Question

What should the following equation be multiplied by in order to eliminate the fractions?2y/3+1/3=y/2+1/6

Answer 1

Answer:

The equation should be multiplied by 6

Step-by-step explanation:

Given:

`(2y)/(3)\text{ + }(1)/(3)\text{ = }(y)/(2)\text{ + }(1)/(6)`

To find:

the number to be multiplied by the given equation to eliminate the fractions

To eliminate the fractions, we need to eliminate the denominators. This will be done using LCM of the denominators

`\begin{gathered} On\text{ the right side, the LCM = 3} \\ On\text{ the left side, the LCM}=\text{ 6} \\ We\text{ need to elimnate both denominators, so the LCM for both will be 6} \\ \\ Multiply\text{ both sides by 6:} \\ 6((2y)/(3))\text{ + 6\lparen}(1)/(3))\text{ = 6\lparen}(y)/(2))\text{ + 6\lparen}(1)/(6)) \end{gathered}`
`\begin{gathered} 4y\text{ + 2y = 3y + 1} \\ 6y\text{ = 3y + 1} \\ As\text{ we can see there is no more fraction} \\ \\ Hence,\text{ the equation should multiplied by 6} \end{gathered}`