What Is a Ratio?

What is a ratio?

A ratio is a very useful in everyday mathematics (and life) as it compares values. A ratio gives you the relative sizes of two sets but not the actual numbers of objects in those sets.

Sample Problem 2

A room is 16 feet, 6 inches long, and the ratio of the length to the width is 4 to 5. What is the width of the room?

Step #1 for Solving Ratio Problems

Change the quantities to the same units; then reduce the ratio to its simplest form. For example, what is the ratio of 6 minutes to 8 hours? First, change the hours to minutes: 8 hours = 8 × 60 = 480 minutes Write the ratio as a fraction and simplify: 6/480 = 1/80 We found that the ratio of 6 minutes to 8 hours is 1:80

Step #3 for Solving Ratio Problems

Follow the order. Make sure that there are the same items in the numerator and denominator. For example, if the ratio of Olga's classical CDs to her rock CDs is 14 to 25, the right setup is this: - classical/rock = 14/25 This setup is wrong: - classical rock = 25/14

Ratio Example

For example, the fact that the ratio of green marbles to red marbles in a box is 2 to 3 tells us that for every 2 green marbles there are 3 red marbles; however, it does not tell us the number of green or red marbles.

Sample Problem 1

Sample Problem 1 In a bag of blue and yellow candies, the ratio of blue candies to yellow candies is 3:5. If the bag contains 60 yellow candies, how many blue candies are there?

Solution to Sample Problem 1

Step 1: Let the number of blue candies be x. Next, write the items in the ratio as a fraction: blue/yellow = 3/5 = x/60 Step 2: Solve the equation by cross-multiplication: 3 × 60 = 5x 180 = 5x To isolate the variable, x, divide both sides by 5: x = 36 Solution: There are 36 blue candies in the bag.

Solution to Sample Problem 2

Step 1: Since the length is given in both feet and inches, let's convert it to inches using the fact that 1 foot equals 12 inches. 16 feet, 6 inches = (16 × 12) + 6 = 192 + 6 = 198 We found that the length is 198 inches. Step 2: Let x represent the width. We can now set up the equation: WIDTH/LENGTH = 4/5 = X/198 Step 3: Solve the equation by cross-multiplication: 4 × 198 = 5X 792 = 5X Divide both sides by 5: X = 158.4 inches We found that the width is 158.4 inches. Step 4: Convert inches to feet so that the units for the width are consistent with the units for the length. Since 1 foot is 12 inches, we divide 158.4 inches by 12 to find out how many feet are in 158.4 inches: 158.4 ÷ 12 = 13.2. The width is 13.2 feet OR 13 feet, 2.4 inches Solution: The room width is 13 feet, 2.4 inches

Order is Important When Writing a Ratio

The order of terms in a ratio is important. Notice that in the example "the ratio of green marbles to red marbles," the value for the green marbles (2) came first in the ration 2:3. This order is important: whichever word comes first, its number must come first as well.

Step #2 for Solving Ratio Problems

Write the items in the ratio in fraction form.