Question

what is the common denominator of this equation y/7+3y/3-2/7=5/14y

Answer 1

To find the common denominator of the equation

\[
\frac{y}{7} + \frac{3y}{3} - \frac{2}{7} = \frac{5}{14}y,
\]

let's first identify the denominators present in the equation:

1. The denominators are \(7\), \(3\), and \(14\).

Next, we need to find the least common multiple (LCM) of these denominators to use as the common denominator.

- The multiples of \(7\): 7, 14, 21, 28, ...
- The multiples of \(3\): 3, 6, 9, 12, 15, 18, 21, 24, ...
- The multiples of \(14\): 14, 28, 42, ...

The smallest common multiple of \(7\), \(3\), and \(14\) is \(42\).

Therefore, the common denominator for the equation is \(42\).

Now, if we want to solve the equation using this common denominator, we can multiply every term by \(42\) to eliminate the denominators:

\[
42\left(\frac{y}{7}\right) + 42\left(\frac{3y}{3}\right) - 42\left(\frac{2}{7}\right) = 42\left(\frac{5}{14}y\right)
\]

This will give us a simpler equation to work with.