Write a ratio: word problems

Key Notes :

Definition of a Ratio

• A ratio is a comparison of two quantities using division.
• It shows how many times one value is contained within another.

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Ways to Write a Ratio

• Using a colon: 3:4
• As a fraction: 3/4
• In words: “3 to 4”

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Understanding the Order in Ratios

• The order of the numbers in a ratio is important.
• Example: If a problem says “There are 2 apples for every 3 oranges,” the correct ratio is 2:3, not 3:2.

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Solving Word Problems with Ratios

• Step 1: Identify the two quantities being compared.
• Step 2: Determine the correct order of the ratio based on the problem.
• Step 3: Write the ratio in the preferred form (colon, fraction, or words).

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Equivalent Ratios

• Ratios can be scaled up or down just like fractions.
• Example: If the ratio of boys to girls is 2:3, then multiplying both by 2 gives 4:6, which is an equivalent ratio.

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Common Ratio Word Problems

• Comparing objects (e.g., “There are 5 red balls and 3 blue balls. What is the ratio of red to blue balls?”)
• Comparing distances, prices, or measurements (e.g., “A recipe uses 2 cups of sugar for every 5 cups of flour. Write the ratio of sugar to flour.”)
• Real-life applications (e.g., “For every 3 students in a classroom, there are 2 desks. Write the ratio of students to desks.”)

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Simplifying Ratios

• Just like fractions, ratios should be simplified when possible.
• Example: A ratio of 10:15 simplifies to 2:3 by dividing both numbers by 5.

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Using Ratios in Proportions

• Ratios help in solving problems where one part of the ratio is missing.
• Example: If a map has a scale of 1:100, then 3 cm on the map represents 300 cm in real life.

Learn with an example

Let’s practice!🖊️