1. 7 Math – Ratios and Rates

2. Vocabulary Ratio – Comparing THINGS using division
ex. apples to oranges (apples : oranges)
ex. teachers to students (teachers : students)
Rate – Ratio of two different units of MEASUREMENT
ex. miles per gallon
ex. Babysitter cost per hour
Unit Rate – A rate with a denominator of 1
ex. $2.49/1 gallon of gas
Complex Fraction – A fraction in the numerator, denominator, or both when finding a ratio or rate
ex. I paid my babysitter $ for 8 ½ hours of work. What is her rate per hour cost?

3. Ratios
To find ratios, place the FIRST item in question in the numerator spot of a fraction. Place the SECOND item in question in the denominator spot of a fraction.
ex. There are 5 boys in the class and 7 girls. What is the ratio of boys to girls in class?
boys = 5 = The ratio of boys to girls is 5/7
girls 7
Let’s come up with a ratio question together.

4. Rates
The same as ratios, place the first item that is mentioned in the numerator location of the fraction.
ex. The Hogwarts train travels 112 miles in 65 minutes. What is the speed of the Hogwarts train?
Let’s come up with a rate question together.

5. Ratio Tables
The table below shows the average height (in feet) for Redwood tree growth compared to the tree’s age.
Use the first ratio in the table to find the rate of growth.
5/10 = 1/2 = for every 1 year in age, it grows 2 feet in height
5 = age; 10 = height
***TIP! This can be shown in graph form, too!
Tree Height 10 20 40 80
Tree Age 5

6. Gingerbread Cookies!
My son wants to make a BIG batch of gingerbread cookies. I’ll need 15 cups of gingerbread dough. The recipe calls for 1/2 tablespoon of ginger for every 3/4 cups of flour. How much ginger and how much flour will I have to use?
Ginger
Flour
Dough
1/2
3/4
½ + ¾ = 5/4 2 3 5 6 9 15