Question

How do you solve `\frac { a } { 45} = \frac { 3} { 15}`?

Answer 1

Multiply both sides by 45 and you get `a=9`

Explanation:

You can answer this question two ways; one by raising both fractions to the least common denominator and evaluate the numerators directly.

The other option is that you can remove the fraction from the left-hand side (LHS) by multiplying both sides by the denominator in the LHS and evaluating the RHS fraction.

Option 1:

Since 45 is a multiple of 15 (3*15, specifically), you can raise the RHS fraction like so:

`a/45=3/3*3/15 rArr a/45=9/45`

Since both `a` and `9` are using the same denominator, you can conclude that `a=9`.

Option 2:

If you multiply both sides by the denominator in the LHS, you get `a` alone on the LHS:

`a/45*45=3/15*45 rArr a=3/15*45`

We can reduce `3/15` to a lower denominator by dividing the top and bottom by 3, which gives us `1/5`.

Now the equation looks like `a=1/5*45` or `a=45/5`

Evaluating the fraction on the RHS gives us `a=9`