Question

What number should be multiplied with the sum of -2/9 and -4/15 to get -20/45.



Please find the answers.
please write the steps too​

Answer 1

$\Large {\underline { \sf {Answer :}}}$

$\longrightarrow\underline{ \boxed{\sf { Required \; Number = \dfrac{10}{11}}} }$

$\Large {\underline { \sf {Clarification :}}}$

Here, we are asked to find the number which should be multiplied with the sum of $\sf{ \dfrac{-2}{9} }$ and $\sf{ \dfrac{-4}{15} }$ to get $\sf{ \dfrac{-20}{15} }$.

Required Steps :

• Step 1 : Firstly, we'll calculate the sum of $\sf{ \dfrac{-2}{9} }$ and $\sf{ \dfrac{-4}{15} }$ by adding these two fractions.

• Step 2 : Then, we'll assume the the number which should be multiplied with the sum of $\sf{ \dfrac{-2}{9} }$ and $\sf{ \dfrac{-4}{15} }$ to get $\sf{ \dfrac{-20}{15} }$ as x.

• Step 3 : Then, we'll form a linear equation.

• Step 4 : By using transposition method, we'll solve for x and will find the required number.

⠀⠀⠀⠀Transposition Method

• This is the method used to solve a linear equation having variables and constants.

• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\Large {\underline { \sf {Explication \; of \; steps :}}}$

★ Find the sum of -2/9 and -4/15 :

$\longrightarrow \sf { \dfrac{-2}{9} + \dfrac{-4}{15} }$

L.C.M of 9 and 15 is 45.

$\longrightarrow \sf { \dfrac{-10 +(-12) }{45} }$

Removing the brackets in the numerator.

• (+) × (-) = (-)

$\longrightarrow \sf { \dfrac{-10 -12 }{45} }$

$\longrightarrow \sf { \dfrac{-22 }{45} }$

Therefore, sum of $\sf{ \dfrac{-2}{9} }$ and $\sf{ \dfrac{-4}{15} }$ is $\sf{ \dfrac{-22}{45} }$.

Now, let the number which should be multiplied with the sum of $\sf{ \dfrac{-2}{9} }$ and $\sf{ \dfrac{-4}{15} }$ to get $\sf{ \dfrac{-20}{15} }$ be x.

★ According to the question :

$\longrightarrow \sf { \dfrac{-22 }{45} \times x = \dfrac{-20}{45}}$

Transposing -22/45 from L.H.S to R.H.S, as it is in the form of multiplication in L.H.S, it will become in the form of division in R.H.S.

$\longrightarrow \sf { x = \dfrac{-20}{45} \div \dfrac{-22 }{45}}$

$\longrightarrow \sf { x = \dfrac{-20}{ \cancel{45}} \times \dfrac{ \cancel{45} }{-22}}$

$\longrightarrow \sf { x = \dfrac{-20}{-22} }$

• (–) ÷ (–) = (+)

$\longrightarrow \sf { x = + \dfrac{20}{22} }$

$\longrightarrow\underline{ \boxed{\sf { x = \dfrac{10}{11}}} } \; \bigstar$

$\therefore$ The required number is 10/11.