Word Problems Involving Writing a Ratio

Writing a ratio from a word problem is a two-step skill: first you read carefully to identify the two quantities and their correct order, then you write the ratio in the form the problem requires. This lesson gives you a reliable strategy and plenty of practice with GED-style questions.

What Makes a Good Ratio Problem Strategy?

Many students rush past the wording and mix up the order of the quantities. A strong strategy forces you to slow down and identify exactly what is being compared to what.

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Key vocabulary to recognize:

• “for every”, “per”, “to”, “for each” — signal a ratio relationship.
• “out of”, “out of every” — often signal a part-to-whole ratio.
• “compared to”, “relative to” — signal a comparison ratio.

Strategy for Writing a Ratio from a Word Problem

Step 1: Read and underline the two quantities being compared

The problem will name two things. Underline each one.

Step 2: Identify the order

The first quantity mentioned in the ratio description goes in front (or in the numerator if written as a fraction). Pay close attention to the phrasing: “the ratio of A to B” means A comes first.

Step 3: Write the ratio

Use colon, fraction, or word form as the question requests.

Step 4: Simplify if possible

Divide both numbers by their GCF.

Step-by-Step Summary

1. Identify the two quantities.
2. Determine the correct order (which is first).
3. Write the ratio as \(\color{blue}{a : b}\) or \(\color{blue}{\frac{a}{b}}\).
4. Simplify by dividing by the GCF.

Watch: Ratio Word Problem Examples (Video Lesson)

Khan Academy works through several ratio word problem examples:

Worked Examples

Example 1: A box contains 8 red pens and 12 blue pens. Write the ratio of red pens to blue pens in simplest form.

Red to blue: \(\color{blue}{8 : 12}\). \(\color{blue}{\text{ GCF }(8, 12) = 4}\). Simplified: \(\color{blue}{2 : 3}\).

Example 2: At a school, 180 students play sports and 60 do not. What is the ratio of students who play sports to the total number of students?

\(\color{blue}{\text{ Total } = 180 + 60 = 240}\). Ratio: \(\color{blue}{180 : 240}\). \(\color{blue}{\text{ GCF }(180, 240) = 60}\). Simplified: \(\color{blue}{3 : 4}\).

Example 3: A recipe uses 2 cups of milk for every 3 cups of flour. If you use 9 cups of flour, how many cups of milk do you need? Write the original ratio and use it to solve.

Ratio milk to flour: \(\color{blue}{2 : 3}\). Scale factor: \(\color{blue}{9 \div 3 = 3}\). Milk: \(\color{blue}{2 \times 3 = 6}\) cups.

Example 4: On a test, a student answered 35 questions correctly out of 40 total. Write the ratio of correct to incorrect answers in simplest form.

\(\color{blue}{\text{ Incorrect } = 40 – 35 = 5}\). Correct to incorrect: \(\color{blue}{35 : 5}\). \(\color{blue}{\text{ GCF }(35, 5) = 5}\). Simplified: \(\color{blue}{7 : 1}\).

More Practice: Introduction to Ratios Video

This Khan Academy video walks through what a ratio is and how to identify it from real-world situations:

Exercises

1. A parking lot has 24 cars and 16 motorcycles. Write the ratio of motorcycles to cars in simplest form.
2. Out of 50 workers, 30 work full-time and 20 work part-time. Write the ratio of part-time to total workers in simplest form.
3. A store sold 45 fiction books and 30 non-fiction books. Write the ratio of fiction to non-fiction in simplest form.
4. A juice mixture uses 3 parts orange juice to 2 parts grapefruit juice. If you use 12 parts orange juice, how much grapefruit juice do you need?
5. In a survey, 56 people preferred coffee and 21 preferred tea. Write the ratio of coffee to tea in simplest form.
6. There are 150 students and 6 teachers. Write the ratio of students to teachers in simplest form.

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Answers

1. \(\color{blue}{16 : 24}\); \(\color{blue}{\text{ GCF } = 8}\); \(\color{blue}{2 : 3}\)
2. \(\color{blue}{20 : 50}\); \(\color{blue}{\text{ GCF } = 10}\); \(\color{blue}{2 : 5}\)
3. \(\color{blue}{45 : 30}\); \(\color{blue}{\text{ GCF } = 15}\); \(\color{blue}{3 : 2}\)
4. Scale factor: \(\color{blue}{12 \div 3 = 4}\); Grapefruit juice = \(\color{blue}{2 \times 4 = 8}\) parts.
5. \(\color{blue}{56 : 21}\); \(\color{blue}{\text{ GCF } = 7}\); \(\color{blue}{8 : 3}\)
6. \(\color{blue}{150 : 6}\); \(\color{blue}{\text{ GCF } = 6}\); \(\color{blue}{25 : 1}\)

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Frequently Asked Questions

How do I know which quantity goes first in a ratio?

Follow the order in the problem. “The ratio of A to B” means A is first. If the problem says “compare B to A,” then B is first. When in doubt, re-read the sentence that asks the question.

Should I include the units in a ratio?

Ratios compare quantities of the same type (both in the same units), so the units cancel. Write the numbers only. If the units are different, convert to the same unit before writing the ratio.

What is the difference between a ratio and a rate?

A ratio compares two quantities of the same kind. A rate compares two quantities of different kinds (such as miles per hour). Rates are a special type of ratio where units are different and are usually kept in the answer.

Related Topics

• Write a Ratio
• Using a Fraction to Write Down a Ratio
• Ratio Tables
• Finding Equivalent Ratio
• Word Problems Involving Comparing Ratio