Rates and Ratios Review
Name ______Date ______
Math 7 Notes
Ratios & Proportions:
Ø Ratios are a comparison between two things (usually written as a fraction)
Ø Proportions are two equal ratios
Example 1: There are 40 animals in a pet shop that sells puppies and kittens, and 25 of the animals are puppies. Identity the ratio that is equivalent to the total number of animals to the number of kittens at the pet shop.
1) 8 : 5 2) 5 : 8 3) 8 : 3 4) 5 : 3
Word Problem: à Always write your “word” ratio first when setting up a proportion
Example 2: There are 120 calories in 4 teaspoons of jelly.
How many calories are in 6 teaspoons of jelly?
Rate is a ratio that compares two quantities of different units.
Example 4: Serena is flying to Paris. It takes the plane 7 hours to travel 3,654 miles from New York to Paris. Express this relationship as a rate.
1) 504 mph 2) 511 mph 3) 522 mph 4)26,492 mph
Unit Price & Best Buy:
Unit Price is the cost for one item. Best buy is the item(s) with the lowest unit cost.
Example 5: Find the unit rate for each pack of t-shirts. Which is the better buy?
A 7 pack of t-shirts costs $38.50 A 15 pack of t-shirts costs $78.00
Find the unit rate. Find the unit rate
Constant of Proportionality is the constant ratio, the unit rate
Ø In graph form: y = 4x, the constant of proportionality is ______?
Ø In table form: the constant of proportionality is always:
Example:
Gus types 45 words in 1½ minutes. The table below shows this relationship.
Time (min) / 1.5 / 2.5 / 3.5# of Words / 45 / 75 / 105
What is the value of the constant for this proportional relationship?
Graphing an Equation from a table
Part A:
x / y / (x,y)0
1
2
3
Complete the table for the equation y = 3x.
Part B:
Graph the equation y = 3x on a coordinate plane. Connect the points with a line.
Part C:
Identify the constant of proportionality from the graph. Answer: ______
Name ______Date ______
Math 7 Homework
1. Express the unit price of a notebook that costs $40.00 for a case of 16
1) $0.40
2) $0.60
3) $1.50
4) $2.50
2. A survey was taken at a local deli to determine whether students prefer coffee or tea. There were 178 people that were surveyed and 56 of them said that they prefer tea. What is the ratio of people who prefer coffee to the total number of people surveyed?
3. You can do 90 sit-ups in 2 minutes. Write and solve a proportion to find out how many sit-ups you can do in 3 minutes. Show work below!
Answer: ______
4. Nolan is jogging from his house to Mark’s house. The distance he covers is 2 miles in 27 minutes. Express this relationship as a rate.
5. A billboard is 20 feet in height. The designer used a scale of 0.25 inch on his paper sketch represents 5 feet of actual distance. Which of the following proportions can be used to find x, the height of the billboard on the sketch?
1) =
2) =
3) =
4) =
6) Using the table below, what is the value of the constant for this proportional relationship? Show work below!
Gallons of Gasoline / 3 / 4 / 5 / 9Miles Driven / 18 / 24 / 30 / 54