 17

$6 z^{6}-21 z^{4}-12 z^{2}$

Sol :

Multiple Choice Questions (MCQs)

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Question 18

A rectangular parking lot has an area of $5 x^{2}+17 x+6$ square units. One of its sides is

(a) $(5 x+6)$

(b) $(x+2)$

(c) $(5 x+2)$

(d) $(5 x+1)$

Sol :

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Question 19

The complete factorisation of $-12 b^{5}-b^{3}+b$ is

(a) $-b\left(12 b^{4}+b^{2}-1\right)$

(b) $b(2 b-1)(2 b+1)\left(1+3 b^{2}\right)$

(c) $-b\left(4 b^{2}-1\right)\left(3 b^{2}+1\right)$

(d) $b(1-2 b)(1+2 b)\left(1+3 b^{2}\right)$

Sol :

High Order Thinking Skills (HOTS)

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Question 20

The binomial $x-3$ is not a factor of which of the following trinomials ?

(a) $2 x^{2}-x-15$

(b) $3 x^{2}-13 x+12$

(c) $2 x^{2}-8 x+6$

(d) $2 x^{2}-7 x-3$

Sol :

S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1C

Exercise 1C

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Question 1

Answer True (T) or False (F) :
(i) $\frac{10}{21} \div \frac{8}{9}=\frac{8}{9} \div \frac{10}{21}$
(ii) Addition distributes over multiplication in rational numbers.
(iii) The reciprocal of $-5$ is $\frac{1}{5}$.
(iv) $\frac{3}{4} \div \frac{-8}{7}$ is a rational number.
(v) $0 \times \frac{4}{5}=\frac{4}{5} \times 0$ implies that 0 is the multiplicative identity for rational numbers.

Sol :

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Question 2

Multiply :

(i) $\frac{6}{7}$ by $\frac{2}{3}$

(ii) $\frac{-9}{11}$ by $\frac{22}{63}$

(iii) $\frac{-12}{13}$ by $\frac{-5}{18}$

(iv) $\frac{-90}{11}$ by $\frac{-55}{72}$

(v) $5 \frac{1}{7}$ by $-2 \frac{1}{3}$

(vi) $\frac{18}{35}$ by $-3 \frac{1}{8}$

Sol :

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Question 3

Simplify:

(i) $\left(\frac{-6}{7} \times \frac{-28}{18}\right)+\left(\frac{-11}{13} \times \frac{65}{22}\right)$

(ii) $\left(\frac{-4}{5} \times \frac{15}{8}\right)+\left(\frac{-1}{3} \times \frac{-9}{7}\right)-\left(\frac{2}{9} \times \frac{27}{14}\right)$

Sol :

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Question 4

Fill in the blanks :

(i) $\frac{-18}{37} \times \frac{11}{40}=\frac{11}{40} \times$

(ii) $-19 \times \frac{-5}{12}=\frac{-5}{12} \times$

(iii) $\left(\frac{6}{11} \times \frac{-20}{21}\right) \times\left(\frac{-7}{8}\right)=\ldots . . \times\left(\frac{-20}{21} \times \frac{-7}{8}\right)$

(iv) $\frac{-21}{40} \times\left(\frac{3}{7} \times \frac{17}{-24}\right)=\left(\frac{-21}{40} \times \frac{17}{-24}\right) \times \ldots .$

(v) $\frac{2}{9} \times\left(\frac{-4}{9}+\frac{6}{17}\right)=\frac{2}{9} \times \ldots . .+\ldots . . \times \frac{6}{17}$

Sol :

Verify the statements given in Q5 to Q7. Also name the properties of multiplication illustrated by these statements.

