This study guide provides an overview of the topics that will be covered on an upcoming math test: ratios and proportions, unit rates, and similar triangles. It defines key concepts such as ratios, equivalent ratios, simplest form, rates, unit rates, proportions, and similar triangles. Examples are provided to illustrate how to work with and solve each type of problem. The document instructs students on how to write and solve ratios, unit rates, proportions, and use proportions to solve for missing values in similar triangles.

1. Name __________________________________________ Date ____________
Polizzi/Denman/Taylor Math – 6
Study Guide
Math Test
Ratios & Proportions
Topics on Test:
1. Ratios
- equivalent
- simplest form
2. Unit Rates
3. Proportions
4. Similar Triangles
Ratios:
 ratio – a comparison of two quantities; can be written 3 different ways (see below)
Ratio
If there are 5 erasers and 3 pencils,
the ratio of erasers to pencils can be written as:
5
5 to 3, 5:3, or
3
 equivalent ratios – you can find equivalent ratios by multiplying or dividing both quantities
by the same amount
For example:
2 4 6 8 40 20 8 4
x2= x3= x4= 2= 5=  10 =
3 6 9 12 60 30 12 6
 simplest form – when the only common factor of the numerator and denominator is 1.
To write a fraction in simplest form, divide the numerator and denominator by the GCF.
For example: Write 20 in simplest form.
28
The GCF or 20 and 28 is 4. (20: 1, 2, 4, 5, 10, 20)
(28: 1, 2, 4, 7, 14, 28)
Divide the numerator and denominator by 4.
20 ÷ 4 = 5
28 ÷ 4 = 7
Rates:

2.  rate – a comparison of two quantities with different units of measure
Rate
The average Dalmatian can run 15,400 feet
in 5 minutes.
The rate 15,400 feet compares the number of
5 minutes
feet to the number of minutes. This can be read
“15,400 feet per 5 minutes.”
Other examples:
150 heartbeats 16 miles 5 feet
2 minutes 3 hours 12 seconds
 unit rate – a comparison of two quantities when there is only 1 unit
Unit Rate
A typical fire engine can hold 500 gallons of water.
This water is used up in 10 minutes of continuous
spraying. What is the rate of gallons per minute?
The rate that compares 500 gallons with 10 minutes
is 500 gallons
10 minutes.
if you divide both numbers by ten, you get the
unit rate of 50 gallons
1 minute.
Other examples:
$12 = $1.50 6 waves = 0.6 waves
8 pounds 1 pound 10 seconds 1 second
Proportions:
 proportion – a pair of equal ratios; the cross product of the two ratios are equal
Proportion
2 6
5 = 15 5 x 6 = 30 2 x 15 = 30
For 2 ratios, a cross product is the result of
multiplying the top value in one ratio by the
bottom value in the other.
Other examples:
6 feet = 9 feet 6 x 15 = 90 & 10 x 9 = 90 1 cat = 4 cats 1 x 8 = 8 & 2 x 4 = 8
10 seconds 15 seconds 2 dogs 8 dogs
 solving proportions – use cross products to solve proportions
x=3
15 5
Step 1: 5x = 15 x 3 Find the cross products
Step 2: 5x = 45 Multiply
Step 3: x = 9 What number times 5 equals 45?
Another example: 6 = x 8x = 6 x 12 8x = 72 x=9
8 12

3. Similar Triangles:
 similar: figures that have the same shape but not the same size are similar
Example:
Triangle A is similar to triangle B
Triangle A Triangle B
21 18 The triangles are similar, so the matching sides are proportional.
x y
15 5
21 15
= Step 1: Write a proportion using the sides that match each other.
x 5
15x = 21 x 5 Step 2: Write the cross products.
15x = 105 Step 3: Multiply. What number times 15 equals 105?
x = 105  15 Step 4: Use division to undo multiplication.
x=7