Question

Determine what you would need to multiplyby in order to Clear the Equation of fractions?(Least Common Multiple)

Answer 1

hello

to clear the fraction, we need to multiply through a certain number

$\frac{2}{3}x\text{ }+\text{ }\frac{4}{5}\text{ }=\text{ }\frac{7}{2}$

to clear the fraction, we could easily multiply through the denominator and get the answer to multply through the fraction i.e 3 * 5 * 2

$3\times\text{ 5}\times\text{ 2}=\text{ 30}$

we'll now multiply through the whole equation by 30 to clear the fraction

$\begin{gathered} (30\text{ }\times\text{ }\frac{2}{3})\text{ }+\text{ (30}\times\text{ }\frac{4}{5})\text{ = }\frac{7}{2}\text{ }\times\text{ 30} \\ 20x\text{ }+\text{ 24 = 105} \end{gathered}$

i'll go ahead and finish solving the question by solving for x

20x + 24 = 105

to solve this, we'll collect liketerms and the divde through to solve for x

$\begin{gathered} 20x\text{ }+\text{ 24 = 105} \\ \text{collect like terms} \\ 20x\text{ = 105 }-\text{ 24} \\ 20x\text{ = 81} \\ \text{divide through by x} \\ x\text{ }=\text{ }\frac{81}{20} \\ x\text{ = 4.05} \end{gathered}$

the number to multiply through to clear the fraction is 30