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Question 5

(i) $\frac{4}{5} \times \frac{7}{9}=\frac{7}{9} \times \frac{4}{5}$

(ii) $\frac{8}{7} \times \frac{9}{-10}=\frac{9}{-10} \times \frac{8}{7}$

Sol :

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Question 6

(i) $\left(\frac{3}{4} \times \frac{1}{2}\right) \times \frac{5}{7}=\frac{3}{4} \times\left(\frac{1}{2} \times \frac{5}{7}\right)$

(ii) $\left(-\frac{7}{6} \times \frac{-2}{5}\right) \times \frac{3}{8}=\frac{-7}{6} \times\left(\frac{-2}{5} \times \frac{3}{8}\right)$

Sol :

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Question 7

(i) $\frac{2}{3} \times\left(\frac{4}{5}+\frac{7}{8}\right)=\left(\frac{2}{3} \times \frac{4}{5}\right)+\left(\frac{2}{3} \times \frac{7}{8}\right)$

(ii) $\frac{-6}{15} \times\left(\frac{7}{8}+\frac{-5}{12}\right)=\left(\frac{-6}{15} \times \frac{7}{8}\right)+\left(\frac{-6}{15} \times \frac{-5}{12}\right)$

Sol :

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Question 8

Use the distributivity of multiplication of rational numbers over addition to simplify :

(i) $\frac{7}{4} \times\left(\frac{5}{8}+\frac{1}{2}\right)$

(ii) $\frac{-3}{8} \times\left(\frac{4}{7}+\frac{-11}{7}\right)$

(iii) $\frac{-2}{5} \times\left(\frac{3}{8}-25\right)$

Sol :

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Question 9

Find the multiplicative inverse, $i \cdot e_{\text {s }}$, the reciprocal of

(i) 6

(ii) $-23$

(iii) $\frac{11}{20}$

(iv) $\frac{-19}{16}$

(v) $\frac{11}{-5}$

(vi) $\frac{-7}{-8}$

(vii) $\frac{4}{5} \times \frac{15}{8}$

(viii) $0 \times \frac{2}{9}$

Sol :

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Question 10

Match the mathematical sentence in Column A with the property illustrated by the statement in Column B.

Column A	Column B
(i) $\frac{1}{3} \times 0=0$ (ii) $\frac{-2}{5} \times 1=\frac{-2}{5}$ (iii) $\frac{1}{4} \times 4=1$ (iv) $\frac{-6}{7} \times \frac{2}{3}=-\frac{4}{5}$ (v) $0 \times-\frac{7}{8}=\frac{-7}{8} \times 0$	(a) Property of 1 (b) Closure Property (c) Property of 0 (d) Commutative Property (e) Multiplicative Inverse

Sol :

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Question 11

Divide :

(i) $\frac{5}{9}$ by 15

(ii) $\frac{7}{18}$ by $\frac{-14}{51}$

(iii) $\frac{10}{33}$ by $\frac{2}{-11}$

(iv) $-18$ by $\frac{(-36)}{37}$

(v) $\frac{-24}{50}$ by $\frac{-4}{75}$

Sol :

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Question 12

Evaluate :

(i) $\left(\frac{5}{9} \div \frac{15}{36}\right) \div\left(-\frac{5}{6}\right)$

(ii) $\left(\frac{-3}{29} \div \frac{9}{87}\right) \div \frac{-1}{7}$

Sol :

Multiple Choice Questions (MCQs)

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Question 13

Which property of multiplication is not involved in the following :

$32 \times \frac{1}{4}=(8 \times 4) \times \frac{1}{4}=8 \times\left(4 \times \frac{1}{4}\right)=8 \times 1=8$

(a) Associative property

(b) Multiplicative inverse property

(c) Commutative property

(d) Property of 1

Sol :

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Question 14

$(-36) \times\left(\frac{-35}{76}\right) \times\left(\frac{19}{15}\right) \times\left(\frac{3}{-2}\right)^{-1}$ equals

(a) -64

(b) -14

(c) 14

(d) 64

Sol :

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Question 15

Which of the following statements is true ?

(a) $\frac{16}{21} \div\left(\frac{-4}{9} \div \frac{8}{9}\right)=\left(\frac{16}{21} \div \frac{-4}{5}\right) \div \frac{8}{9}$

(b) $\left(\frac{9}{20}-\frac{17}{40}\right) \div \frac{10}{3}=\left(\frac{9}{20} \div \frac{10}{3}\right)-\left(\frac{17}{40} \div \frac{10}{3}\right)$

(c) $0 \div-\frac{13}{14}=0$

Sol :

High Order Thinking Skills (HOTS)

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Question 16

Subtract the additive inverse of $\frac{5}{6}$ from the multiplicative inverse of $\frac{-5}{7} \times \frac{14}{15}$

