3A Understand Ratios Study Guide

📘 Key Vocabulary

Ratio — a comparison of two quantities. It tells you "for every ___ of one thing, there are ___ of another." (razón / proporción)

Part-to-Part — a ratio that compares one part of a group to another part of the same group. (parte a parte)

Part-to-Whole — a ratio that compares one part of a group to the entire group (the total). (parte al total)

Comparison — looking at two or more things to see how they are the same or different. (comparación)

Equivalent Ratio — two ratios that represent the same comparison (like 1:2 and 2:4). (razón equivalente)

🖼️ Visual Example — Three Ways to Write a Ratio

There are 3 red apples and 5 green apples in a basket.

3 : 5
with a colon

3 to 5
with words

3/5
as a fraction

Part-to-Part: red to green = 3 : 5 — comparing one part to another part.

Part-to-Whole: red to total = 3 : 8 — comparing one part to the whole group (3 + 5 = 8 total).

🔢 Step-by-Step — Writing Ratios

1 Read the problem. What two quantities are being compared?
2 Decide the order. The first thing mentioned goes first in the ratio.
3 Decide the type: Is it part-to-part or part-to-whole?
4 Write the ratio in any of the three forms (colon, words, or fraction).
5 Simplify if possible (divide both parts by the GCF).

Example: A class has 12 boys and 18 girls. Write the ratio of boys to girls.

Part-to-Part: 12 : 18
Simplify (GCF = 6): 12 ÷ 6 = 2 and 18 ÷ 6 = 3
Answer: 2 : 3 (or "2 to 3" or "2/3")

📐 Formula Box

Part-to-Part Ratio: Part A : Part B

Part-to-Whole Ratio: Part A : (Part A + Part B)

Simplify: Divide both parts by their GCF

⚠️ Watch Out!

Order matters! The ratio 3:5 is NOT the same as 5:3. Always match the order the problem asks for.
Part-to-Part vs. Part-to-Whole: If a problem says "ratio of boys to girls," that is part-to-part. If it says "ratio of boys to all students," that is part-to-whole.
A ratio is NOT a fraction in every context. A ratio of 3:5 compares two things; the fraction 3/5 is just one way to write it.
Always simplify if possible. 6:10 should be written as 3:5.

✏️ Practice Problems

Write your ratio using a colon, like 3:5. Simplify your answer.

1. A bag has 4 red marbles and 6 blue marbles. What is the ratio of red to blue marbles? (Simplify.)

2. There are 10 cats and 15 dogs at a shelter. What is the ratio of cats to the total number of animals? (Simplify.)

3. A recipe uses 2 cups of flour for every 3 cups of milk. If you use 6 cups of flour, how many cups of milk do you need?