Question

simplify the following with explaination :)​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• $\sf \bigg[ \bigg(\dfrac{3}{4} \: - \: \dfrac{2}{3} \bigg) \div \dfrac{1}{4} \bigg] \: * \: 21$

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Simplify it.

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• $\sf \bigg[ \bigg(\dfrac{3}{4} \: - \: \dfrac{2}{3} \bigg) \div \dfrac{1}{4} \bigg] \: * \: 21$

First,

Let's simply inside ( ),

• $\sf \bigg[ \bigg(\dfrac{3}{4} \: - \: \dfrac{2}{3} \bigg) \div \dfrac{1}{4} \bigg] \: * \: 21$

Taking LCM,

• $\sf \bigg[ \bigg(\dfrac{3 \: * \: 3}{4 \: * \: 3} \: - \: \dfrac{2 \: * \: 4}{3 \: * \: 4} \bigg) \div \dfrac{1}{4} \bigg] \: * \: 21$

• $\sf \Big[ \Big(\dfrac{9}{12} \: - \: \dfrac{8}{12} \Big) \div \dfrac{1}{4} \Big] \: * \: 21$

• $\sf \Big[ \Big(\dfrac{1}{12} \Big) \div \dfrac{1}{4} \Big] \: * \: 21$

Now,

• ÷ symbol will become * and $\sf \dfrac{1}{4}$ will become it's reciprocal i.e $\sf \dfrac{4}{1}$

Continuing,

• $\sf \Bigg[ \dfrac{1}{\dfrac{12}{\dfrac{1}{4}}} \Bigg] \: * \: 21$

• $\sf \bigg[ \dfrac{1}{12} \: * \: \dfrac{4}{1} \bigg] \: * \: 21$

• $\sf \bigg[ \dfrac{1}{12} \: * \: 4 \bigg] \: * \: 21$

• $\sf \bigg[ \dfrac{1}{\cancel{12}^{\large{3}}} \: * \: \cancel{4}^{\large{1}} \bigg] \: * \: 21$

• $\sf \bigg[ \dfrac{1}{3} \bigg] \: * \: 21$

• $\sf \dfrac{1}{3} \: * \: 21$

• $\sf \dfrac{1}{\cancel{3}^{\large{1}}} \: * \: \cancel{21}^{\large{7}}$

• $\sf 1 \: * \: 7$

• $\sf 7$

Therefore,

• Answer = 7.

Answer 2

Answer:

[(3/4-2/3)/1/4] *21

= [(9-8)/12 * 4/1] *21

= (1/12*4) *21

= 1/3 * 21

= 7