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Ex.1.3 Q2 Integers - NCERT Maths Class 7

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Question

Verify the following:

(a)

\(18 \times  [ 7 +(-3) ]  =[ 18 \times 7]+[18 \times (-3)]\)

(b)

\(\begin{align}&\left( -21 \right) \!\times\! \left[ {\left( -4 \right)\!+\! \left( -6 \right)} \right] \\&= \!\left[ {\left( -21 \right) \!\times\! \left( -4 \right)} \right] \!+\! \left[ {\left( -21 \right) \!\times\! \left( -6 \right)} \right]\end{align}\)

 Video Solution
Integers
Ex 1.3 | Question 2

Text Solution

Steps:

a)
\(18 \!\times\![ 7 + (-3)]= [ 18\times 7]\!+\! [ 18 \times(-3)]\)

L.H.S

\[\begin{align} &= 18 \times [ {{\rm{ 7 + }}\left( {{\rm{-3}}} \right)}]\left(\text{Open brackets} \right)\\&= {\rm{ }}18 \times {\rm{ }}4 \\&= 72\end{align}\]

R.H.S

\[\begin{align} &=[ 18\!\times\!7] \!+\![18 \!\times\!(-3)](\text{Open brackets})\\&= [18 \times7 ] + [ 18 \times (-3)]\\&= 126 + \left( {-54} \right) \\&= 72\end{align}\]

\[\begin{align}18 \!\times\![7 +( -3)] &\!=\! [18 \times 7] \!+\! [18 \!\times \!(-3)]\\72 &\!=\! 72\\\rm{L.H.S} &\!=\! \rm{R.H.S}\text{(Hence verified)}\end{align}\]

b)
\[\begin{align}&{\rm{}}(-21) \times [ (-4) + ( -6)] \\&= [(-21) \times(-4)] + [(-21) \times(-6)]\end{align}\]

L.H.S
\[\begin{align} &= (-21)\!\times\![(-4) \!+\! ( -6)](\text{Open brackets})\\&=[-21 \times(- 4 - 6)]\\&= - 21 \times  - 10 \\&= 210\end{align}\]

R.H.S
 \[\begin{align}&=[(-21)  \times(-4)]  +[(-21)\times(-6)]\\&= {\rm{ }}\left[ {-21 \times -4} \right]{\rm{ }} + {\rm{ }}\left[ {-21{\rm{ }} \times {\rm{ }}-6} \right]\\&= {\rm{ }}\left[ {84} \right]{\rm{ }} + {\rm{ }}\left[ {126} \right]\\& = 210\end{align}\]

\[\begin{align}\left( {-21} \right) \times \left[ {\left( {-4} \right) + \left( {-6} \right)} \right] &= \,\left[ {\left( {-21} \right) \times \left( {-4} \right)} \right] + \left[ {\left( {-21} \right){\rm{ }} \times {\rm{ }}\left( {-6} \right)} \right]\\210\, &= \,210\\
{\rm{L.H.S}}\,{\rm{ }}&= {\rm{R.H.S}}\text{(Hence verified.)}\end{align}\]

 

  
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