Question

answers of all questions with full working correctly​

Answer 1

$\large\sf\underline{Question\:1\::}$

• Divide the sum of $\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ by their difference .

‎

‎

$\large\sf\underline{Solution\::}$

$\small{\mathfrak{1^{st}\:step\:-}}$

Sum of $\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ .

$\sf\longmapsto\:\frac{65}{12} + \frac{12}{7}$

• LCM of 12 and 7 = 87

$\sf\longmapsto\:\frac{(65 \times 7)+(12 \times 12)}{84}$

• Multiplying the terms in numerator

$\sf\longmapsto\:\frac{455+144}{84}$

• Adding the terms in numerator

$\sf\longmapsto\:\frac{599}{84}$ ☆

‎

$\small{\mathfrak{2^{nd}\:step\:-}}$

Difference of $\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ .

$\sf\longmapsto\:\frac{65}{12} - \frac{12}{7}$

• LCM of 12 and 7 = 87

$\sf\longmapsto\:\frac{(65 \times 7)-(12 \times 12)}{84}$

• Multiplying the terms in numerator

$\sf\longmapsto\:\frac{455-144}{84}$

• Subtracting the terms in numerator

$\sf\longmapsto\:\frac{311}{84}$ ☆

‎

‎ $\small{\mathfrak{3^{rd}\:step\:-}}$

Dividing the sum of $\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ by their difference .

• Sum of$\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ = $\sf\:\frac{599}{84}$

• Difference of $\sf\:\frac{65}{12}$ and $\sf\:\frac{12}{7}$ = $\sf\:\frac{311}{84}$

Dividing them :

$\sf\longmapsto\:\frac{599}{84} \div \frac{311}{84}$

$\sf\longmapsto\:\frac{599}{\cancel{84}} \times \frac{\cancel{84}}{311}$

$\small{\underline{\boxed{\mathrm\pink{⟼\:\frac{599}{311}}}}}$ ★

_________________________

$\large\sf\underline{Question\:2\::}$

• The sum of the addictive inverse and multiplicative inverse of $\sf\:\frac{1}{5}$ is ?

‎

$\large\sf\underline{Solution\::}$

• Addictive inverse of $\sf\:\frac{1}{5}$ = $\sf\:\frac{-1}{5}$

• Multiplicative inverse of $\sf\:\frac{1}{5}$ = $\sf\:5$

Their sum :

$\sf\longmapsto\:\frac{-1}{5}+5$

• LCM of 5 and 1 = 5

$\sf\longmapsto\:\frac{-1+(5 \times 5)}{5}$

• Multiplying the terms in numerator

$\sf\longmapsto\:\frac{-1+25}{5}$

• Subtracting the terms in numerator

$\small{\underline{\boxed{\mathrm\pink{⟼\:\frac{24}{5}}}}}$ ★

‎ _________________________

$\large\sf\underline{Question\:3\::}$

• The product of two rational numbers is $\sf\:\frac{-28}{81}$ . If obe of the number is $\sf\:\frac{14}{27}$ , then find the other number.

‎

$\large\sf\underline{Solution\::}$

Let the other number be x.

So according to the question :

$\sf\longmapsto\:\frac{14}{27} \times x =\frac{-28}{81}$

$\sf\longmapsto\:\frac{14x}{27} =\frac{-28}{81}$

• Cross multiplying

$\sf\longmapsto\:14x \times 81 =-28 \times 27$

• Multiplying the terms

$\sf\longmapsto\:1134x =-756$

• Transposing 1134 to the other side

$\sf\longmapsto\:x =\cancel{\frac{-756}{1134}}$

$\small{\underline{\boxed{\mathrm\pink{⟼\:x\:=\frac{-2}{3}}}}}$ ★

‎ _________________________

$\large\sf\underline{Question\:4\::}$

• If a = 7 , then the value of $\sf\:-[\frac{1-2a}{a-5}]$ is ______

‎

$\large\sf\underline{Solution\::}$

$\sf\longmapsto\:-[\frac{1-2a}{a-5}]$

• Substituiting the value of a as 7

$\sf\longmapsto\:-[\frac{1-2(7)}{7-5}]$

• Simplifying the fraction

$\sf\longmapsto\:-[\frac{1-14}{2}]$

$\sf\longmapsto\:-[\frac{-13}{2}]$

$\small{\underline{\boxed{\mathrm\pink{⟼\:\frac{13}{2}}}}}$ ★

‎ _______________________

$\large\sf\underline{Question\:5\::}$

• The multiplicative inverse of $\sf\:\frac{-a}{b}$ is ___

‎

$\large\sf\underline{Solution\::}$

Multiplicative inverse of a number is a number which when multiplied by the original number given 1 .

So multiplicative inverse of $\sf\:\frac{-a}{b}$ is :

$\small{\underline{\boxed{\mathrm\pink{\frac{-b}{a}}}}}$ ★

Since :

$\sf\longmapsto\:\frac{-a}{b} \times \frac{-b}{a}$

• Multiplying the fraction

$\sf\longmapsto\:\cancel{\frac{ab}{ab}}$

$\sf\longmapsto\:1$

‎

________________________

$\large\sf\underline{Question\:6\::}$

• Which of the following properties of rational numbers is given below ?

$\sf\:\frac{7}{4} \times (\frac{-8}{3} +\frac{-13}{12})=\frac{7}{4} \times \frac{-8}{3} +\frac{7}{4} \times \frac{-13}{12}$

‎

$\large\sf\underline{Solution\::}$

So the given rational number indicates :

$\small{\underline{\boxed{\mathrm\pink{Distribution\:of\:multiplication\:over\:addition.}}}}$ ★

‎

_________________________

$\large\sf\underline{Question\:7\::}$

• If $\sf\:x = \frac{2+3 \times 2}{-5}$ , then find the value of | - x| .

‎

$\large\sf\underline{Solution\::}$

• Simplifying the value of x

$\sf\longmapsto\:x = \frac{2+6}{-5}$

$\sf\longmapsto\:x = \frac{8}{-5}$

So | - x| =$\small{\underline{\boxed{\mathrm\pink{\frac{8}{5}}}}}$ ★