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
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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
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[tex] \Large {\underline { \sf {Answer :}}}[/tex]
[tex] \longrightarrow\underline{ \boxed{\sf { Required \; Number = \dfrac{10}{11}}} } [/tex]
[tex] \Large {\underline { \sf {Clarification :}}}[/tex]
Here, we are asked to find the number which should be multiplied with the sum of [tex] \sf{ \dfrac{-2}{9} } [/tex] and [tex] \sf{ \dfrac{-4}{15} } [/tex] to get [tex] \sf{ \dfrac{-20}{15} } [/tex].
Required Steps :
• Step 1 : Firstly, we'll calculate the sum of [tex] \sf{ \dfrac{-2}{9} } [/tex] and [tex] \sf{ \dfrac{-4}{15} } [/tex] by adding these two fractions.
• Step 2 : Then, we'll assume the the number which should be multiplied with the sum of [tex] \sf{ \dfrac{-2}{9} } [/tex] and [tex] \sf{ \dfrac{-4}{15} } [/tex] to get [tex] \sf{ \dfrac{-20}{15} } [/tex] 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
[tex] \Large {\underline { \sf {Explication \; of \; steps :}}}[/tex]
★ Find the sum of -2/9 and -4/15 :
[tex] \longrightarrow \sf { \dfrac{-2}{9} + \dfrac{-4}{15} } [/tex]
L.C.M of 9 and 15 is 45.
[tex] \longrightarrow \sf { \dfrac{-10 +(-12) }{45} } [/tex]
Removing the brackets in the numerator.
[tex] \longrightarrow \sf { \dfrac{-10 -12 }{45} } [/tex]
[tex] \longrightarrow \sf { \dfrac{-22 }{45} } [/tex]
Therefore, sum of [tex] \sf{ \dfrac{-2}{9} } [/tex] and [tex] \sf{ \dfrac{-4}{15} } [/tex] is [tex] \sf{ \dfrac{-22}{45} } [/tex].
Now, let the number which should be multiplied with the sum of [tex] \sf{ \dfrac{-2}{9} } [/tex] and [tex] \sf{ \dfrac{-4}{15} } [/tex] to get [tex] \sf{ \dfrac{-20}{15} } [/tex] be x.
★ According to the question :
[tex] \longrightarrow \sf { \dfrac{-22 }{45} \times x = \dfrac{-20}{45}} [/tex]
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.
[tex] \longrightarrow \sf { x = \dfrac{-20}{45} \div \dfrac{-22 }{45}} [/tex]
[tex] \longrightarrow \sf { x = \dfrac{-20}{ \cancel{45}} \times \dfrac{ \cancel{45} }{-22}} [/tex]
[tex] \longrightarrow \sf { x = \dfrac{-20}{-22} } [/tex]
[tex] \longrightarrow \sf { x = + \dfrac{20}{22} } [/tex]
[tex] \longrightarrow\underline{ \boxed{\sf { x = \dfrac{10}{11}}} } \; \bigstar [/tex]
[tex] \therefore[/tex] The required number is 10/11.