What should the following equation be multiplied by in order to eliminate the fractions?

Question

2y/3+1/3=y/2+1/6

6

9

5

25

Answer 1

To eliminate the fractions in the equation

\[ \frac{2y}{3} + \frac{1}{3} = \frac{y}{2} + \frac{1}{6}, \]

we need to find the least common multiple (LCM) of the denominators present: 3, 2, and 6.

The LCM of 3, 2, and 6 is 6. Therefore, we can multiply both sides of the equation by 6 to eliminate the fractions.

Let's verify this:

1. Multiply each term by 6:
   • \( 6 \cdot \frac{2y}{3} = 4y \)
   • \( 6 \cdot \frac{1}{3} = 2 \)
   • \( 6 \cdot \frac{y}{2} = 3y \)
   • \( 6 \cdot \frac{1}{6} = 1 \)

So the equation becomes:

\[ 4y + 2 = 3y + 1. \]

Thus, the answer is 6.