Exercise 6B
Q1 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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:
$=-6 a^{4} b^{2} x^{2}+6 a^{4} b^{2} x^{2}$
=0
(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
Q2 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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: $=14 r^{3}-10 r^{3}$
$=4 r^{3}$
Q3 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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)
$\begin{aligned}&-c^{2}+5 c \\&\frac{-4 c^{2}+8 c}{-5 c^{2}+13 c}
\\\hline\end{aligned}$
Q4 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
Question 4
(i)
$\begin{aligned}&2 a+3 b+1 \\&\frac{4 a+2 b+7}{6 a+5
b+8}\end{aligned}$
(ii)
$\begin{aligned}&x^{2}+2 x-7 \\ &x^{2}-5 x+3 \\\hline &2
x^{2}-3x-4\end{aligned}$
Q5 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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)
$\begin{gathered}a^{2}-6 \\-4 a^{2}+2 \\-7 a^{2}+5 \\\hline-10 a^{2}-1
\\\hline\end{gathered}$
Q6 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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)
$\begin{aligned}x^{3}+6x^{2}\phantom{+3x-7~~}&\\5x^{2}+3x\phantom{+5x}&\\5x-7&
\\ \hline x^{3}+11x^{2}+8x-7 \\\hline\end{aligned}$
Q7 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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
Q8 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
Question 8
| (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)
Q9 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
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:
$=2 y^{2}-5-2 y+2 \times\left(y^{2}-3 y+6\right)+2 x\left(y^{2}-4 y+2\right)$
$=2 y^{2}-5-2 y+2 y^{2}-6 y+12+2 y^{2}-8 y+4$
$=6 y^{2}-16 y+11$
Q10 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper
Question 10
Find the perimeter of triangle
Sol:
$=A B+B C+A C$
$=3x-7+2x+5+(-x+11)$
$=3x-7+2x+5-x+11$
$=4x+9$
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