Simplifying Ratios

Ratios simplify the same way fractions do. A garden has 15 roses and 20 tulips, so the ratio of roses to tulips is 15 to 20. Write it as a fraction, $\frac{15}{20}$. Both numbers divide by 5, which gives $\frac{3}{4}$: the ratio is 3 to 4.

Why is it the same ratio? The 15 roses and 20 tulips can be planted in 5 equal beds, each with 3 roses and 4 tulips. Every bed has the same mix as the whole garden, so 3 for every 4 describes all of it. Dividing both numbers by the same number never changes the comparison; it just shows it with smaller numbers.

Divide by the greatest common factor and you finish in one step. On the board the ratio is written as a fraction, and you type the simpler fraction as your next line. The board only accepts a finished answer in lowest terms, so if a common factor is left, keep going.