Grade: 5 Subject: SAT/ACT Skills Unit: Ratios Introduction SAT Math: Problem Solving + Data Analysis ACT Section: Math

Ratio Basics

Learn what ratios are and how to use them to compare quantities - a key skill for SAT and ACT success!

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What is a Ratio?

A ratio is a way to compare two quantities. It tells us how much of one thing there is compared to another.

Imagine you have a bag with 3 red apples and 2 green apples. The ratio of red apples to green apples is 3 to 2. This means for every 3 red apples, there are 2 green apples.

Three Ways to Write a Ratio

You can write the same ratio in three different ways:

3:2
Using a colon
3 to 2
Using words
3/2
As a fraction

All three ways mean exactly the same thing!

Visualizing Ratios with Blocks

For every 2 red blocks, there are 3 blue blocks
Ratio: 2:3
For every 4 green blocks, there is 1 amber block
Ratio: 4:1

Part-to-Part vs. Part-to-Whole Ratios

Part-to-Part Compares one part of a group to another part. Example: 3 boys to 5 girls (3:5)
Part-to-Whole Compares one part to the total. Example: 3 boys out of 8 students (3:8)

Tape Diagram Example

A class has 12 boys and 8 girls
Boys:
12
Girls:
8

Part-to-Part: Boys to Girls = 12:8 = 3:2 (simplified)
Part-to-Whole: Boys to Total = 12:20 = 3:5 (simplified)

Real-World Examples

Recipe
Recipe Ingredients
2 cups flour to 1 cup sugar (2:1)
Classroom
Classroom
15 boys to 10 girls (3:2)
Sports
Game Record
8 wins to 4 losses (2:1)
Money
Savings
$3 saved to $1 spent (3:1)

Simplifying Ratios

Just like fractions, ratios can be simplified by dividing both numbers by their greatest common factor (GCF).

How to Simplify a Ratio

  1. Find the GCF of both numbers
  2. Divide both numbers by the GCF
  3. Write the new, simplified ratio
6:9
->
Divide both by 3
2:3
12:8
->
Divide both by 4
3:2

Worked Examples

Example 1: Writing a Ratio from a Picture

Problem: Look at the shapes below. What is the ratio of circles to squares?

O
O
O
O
S
S
S
S
S
S
1 Count the circles: There are 4 circles
2 Count the squares: There are 6 squares
3 Write the ratio: Circles to Squares = 4:6
4 Simplify by dividing both by 2: 4 / 2 = 2 and 6 / 2 = 3
Answer: The ratio of circles to squares is 2:3
Example 2: Word Problem

Problem: A bag has 6 apples and 9 oranges. What is the ratio of apples to oranges in simplest form?

1 Identify the quantities: 6 apples and 9 oranges
2 Write the ratio in order (apples to oranges): 6:9
3 Find the GCF of 6 and 9. Factors of 6: 1, 2, 3, 6. Factors of 9: 1, 3, 9. GCF = 3
4 Divide both by 3: 6 / 3 = 2 and 9 / 3 = 3
Answer: The ratio of apples to oranges is 2:3
Example 3: Part-to-Whole Ratio

Problem: On a soccer team, there are 8 players who wear glasses and 12 players who don't. What is the ratio of players with glasses to the total number of players?

1 Find the total number of players: 8 + 12 = 20 players
2 Write the part-to-whole ratio: Players with glasses to Total = 8:20
3 Find the GCF of 8 and 20. GCF = 4
4 Simplify: 8 / 4 = 2 and 20 / 4 = 5
Answer: The ratio of players with glasses to total players is 2:5

Practice

Try these problems on your own. Click "Check Answer" to see if you're correct!

Question 1

Look at the blocks below. What is the ratio of red blocks to blue blocks?

Question 2

Simplify the ratio 10:15 to its lowest terms.

Question 3

A recipe calls for 4 cups of water and 2 cups of rice. What is the ratio of water to rice?

Question 4

"There are 5 cats for every 2 dogs" can be written as which ratio?

Check Your Understanding: Ratio Race

Test yourself with this quick game! Answer 6 questions to see how well you understand ratios.

Ratio Race

Score: 0/6
Question 1 of 6
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0/6
Keep practicing!

Next Steps

  • Review any concepts that felt challenging, especially simplifying ratios
  • Practice identifying ratios in your daily life - recipes, sports scores, classroom counts
  • Move on to the next lesson when you can confidently write and simplify ratios
  • Remember: Order matters! "Apples to oranges" is different from "oranges to apples"

SAT/ACT Test Tip

On the SAT and ACT, ratio questions often ask you to find a missing value or set up an equation. Mastering the basics now will make those problems much easier! Always pay attention to the order of the ratio - the test will try to trick you by switching the order.