4-1: Ratio and Proportion
Objectives:
• You will be able to find ratios, rates and unit rates.
• You will be able to solve problems using proportions.
Definitions:
proportions
ratio
A ____________ is a comparison of two numbers using __________________.
a
b
a : b
The ratio of a to b can be written as __________ or _______.
units
If a and b represent quantities measured in different ____________, then the rate
ratio of a to b is called a __________. Examples: 55 mi/hr, 3 tsp/4 hours, 36 inches: 3 feet
rate
unit
1
A __________ __________ is a rate with a denominator of _____.
Example: 55 miles/1 hour, $2.95/1 gallon
Example of Unit Rates:
1. The following table gives prices for different sizes of the same brand of apple juice. Find the unit rate (cost per ounce) for each size bottle.
a. 16 oz.
ratio = unit rate = b. 32 oz.
ratio = unit rate = c. 64 oz.
ratio = unit rate = d. Which size bottle has the lowest cost per ounce?
(Which bottle gives you the most juice for your money?)
Examples of Unit Conversions:
2.
Convert 7 hours into minutes.
3.
4.
Convert 100 yards into inches.
Convert 55 miles per hour into miles per minute.
5.
A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s speed in miles per hour? (Hint: 1 mile = 5280 feet)
Definitions:
proportion
ratios
A ________________ is an equation in which two __________ are equal.
similar
We use the idea of _________ fractions to solve problems with proportions.
multiplication
cross
We solve proportion problems using __________ ___________________.
** ONLY USE CROSS MULTIPLICATION WHEN RATIOS (FRACTIONS) ARE ON OPPOSITE SIDES OF AN EQUATION (THE EQUAL SIGN)!!! **
Examples of Solving Proportions:
6.
8.
7.
9.
Special Note:
When a combination of things are in either the numerator or denominator, parentheses
put ___________________________ around them.
10.
12.
11.
13.
Special Note:
numerators
When solving real­world problems, make sure both ____________________
denominators
have the same units and both ________________________ have the same units.
14. Suppose you walk 2 miles in 35 minutes. a.
Write a proportion to find how far you could walk in one hour if you continued at the same rate.
b.
Solve the proportion.
15. In 2001, Lance Armstrong won the Tour de France, completing the 3454 km course in about 86.3 hours. Traveling at an average speed, how long would it take him to ride 185 km? Round your answer to the nearest tenth.