Introduction
What Is a Ratio? is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with what is a ratio?.
What Is What Is a Ratio??
What Is a Ratio? means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding What Is a Ratio?
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: The ratio bar shows red and blue sections. What is the ratio of red to blue?
- A. \(5:2\)
- B. \(3:2\)
- C. \(2:5\)
- D. \(2:3\)
Why it works: Look at the lengths in the bar: red takes \(2\) equal units and blue takes \(3\) equal units. Red to blue is \(2:3\).
Answer: \(2:3\)
Visual Model 2
Question: The diagram shows orange and green counters. What is the ratio of orange to green in fraction form?
- A. \(\frac{7}{3}\)
- B. \(\frac{4}{3}\)
- C. \(\frac{3}{7}\)
- D. \(\frac{3}{4}\)
Why it works: Count the counters by color: \(3\) orange and \(4\) green. Since the question asks orange to green, write \(\frac{3}{4}\).
Answer: \(\frac{3}{4}\)
Worked Examples
Example 1
Question: What is the ratio of blue marbles to red marbles in simplest form?
| Type | Count |
|---|---|
| Red marbles | 12 |
| Blue marbles | 8 |
- A. \(3:2\)
- B. \(8:12\)
- C. \(12:8\)
- D. \(2:3\)
- The order is blue to red, so start with \(8:12\).
- Divide both parts by \(4\) to simplify the ratio to \(2:3\).
Answer: \(2:3\)
Example 2
Question: The bar shows two sections. Section A is \(\frac{2}{5}\) of the bar and section B is \(\frac{3}{5}\). What is the ratio of A to B?
- A. \(3:2\)
- B. \(3:5\)
- C. \(5:3\)
- D. \(2:3\)
- Both sections are measured in fifths, so compare the numerators.
- A has \(2\) fifths and B has \(3\) fifths, giving a ratio of \(2:3\).
Answer: \(2:3\)
Example 3
Question: The dots show purple and yellow counters. Express the ratio of purple to yellow in the form \(a:b\).
- A. \(4:5\)
- B. \(9:5\)
- C. \(5:9\)
- D. \(5:4\)
- Count the purple counters first because the question says purple to yellow.
- There are \(5\) purple and \(4\) yellow, so the ratio is \(5:4\).
Answer: \(5:4\)
Real-World Word Problems
Problem 1
Question: A fruit basket contains \(6\) apples and \(4\) oranges. What is the ratio of apples to oranges in simplest form?
- A. \(6:4\)
- B. \(2:3\)
- C. \(4:6\)
- D. \(3:2\)
Why it works: Great start: keep the order the same, apples first and oranges second. Both \(6\) and \(4\) can be divided by \(2\), so \(6:4\) becomes \(3:2\).
Answer: \(3:2\)
Problem 2
Question: A classroom has \(8\) boys and \(10\) girls. Write the ratio of boys to girls in the form "\(a\) to \(b\)".
- A. \(10\) to \(8\)
- B. \(18\) to \(8\)
- C. \(8\) to \(18\)
- D. \(8\) to \(10\)
Why it works: Read the words carefully: "boys to girls" means the boys number comes first. There are \(8\) boys and \(10\) girls, so the ratio is \(8\) to \(10\).
Answer: \(8\) to \(10\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which ratio is equivalent to \(5:15\)?
- A. \(1:2\)
- B. \(5:10\)
- C. \(10:30\)
- D. \(1:3\)
Question 2
A recipe calls for \(2\) cups of flour for every \(3\) cups of sugar. Which fraction represents the ratio of flour to the total amount of flour and sugar?
- A. \(\frac{2}{3}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{2}{5}\)
- D. \(\frac{3}{2}\)
Question 3
A soccer team wins \(12\) games and loses \(4\) games. In simplest form, what is the ratio of wins to total games?
- A. \(4:3\)
- B. \(12:16\)
- C. \(3:1\)
- D. \(3:4\)
Question 4
Which of the following ratios is in simplest form?
- A. \(8:12\)
- B. \(6:9\)
- C. \(10:15\)
- D. \(5:7\)
Question 5
A punch recipe mixes \(1\) part juice with \(4\) parts water. If you use \(8\) cups of juice, how much water should you use?
- A. \(2\) cups
- B. \(12\) cups
- C. \(32\) cups
- D. \(4\) cups
Question 6
Simplify the ratio \(18:27\).
- A. \(3:2\)
- B. \(6:9\)
- C. \(9:6\)
- D. \(2:3\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(1:3\)
A helpful way to check is to simplify. Divide both parts of \(5:15\) by \(5\): \(\frac{5}{5}:\frac{15}{5}=1:3\).
Question 2
Answer: \(\frac{2}{5}\)
First find the total amount of flour and sugar: \(2+3=5\) cups. Flour is \(2\) of those \(5\) cups, so the ratio is \(\frac{2}{5}\).
Question 3
Answer: \(3:4\)
Do not compare wins to losses here; the question asks for wins to total games. The total is \(12+4=16\), and \(12:16\) simplifies to \(3:4\).
Question 4
Answer: \(5:7\)
A ratio is in simplest form when the two numbers have no common factor greater than \(1\). The numbers \(5\) and \(7\) share no common factor except \(1\), so \(5:7\) is already simplified.
Question 5
Answer: \(32\) cups
Use the ratio as a recipe: for every \(1\) cup of juice, there are \(4\) cups of water. With \(8\) cups of juice, multiply \(8 \times 4=32\) cups of water.
Question 6
Answer: \(2:3\)
The greatest common factor of \(18\) and \(27\) is \(9\). Divide both parts by \(9\) to get \(\frac{18}{9}:\frac{27}{9}=2:3\).
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
What Is a Ratio? becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
