Ratio - The comparison of two positive numbers.
Rate - A ratio of two quantities (different units).
Unit Rate - A rate that describes how many units of the first quantity corresponds
to one unit of the second type of quantity.
Proportion - Two equal ratios.
Constant of Proportionality - The unique number (𝑘) that describes the
multiplicative relationship between two quantities, 𝑥 and 𝑦.
Complex Fraction - A fraction where either the numerator, denominator,
or both are fractions.
Independent Variable - The variable that is subject to choice and
is not influenced by another variable.
Dependent Variable - Relies on the values of the independent variable.
Similar Figures - Figures that have the same shape but not the same size.
Scale Drawing - A reduced or enlarged drawing of an original drawing.
All lengths between points or figures in the drawing are
proportional to the lengths in the actual picture.
Scale Factor - Gives the ratio of what the scale drawing represents
in relation to the actual object.
 There are three ways to write a ratio: in words, as a fraction, and with a colon.
▪ 3 to 5
Example:
▪
3
▪ 3:5
5
 Know how to write a ratio as a fraction in simplest form.
Example: There are 10 boys and 15 girls. Write the ratio of boys to girls in simplest form.
Answer:
10
15
=
2
3
Example: There are 10 boys and 15 girls. Write the ratio of boys to total number of kids in
simplest form.
Answer:
10
25
=
2
5
 Know how to find the rate/unit rate in a given problem. Be able to compare unit rates
or unit prices.
Example: 4 pairs of pants are $24 
$24
4 pairs
Example: 10 inches of snow in 2 hours 

$6
1 pair
10 inches
2 hours

or $6/pair of pants
5 inches
1 hour
or 5 in/hr
 If two ratios are equal (proportional), then their cross-products are equal.
Example:
Example:
 Analyze word problems, pick out the necessary information, and form a proportion in
order to solve the question.
Example: Jaycee bought 8 gallons of gas for $31.12. How much would Jaycee pay for 11 gallons?
Answer:
$31.12
8 gallons
=
𝑥
11 gallons
 Understand how to find missing values on a table if it is a proportional relationship.
Understand how to determine if a table shows a proportional relationship.
 Identify whether a graph shows a proportional relationship or not.
o Straight line
and
o Goes through the origin (0, 0)
 Be able to identify a constant of proportionality (𝒌) from a table or graph.
To find the constant of proportionality, we divide:
𝒚
𝒙
If a relationship does not have a constant of proportionality, it is not a proportional
relationship.
Understand that the unit rate is the same as the constant of proportionality.
The unit rate/constant of proportionality can be found on a graph at the point (1, 𝑘).
 Be able to create an equation using the constant of proportionality in the form 𝒚 = 𝒌𝒙.
Example: If you find 𝑘 = 3, then the equation of the line is 𝑦 = 3𝑥.
 Complex fractions can be rewritten as division problems.
1⁄ miles
Example: 1 2
⁄ hours
3
=
1
2
÷
1
3
=
1
2
×
3
1
=
3
2
1
or 1 2 miles/hour
 Dimensional Analysis - You can convert one rate to an equivalent rate by multiplying
by a unit ratio or its reciprocal. When you convert rates, you include the units in your
computation.
Example: If an object is traveling at a rate of 10 feet per second,
how many inches is it going per second?
Answer:
10 feet
1 second
∙
12 inches
1 foot
=
10∙12 inches
1∙1 second
=
120 inches
1 second
or 120 inches/second
 Know that similar figures have corresponding sides that are proportional to each other.
Example:
Answer:
12 x
=
10 5
or
12 10
=
𝑥
5
 A scale drawing can be used to reduce or enlarge a figure from the actual size.
A constant of proportionality (also called the scale factor) exists between
corresponding lengths of the two images. If this does not exist, the drawing is not a
true scale drawing.
Example: Is the second picture a
scale drawing of the first?
Example: Find the distance between Riverside and
Milton if they are 12 cm apart on a map
with a scale of 4 cm : 21 km.
4 cm
21 km
=
12 cm
𝑥