1. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is a “ratio”? How do you write a ratio?
ratio: a comparison of two numbers by division – There are three ways to compare two numbers: a to b a : b You can write a ratio to compare a part to a part or part to a whole. The first item being compared is always the first number and the second item being compared is the second number of the ratio. Example: A recipe calls for 4 cups of cereal and 2 cups of pretzels. Write this as a ratio. a b
read as “to”

2. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is a “rate”? What is a “unit rate”?
rate: a ratio that compares two quantities measured in different units. Example: is read as “120 miles ‘per’ or ‘each’ 4 hours” unit rate: the rate in which the denominator is 1 (rate ‘per’ 1 unit of a given quantity) - Unit rate is used in everyday life to determine the best value. It can be found by simplifying the fraction to a denominator of “1” or simply dividing the numerator (top number) by the denominator (bottom number. Example: = or 120  4 = 30 mph The above unit rate is read as “30 miles ‘per’ hour” (30 m/h or 30 mph)
120 miles
4 hours
120 miles
4 hours
 4
30 miles
1 hours

3. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is an Equivalent Ratio?
Remember……
Write the ratios as fractions.
Compare the two fractions to see
Multiply both sides by 3 × 18
Simplify
2:3 and 10:18
Two ratios are equivalent if their cross products are equal.
The cross products are not equal, so the ratios are not equivalent.

4. h What is a constant? What is a variable? Proportion Table?
Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is a constant?
What is a variable?
Proportion Table?
constant: a term that has no variable
Examples: 5, 104
h p h
Proportional quantities have a constant ratio. This constant ratio is called the constant of variation. The constant of variation often represents a rate or a cost.

5. The constant of variation is 1. The cost is $1 per guest.
Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is the cost per guest? The constant of variation, which often represents a rate or a cost, will tell you the answer. To find the constant of variation, divide "Cost" by "Guests".
The constant of variation is 1. The cost is $1 per guest.
Coordinate Plane
Ratios Table

6. Start at the origin.
The x-coordinate is -4 .
Since the x-coordinate is negative, count four units to the left.

7. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
What is a “proportion”? What is the “extremes of the proportion”? What is the “means of the proportion”? What are “cross products”? Why do “cross products” work?
proportion: equal ratios (in other words, equal fractions) Example: extremes of the proportion: the first cross product of a proportion. In the above proportion, the “extremes of the proportion” are a and d. means of the proportion: the second cross product of a proportion. In the above proportion, the “extremes of the proportion” are b and c. cross products: the product of the means equals the product of the extremes (in the above example, ad = bc). Rule: ad = bc Example: Show that = . a b c d
for b ≠ 0 and d ≠ 0 = 4 5 12 15
60 = 60 

8. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
POTD
Find each unit rate.
1. You pay $4.50 for 2 gallons of orange juice.
2. You pay $21.60 for a 20-lb bag of dog food.
3. A bird flies at a speed of 384 in./s. What is its
speed in units of ft/min?
4. A job takes 96 person-days. How many
workers are needed to complete the job in
24 days?
$2.25/gal
$1.08/lb
1,920 ft/min 4

9. Does each pair of ratios form a proportion? Explain. 3. 4.
Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
Lesson Quiz
Solve each proportion.
1. 2.
Does each pair of ratios form a proportion? Explain.
3. 4.
nautical miles equals about 115 statute miles. About how far in nautical miles is 50 statute miles? Round to the nearest whole number. a 12 5 6 3 8 6 x = 10 = 16 2 9
0.4
1.8 21 50 14 25 = =
Yes; the cross products are equal.
No; the cross products are not equal.
about 43 nautical miles

10. Module 1: Ratios and Proportional Relationships: Topic A: Proportional Relationships
Solve.
1. Parallelogram ABCD ~ parallelogram EFGH.
Find the value of x.
2. A girl who is 4 feet tall casts a shadow that is 6 feet long. The tree next to her casts a shadow that is 12 feet long. How tall is the tree?
3. The scale on a map is 3 in. : 100 mi. What is the actual distance between two towns that are 9 in. apart on the map? 12
8 ft
300 mi