Sol :

SChand Composite Mathematics Class 7 Chapter 6 Algebraic Expression Exercise 6B

Exercise 6B

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Question 1

Add:

(i) 2x, 3x, x, 5x

Sol:

=2x+3x+x+5x

=11x

(ii) 8m, 3m, 4m , 2m

Sol:

=8m+3m+4m+2m

=17m

(iii) $-3 b^{2}, 5 b^{2}$

Sol:

$=-3 b^{2}+5 b^{2}$

$=2 b^{2}$

(iv) -7x, 2x, 4x ,-x

Sol:

=-7x+2x+4 x+(-x)

=-7x+2x+4x-x

=-8 x+6x=-2x

(v) -x ,-x, -x

Sol:

=-x +(-x)+ (-x)

=-x-x-x

=-3x

(vii) $4 b x^{2},-9 b x^{2} .$

Sol:

$=4 b x^{2}+\left(-9 b x^{2}\right)$

$=4 b x^{2}-9 b x^{2}$

$=-5 b x^{2}$

(v) 0, y

Sol:

0+y = y

(viii) $\frac{1}{2} ax, \frac{1}{2}ax$

Sol :

$=\frac{1}{2} a x+\frac{1}{2} a x$

$1a x=a x$

(ix) 2y, -5y ,6y, -4y

Sol:

=2y+(-5y)+6y+(-4y)

=2y-5y+6y-4y

=8y-9y=-y

(x) -9xy, -xy

Sol :

=-9xy+(-xy)

=-9xy-xy

=-10xy

(xi) 0,$-7 b^{2} y^{2}$

Sol :

$=0+\left(-7 b^{2} y^{2}\right)$

$=-7 b^{2} y^{2}$

(xii) $-6 a^{4} b^{2} x^{2}+6 a^{4} b^{2} z_{1}^{2}$

Sol:

$=-6 a^{4} b^{2} x^{2}+6 a^{4} b^{2} x^{2}$

(xiii) $a b^{3} c,-2 a b^{3} c,-2 a b^{3} c$

Sol:

$=a b^{3} c+\left(-2 a b^{3} c\right)+\left(-2 a b^{3} c\right)$

$=a b^{3} c-2 a b^{3} c-2 a b^{3} c$

$=a b^{3} c-4 a b^{3} c=-3 a b^{3} c$

(xiv) 6(a+b), 3(a+b)

Sol:

$=6(a+b)+3(a+b)$

$=6 a+6 b+3 a+3 b$

$=9 a+9 b=9(a+b)$

(xv) 2a, 3b, 4c

Sol :

= 2a+3b+4c

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Question 2

Simplify:

(i) e+e+e+e+e+e+e

Sol: 7e

(ii) $3 p+p-p+p-p$

Sol:$3 p$

(iii) $k+3 k-2 k+7 k-5 k$

Sol: $=11 k-7 k .$

$=4 k$

(iv) 8$r^{3}$ - $10 r^{3}+6 r^{3}$

Sol: $=14 r^{3}-10 r^{3}$

$=4 r^{3}$

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Question 3

(i)

$\begin{aligned}&6 a+4 b \\&2 a+5 b \\&\hline 8 a+9 b \\&\hline\end{aligned}$

(ii)

$\begin{aligned}&2 x+5 y \\&\frac{3 x+y}{4 x+6 y}\end{aligned}$

(iii)

$\begin{array}{r}5 t-1 \\-6 t+4 \\\hline-t+3 \\\hline\end{array}$

(iv)

$\begin{aligned}&3 a+b \\&a-b \\ \hline&4 a \\\hline\end{aligned}$

(v)

$\begin{array}{r} x^{2}+2 \\-6 x^{2}+3 \\\hline-5 x^{2}+5 \\\hline\end{array}$

(vi)

$\begin{array}{r}-6x-2 \\-x-5 \\\hline-7x-7 \\\hline\end{array}$

(vii)

$\begin{aligned}&3 a b-9xy \\&7 a b+4xy \\\hline &10 a b-5x y \\\hline\end{aligned}$

(viii)

