# Ex.1.3 Q5 Integers Solution - NCERT Maths Class 7

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## Question

Find the product, using suitable properties: –

a) $$26 × (–48) + (–48) × (–36)$$

b) $$8× 53 × (–125)$$

c) $$15× (–25) × ( –4) × (–10)$$

d) $$(–41) × 102$$

e) $$625 ×–35 × (–625) × 65$$

f) $$7 × (50–2)$$

g) $$(–17) × (–29)$$

h) $$(–57) × (–19) + 57$$

Video Solution
Integers
Ex 1.3 | Question 5

## Text Solution

Steps:

(a) $${{26 \times }}\left( {{\rm{-48}}} \right)\,{\rm{ + }}\left( {{\rm{-48}}} \right){\rm{ \times }}\left( {{\rm{-36}}} \right)$$

Using distributive property, we get

\begin{align}{{{(a}}\,{ \times b)}}\,\,{{ + }}\,\,{{(b}}\,{{ \times }}\,{{c)}}\,&= \,{{b \times }}\,{{(a + c)}}\\ \,\,&=\,{{(}} - {{48)}}\,\,{{ \times }}\,{{[26}}\,{{ + }}\,{{(}} - {{36)]}}\\ \,\, &= \,{{(}} - {{48)}}\,\,{{ \times }}\,\,{{[26}} - {{36]}}\\\,\,&=\,{{(}} - {{48)}}\,\,{{ \times }}\,{{ [(}} - {{10)]}}\\&=\,{{480}}\end{align}

(b) $${{8 \times 53 \times }}\left( {{\rm{-125}}} \right)$$

Using associative property, we get

\begin{align}({a \times b}) \times c &= a \times ( {b \times c})\\&= 8 \times 53 \times \left( {-125} \right)\\ &= 8 \times -6625\\ &= -53000\end{align}

(c) $${{}}\,\,\,15 \times \left( {-25} \right) \times \left( {-4} \right) \times \left( {-10} \right)$$

Using associative property, we get

\begin{align} &= 15 \times \left[ {\left( {-25} \right) \times \left( {-4} \right) \times \left( {-10} \right)} \right]\\ &= 15 \times \left[ {100 \times \left( {-10} \right)} \right]\\ &= 15 \times \left[ {1000} \right]\\ &= -15000\end{align}

(d) $${\rm{}}\left( {-41} \right){\rm{ }} \times {\rm{ }}102$$

Using distributive law, we get

\begin{align}&=\,{{(}} - {{41)}}\,{{ \times }}\,{{(100}}\,{{ + }}\,{{2)}}\dots\,{{[a}}\,{{ \times }}\,{{(b}}\,{{ + }}\,{{c)}}]=\,{{(a}}\,{{ \times }}\,{{b}}\,{{ + }}\,{{a}}\,{{ \times }}\,{{c)]}}\\&={{{(}} - {{41)}}\,{{ \times }}\,{{100}}\,{{ + }}\,{{(}}\, - {{41) \times }}\,{{2}}}\\&= - {{4100}}\, - {{82}}\\&=\, - {{4182}}\end{align}

(e) $${{625}}\,{{ \times }}\left( {{{-35}}} \right){{ + }}\left( {{{-}}\,{{625}}} \right){{ \times }}\,{{65}}$$

Using distributive property, we get

\begin{align} &=\,{625}\,\times[{ (}-{35)}\,{+}\,{(}-{65) }]\,{ }\dots[{ a\times b}\,{+}\,{a\times c}\,{=}\,{a(b+c) }] \\ &=\,{625}\times[\,-{35}\,-{65 }] \\ &=\,{625}\times[-{100 }] \\ &={-62500} \\\end{align}

(f) $$7\times \left( 50-2 \right)$$

Using distributive property, we get

\begin{align}&=7\times { }\,{(50}-{2)}\,{ }\dots[{ a\times}\,{ }{ }\,{(b}-{c)}\,{=}\,{a }\times{ b}-{a }\times{ c }]{ } \\ &=7\times { 50}-{7 }\times { 2} \\ &=350-{14} \\ &=336\end{align}

(g) $$\left( \text{-17} \right)\text{ }\!\!\times\!\!\text{ }\left( \text{-29} \right)$$

Using distributive property, we get

\begin{align} &= \,( - 17)\, \times \,\,[( - 30)\, + 1]\dots[a\, \times \,(b\, + \,c)={a\times b}+{a \times c}]\\ &= \,( - 17)\, \times \,( - 30)\, + \,( - 17)\, \times 1\\ &= \,510\, + ( - 17)\\ &= \,510 - 17\\ &=\,493\end{align}

(h)$${{}}\left( {-57} \right) \times \left( {-19} \right) + 57$$

Using distributive property, we get

\begin{align}&={{{ }} \,\left( { - {{57}}} \right){{ \times (}} - {{19) + 57\,\, 1[a \times b}}\,{{ + }}\,{{a \times c}}\,\,={{ }}\,{{a \times (b + c)]}}}\\&={{{ }}\,{{57 \times 19 + 57 \times 1}}}\\&={{{ }}\,{{57 \times (19 + 1)}}}\\&={{{ }}\,{{57 \times 20}}}\\&={{{ 1140}}}\end{align}

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