[Video Placeholder - Introduction to ratios and proportions]
Duration: 6:30
Understanding Ratios
A ratio compares two quantities. It can be written in three ways:
3 parts blue to 2 parts red → 3:2 → 3/2 → "3 to 2"
Example 1: Simplifying Ratios
Simplify the ratio 24:36
Step 1: Find the greatest common factor (GCF) of 24 and 36
GCF is 12
Step 2: Divide both terms by 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Simplified ratio: 2:3
Try it!
Simplify the ratio 45:60
Understanding Rates
A rate compares quantities with different units. Common examples include speed (miles/hour) and price (dollars/pound).
Example 2: Unit Rate
If a car travels 240 miles in 4 hours, what is its speed in miles per hour?
Step 1: Write as a rate: 240 miles / 4 hours
Step 2: Divide numerator and denominator by 4
240 ÷ 4 = 60
4 ÷ 4 = 1
Unit rate: 60 miles/hour
Practice: Unit Rate
If 5 pounds of apples cost $7.50, what is the price per pound?
$ per pound
Understanding Proportions
A proportion states that two ratios are equal. We can solve proportions using cross-multiplication.
Example 3: Solving Proportions
Solve for x: 3/5 = x/20
Step 1: Cross-multiply
3 × 20 = 5 × x
Step 2: Simplify
60 = 5x
Step 3: Solve for x
x = 12
Try it!
Solve for n: 7/8 = 21/n
n =
Word Problems
Example 4: Ratio Word Problem
The ratio of boys to girls in a class is 3:5. If there are 24 girls, how many boys are there?
Step 1: Set up proportion: boys/girls = 3/5 = x/24
Step 2: Cross-multiply
5x = 3 × 24 → 5x = 72
Step 3: Solve for x
x = 72 ÷ 5 = 14.4
Interpretation: Since we can't have 0.4 of a student, the ratio implies 14.4 boys, suggesting the numbers may need to be whole number multiples (e.g., 15 boys and 25 girls would maintain the ratio)
Example 5: Rate Word Problem
A printer can print 12 pages per minute. How long will it take to print 90 pages?
Step 1: Identify rate: 12 pages / 1 minute
Step 2: Set up proportion: 12/1 = 90/x
Step 3: Cross-multiply
12x = 90
Step 4: Solve for x
x = 90 ÷ 12 = 7.5 minutes
SAT Practice Problem
A recipe calls for a ratio of 2 cups flour to 3 cups sugar. If you use 9 cups of sugar, how many cups of flour should you use?