$\begin{aligned}&-c^{2}+5 c \\&\frac{-4 c^{2}+8 c}{-5 c^{2}+13 c} \\\hline\end{aligned}$

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Question 4

(i)

$\begin{aligned}&2 a+3 b+1 \\&\frac{4 a+2 b+7}{6 a+5 b+8}\end{aligned}$

(ii)

$\begin{aligned}&x^{2}+2 x-7 \\ &x^{2}-5 x+3 \\\hline &2 x^{2}-3x-4\end{aligned}$

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Question 5

(i)

$\begin{array}{r}3 a-4 b \\7 a-2 b \\-2 a+b \\\hline 8 a-5 b \\\hline\end{array}$

(ii)

$\begin{gathered}a^{2}-6 \\-4 a^{2}+2 \\-7 a^{2}+5 \\\hline-10 a^{2}-1 \\\hline\end{gathered}$

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Question 6

(i) $\begin{array}{r}x^{2}-3 x+4 \\4 x^{2}-2 x+7 \\-x^{2}+5 x-2 \\ \hline4x^{2}+0+9 \\\hline\end{array}$

(ii) $\begin{aligned}x^{3}+6x^{2}\phantom{+3x-7~~}&\\5x^{2}+3x\phantom{+5x}&\\5x-7& \\ \hline x^{3}+11x^{2}+8x-7 \\\hline\end{aligned}$

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Question 7

(i) $\left(c^{2}+2cd)+(-3 c d-d^{2}\right)$

Sol:

$=c^{2}+2 c d-3 c d-d^{2}$

$=c^{2}-c d-d^{2}$

(ii) $(x-6)+(3 x-4)+(x-1)$

Sol:

$=x-6+3 x-4+ x-1$

$=5 x-11$

(iii) $3 m n^{2}+4 m^{2} n^{2}+\left(-5 m n^{2}\right)+\left(-m n^{2}\right)$

Sol:

$=3 m n^{2}+4 m^{2} n^{2}-5 m n^{2}-m n^{2}$

$=4 m^{2} n^{2}+3 m n^{2}-6 m n^{2}$

$=4 m^{2} n^{2}-3 m n^{2}$

(iv) $(x-y)+(y-x)+(2 y-x)$

Sol:

=x-y+y-x+2y-x

= 2y-x

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Question 8

Match the expression in column A to the sum in column B

(i) $3 x^{2}+5 x-4+6 x^{2}-x+7$
(ii) $2 y^{2}-3 y+6+y^{2}-5 y-1+(-4)+2 y^{2}-2 y$
(iii) $2 x^{2} y-3 x y^{2}+x^{2} y-4 x^{2} y-2 x y^{2}$
(iv) $x^{2}-y^{2}+2 x^{2}-3 x y+4 y^{2}+3 y^{2}-5 x y-x^{2}$

(A) $5 y^{2}-10 y+1$
(B) $2 x^{2}-8 x y+6 y^{2}$
(C) $9 x^{2}+4 x+3$
(D) $-x^{2} y-5 x y^{2}$

Sol :

(i) - (C)

(ii) - (A)

(iii) - (D)

(iv) - (B)

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Question 9

If P= $2 y^{2}-5-2 y$ , Q= $y^{2}-3 y+6$ and R = $y^{2}-4 y+2$ Find P+2Q+2R

Sol:

$=2 y^{2}-5-2 y+2 \times\left(y^{2}-3 y+6\right)+2 x\left(y^{2}-4 y+2\right)$

$=2 y^{2}-5-2 y+2 y^{2}-6 y+12+2 y^{2}-8 y+4$

$=6 y^{2}-16 y+11$

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Question 10

Find the perimeter of triangle

Sol:

$=A B+B C+A C$

$=3x-7+2x+5+(-x+11)$

$=3x-7+2x+5-x+11$

$=4x+9$

SChand Composite Mathematics Class 7 Chapter 6 Algebraic Expression Exercise 6A

Exercise 6A

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Question 1

Identify Monomials , Binomials and Trinomials from the following express:

(i) 2m+3n

Ans: Binomials

(ii) a- 5b+7c

Ans: Trinomial

(iii) $\frac{2}{7} a^{2}$

Ans: Monomials

(iv) $5 m^{2}-4$

Ans: Binomials

(v) $7 a^{2}+2 b^{2}-4 a b$

Ans: Trinomial

(vi) $\frac{1}{2} x^{3}-y+2$

Ans: Trinomial , Polynomials

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Question 2

Write the coefficient of x in the following:

