New York City SHSAT 2017

RATIOS, PROPORTIONS, AND RATES

Ratios can be expressed in two forms.

The first form is

If you have 15 dogs and 5 cats, the ratio of dogs to cats is (The ratio of cats to dogs is ) As with any other fraction, this

ratio can be reduced: can be reduced to In other words, for every 3 dogs, there is 1 cat.

The second form is a:b.

The ratio of dogs to cats is 15:5 or 3:1. The ratio of cats to dogs is 5:15 or 1:3.

Make sure that you pay attention to what ratio is specified in the problem. Remember that the ratio of dogs to cats is different from

the ratio of cats to dogs.

To solve a proportion, cross multiply and solve for the variable.

A rate is a ratio that compares quantities measured in different units. The most common example is miles per hour. Use the

following formula for such problems:

Remember that although not all rates are speeds, this formula can be adapted to any rate.

Exercise

Distance = Rate × Time

xii. There are 18 white marbles and 6 red marbles in a bag. What is the ratio of red marbles to white marbles?

xiii. If what is the value of y?