7th Grade Math: Understanding Ratios

Ratios in Math

A ratio tells you the relationship between two quantities. For instance, if you run 11 miles every two hours, that's a ratio of 11:2 or 11/2. If your plant grows two centimeters every three days, then the ratio of centimeters to days would be 2:3 or 2/3.

Unit Rates

In word problems, you'll often be asked to calculate unit rates from ratios. Examples of unit rates are cost per item and miles per hour. Unit rates are a simpler way to express ratio relationships, because they tell you the quantity per unit. For instance, if you know that a car travels 120 miles every two hours, the ratio would be 120:2 or 120/2. However, it would be much simpler to calculate a unit rate that tells you how many miles the car travels per hour.

To calculate unit rates, divide the top number in the ratio (or the number on the left) by the bottom number (or the number on the right). In this example, you would divide 120 by two to get 60 (120 ÷ 2 = 60). This means that the car is traveling 60 miles per hour. The number representing the units you'd like to state your answer in should always be on the bottom.

Proportional Relationships

A proportional relationship occurs when a change in one quantity always results in a change in another quantity. For instance, if you're buying cookies for a party, and they cost $0.50 each, then the total cost of the cookies increases by $0.50 for every additional cookie that you buy. If a car uses exactly one gallon of fuel for every 30 miles that it travels, this would also be a proportional relationship. Keep reading to learn some ways to identify proportional relationships.

Graphs

If you're given a graph of the relationship between two things, you can tell visually if there's a proportional relationship. If so, then every one unit change on the x-axis produces the same amount of change on the y-axis, and the line will be straight.

Multiples

If you're given two ratios and are asked to tell if they're proportional, you'll need to use your knowledge of multiples. Use the following steps:

1. Write the ratios as fractions. Label the top left number 'A,' the top right number 'B,' the bottom left number 'C' and the bottom right number 'D.'
2. Compare A and B, and identify which one is larger. Then, compare C with D. If the numbers in one ratio are larger than their counterparts in the other ratio, then the two ratios may be proportional.
3. Find a number that you can multiply by the smaller of A or B to get its counterpart. If the larger number isn't a multiple of the smaller one, then the two ratios are not proportional.
4. Multiply the smaller of C or D by the number you found in step three. If the product is its counterpart, then the two ratios have a proportional relationship.

For instance, 2/3 and 6/9 are proportional because you can multiply the numerator and denominator of 2/3 by three to get 6/9 (2/3 x 3/3 = 6/9). However, 2/3 and 4/5 are not proportional because you cannot multiply the numerator and the denominator by the same number to get 4/5. In other words, three is not a multiple of five.