(i) 2x

Ans: 2

(ii) mx

Ans: m

(iii) -2px

Ans: -2p

(iv) $3 x y^{2}$

Ans: $3 y^{2}$

(v) $-\frac{1}{3} x p$

Ans: $-\frac{1}{3} p$

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Question 3

Write the coefficient of :

(i) $x$ in $-6 x y^{2}$

Ans: $-6 y^{2}$

(ii) $q$ in $q x^{2}$

Ans: $x^{2}$

(iii) a in $\frac{2}{3} a$

Ans: $\frac{2}{3}$

(iv) $x^{2} y$ in $\frac{-4}{9} a$ $x^{2} y$

Ans: $-\frac{4}{9} a$

(v) xy in - 4xyz

Ans: - 4z

(vi) z in -z

Ans: -1

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Question 4

Identify the like terms in each of the following :

(i) $a^{2}, b^{2},2 a^{2}, c^{2}$

Ans: Like terms $a^{2}$ , $2 a^{2}$

(ii) $3 x y, yz, 5 x, \frac{2}{7} y z$

Ans: Like terms yz , $\frac{2}{7} y z$

(iii) $8 m^{2} n, m^{2} p,-m^{2} n, m^{2} n^{2}$

Ans: Like terms $8 m^{2} n$ , $-m^{2} n$

(iv) $c a b^{2}, a^{2} b c, b^{2} a c, c^{2} a b, a b c, a c b^{2}$

Ans: like terms $c a b^{2}$ , $b^{2} a c$ , $a c b^{2}$

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Question 5

identify polynomial from the given algebraic equation

(i) $\frac{4}{9} y^{2}-\frac{4}{9} x^{2}+4$

(ii) $\frac{2}{x}+\frac{3}{x^{2}}-4 x^{2}+3 x+2$

(iii) $3 a^{3}+4 a^{2} b+8 b^{3}$

(iv) $x^{2}-\frac{1}{x^{2}}+2$

Ans: Only I and III are polynomials

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Question 6

Write down the degree of the following polynomials:

(i) $4 x^{2}-x^{4}$

Ans: degree of polynomials = 4

(ii) $4 p^{2}+6 p^{3}+8 p^{8}$

Ans: degree of polynomials = 8

(iii) $m^{2} n^{3}+m n^{2}+4$

Ans: degree of polynomials = 5

( iv) $p^{2} q^{4}+p q^{2}+1$

Ans: degree of polynomials =6

(v) 4

$x^0$= 1

4×1 = $4 \times x^0$

Degree of polynomials =0

SChand Composite Mathematics Class 7 Chapter 5 Exponents & Powers Exercise 5C

Exercise 5C

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Question 1

Is the number written is scientific notation ? Write yes or no

(i) $24 \times 10^{7}$

Ans: No

(ii) $7 \times 10^{4}$

Ans: Yes

(iii) $8.9 \times 5^{2}$

Ans: No

(iv) $0.3 \times 10^{6}$

Ans No

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Question 2

Complete

(i) $54,000,000$

Sol: $5.4 \times 10^7$

(ii) $980,000,000,000$

Sol: $9.8 \times 10^11$

(iii) $50,000,000,000,000$

Sol: $5 \times 10^13$

(iv) $2740,0,000,000$

Sol: $2.74 \times 10^{10}$

OPEN IN YOUTUBE

Question 3

Write in scientific notation:

(i) 72,000

Sol: $7.2 \times 10^{4}$

(ii)8000000

Sol: $8 \times 10^{6}$

(iii) $790,000,000$

Sol: $=7.9 \times 10^{8}$

(iv) $8,040,000,000$

Sol: $8.04 \times 10^{9}$

(v) 31,408,000,000

Sol: $3.1408 \times 10^{10}$

(vi) Saturn is about 1,600,000,000 km from the earth

Ans: $1.6 \times 10^{9}$

(vii) Large distances are also measured in light year. One light year is about 9,460,000,000,000 km. It is the distance light travels in a year

