Ratio Worded Problems Worksheet

Introduction to Ratio Worded Problems

Ratio worded problems are a fundamental concept in mathematics, involving the comparison of two quantities. Ratios can be used to describe relationships between different things, such as the number of boys to girls in a class, the ratio of ingredients in a recipe, or the proportion of votes in an election. In this worksheet, we will explore various types of ratio worded problems, providing you with a comprehensive understanding of how to solve them.

What is a Ratio?

A ratio is a way of comparing two quantities by division. It can be expressed as a fraction, a decimal, or a proportion. For example, if we have 3 boys and 4 girls in a class, the ratio of boys to girls is 3:4 or ³⁄₄.

Types of Ratio Worded Problems

There are several types of ratio worded problems, including:

• Part-to-part ratios: These involve comparing one part of a whole to another part. For example, “In a bag of 12 marbles, 3 are red and 9 are blue. What is the ratio of red marbles to blue marbles?”
• Part-to-whole ratios: These involve comparing one part of a whole to the entire whole. For example, “A pizza has 16 slices, and 4 of them are eaten. What is the ratio of eaten slices to the total number of slices?”
• Whole-to-whole ratios: These involve comparing two entire quantities. For example, “A bookshelf has 12 books on it, and another bookshelf has 8 books. What is the ratio of the number of books on the first bookshelf to the number of books on the second bookshelf?”

Solving Ratio Worded Problems

To solve ratio worded problems, follow these steps:

1. Read the problem carefully: Understand what is being asked and identify the quantities involved.
2. Identify the ratio: Determine the type of ratio (part-to-part, part-to-whole, or whole-to-whole) and write it as a fraction, decimal, or proportion.
3. Use equivalent ratios: If necessary, use equivalent ratios to simplify the problem or find a missing value.
4. Check your answer: Ensure that your solution makes sense in the context of the problem.

Examples of Ratio Worded Problems

Here are some examples of ratio worded problems:

• Example 1: A recipe for making cookies calls for a ratio of 2:3 of sugar to flour. If you need 6 cups of sugar, how many cups of flour do you need?

🤔 Note: To solve this problem, use equivalent ratios to find the amount of flour needed.

Solution: Since the ratio of sugar to flour is 2:3, we can set up a proportion: ²⁄₃ = 6/x. Cross-multiplying, we get 2x = 18, so x = 9. Therefore, we need 9 cups of flour.

• Example 2: A school has 240 students, and the ratio of boys to girls is 3:5. How many boys and girls are there in the school?

📚 Note: To solve this problem, use the ratio to find the number of boys and girls.

Solution: Let’s say the number of boys is 3x and the number of girls is 5x. We know that the total number of students is 240, so 3x + 5x = 240. Combining like terms, we get 8x = 240, so x = 30. Therefore, there are 3(30) = 90 boys and 5(30) = 150 girls.

Ratio Worded Problems Worksheet

Here are some practice problems for you to try:

Conclusion

Ratio worded problems are an essential part of mathematics, and being able to solve them is crucial for real-world applications. By understanding the different types of ratio worded problems and following the steps outlined in this worksheet, you can become proficient in solving these types of problems.

Remember to always read the problem carefully, identify the ratio, use equivalent ratios if necessary, and check your answer to ensure that it makes sense in the context of the problem.

Related Terms:

• Ratio Worksheet Grade 5
• Ratio grade 6 worksheets PDF
• Ratio Worksheet grade 6
• Question ratio CORBETTMATHS pdf