To clear the fractions from the equation \( y = \frac{2}{3}x + \frac{1}{4} \), Rahul needs to multiply the entire equation by a number that is a common multiple of the denominators of the fractions present in the equation.
The denominators in the equation are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12. Therefore, Rahul can multiply the entire equation by 12 to eliminate the fractions.
Let's multiply the equation by 12:
\[ 12y = 12 \left(\frac{2}{3}x\right) + 12 \left(\frac{1}{4}\right) \]
Calculating each term gives:
\[ 12y = 8x + 3 \]
Thus, the rewritten equation is:
\[ 8x - 12y + 3 = 0 \]
So, to clear the fractions and rewrite the equation in standard form, Rahul should multiply by 12.
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