Ans: $9.46 \times 10^{12} \mathrm{~km}$

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3F

Exercise 3F

Question 1

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3E

Exercise 3E

Question 1

(a) 24=3×2×2×2

=3×2³

(b) 36=2×2×3×3

=2²×3²

(d) 180=2×2×3×3×5

=2²×3²×5

(e) 300=2²×3×5²

Question 2

(a) 32 =2⁵

(b) 48= 2⁴ x3

(d) 72= 2³ x 3²

(e) 84= 2² x 3x 7

(f) 100= 2² x5²

(g) 840= 2³x 2 x 5 x 7

(h) 504 = 2³ x 3² x7

(i) 2904= 2³ x 3 x 11²

(j) 13845= 3⁴ x 5x 7²

Question 3

343= 7³

Question 4

(a) When all the factors are prime and their product is the original number.

(b) Prime factors of a number are all prime numbers where the factors of a number do not have to be prime.

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3D

Exercise 3D

Question 1

(a)12= 5+7

(b) 30= 11+19

(d) 72= 31+41

Question 2

(a) 12= 5+7

(b) 30= 13+17

(d) 90= 47+53

Question 3

(a) 15 = 3+5+7

(b) 23= 5+7+11

(d) 55= 13+19+23

Question 4

The five pairs of prime numbers less than 20, whose sum is divisible by 5 —

(2,3) , (3,7), (2,13), (3,17) and (13,17).

Question 5

(a) 151 is divisible by 1 and 151 , so it is a prime number.

(b) 69 is divisible by 1, 3, 2, 69 ,so, it is not a prime number.

(d) 265 is divisible by 1, 5, 53, 265 so it is not a prime number.

Question 6

The tree prime numbers are 5, 7 and 11

5x7x11= 385

Question 7

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3C

Exercise 3C

Question 1

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3B

Exercise 3B

Question 1

260, 7018, 20008, 148

Question 2

48, 594, 3096, 609513

Question 3

524, 71316, 8001008

Question 4

365, 7290, 21340, 845

Question 5

516, 7038, 800712

Question 6

464, 4176, 87544, 900392

Question 7

639, 29304, 38457

Question 8

670, 90020, 57390

Question 9

418, 7909, 17743, 10000001

Question 10

Divisible by 2 and 5 only.

Question 11

Divisible by 6, 8, 10 only.

Question 12

(a) Yes, it is also divisible by its factors because 6 & 9 are not co-prime.

(b) No, it is not divisible by their product because 6 & 9 are not co –prime.

Question 13

705 2 4 is divisible by 3.

Question 14

9 3 2760 is divisible by 9.

Question 15

(a) Yes

(b) Yes

(d) Yes

(e) Yes

(f) Yes

(g) No

(h) Yes

(i) No

Question 16

984 and 1736 are divisible by 8

Sum of 984 and 1736 = 2720, divisible by 8 differences of 1736 and 384= 752, divisible by 8.

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3A

Exercise 3A

Question 1

(a) 1, 2, 3, 4, 6, 12

(b) 1, 2, 7, 14

(d) 1, 3, 7, 21

(e) 1, 2, 3, 4, 6, 8, 12, 24

(f) 1, 23

(g) 1, 2, 3, 6, 7, 14, 21, 42

(h) 1, 5, 17, 85

(i) 1, 73

(j) 1, 2, 4, 23, 46, 92

Question 2

(a) 2, 4, 6, 8, 10

(b) 4, 8, 12, 16, 20

(d) 9, 18, 27, 36, 45

(e) 10, 20, 30, 40, 50

Question 4

List of the multiples of 7 between 1 and 75 – 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Question 4

The all multiples of 9 up to 100 – 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Question 5

(a) The ninth multiple of 75-9 × 75

= 675

(b) The multiples of 10 between 150 and 200 – 160, 170, 180, 190

Question 6

Addition Facts

Even + Even = Even, Example – 2+6=8

Odd + Odd = Even, Example – 3+5=8

Even + Odd = Odd, Example – 4+3=7

Multiplication Facts

Even Even = Even, Example – 24=8

Odd Odd = Odd, Example – 35=15

Even Odd = Even, Example – 25=10