Grade: 5 Subject: SAT/ACT Skills Unit: Ratios Introduction Lesson: 5 of 6 SAT Math: ProblemSolving+DataAnalysis ACT Section: Math

Guided Practice

Work through ratio problems step-by-step with hints and feedback to build your skills and confidence.

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Practice Makes Perfect

The best way to master ratios is through practice. In this lesson, you'll work through problems with guidance, hints when you need them, and detailed explanations.

Problem-Solving Strategy for Ratios

  1. Read the problem carefully - identify what quantities are being compared
  2. Write the ratio in the correct order (the order matters!)
  3. Simplify if needed - find the GCF and divide both numbers
  4. Check your answer - does it make sense in context?

Common Ratio Problem Types

  • Part-to-Part: Comparing two parts of a group (boys to girls)
  • Part-to-Whole: Comparing one part to the total (red marbles to all marbles)
  • Equivalent Ratios: Finding ratios that represent the same relationship
  • Missing Values: Using ratios to find unknown quantities

Worked Examples

Example 1 Part-to-Part Ratio

Problem: A recipe uses 3 cups of flour for every 2 cups of sugar. What is the ratio of flour to sugar?

Solution

  1. Identify quantities: flour = 3 cups, sugar = 2 cups
  2. Write ratio in order asked (flour TO sugar): 3:2
  3. Check if it can be simplified: GCF of 3 and 2 is 1, so already simplified
  4. Answer: The ratio of flour to sugar is 3:2
Example 2 Part-to-Whole Ratio

Problem: In a class of 28 students, 12 are wearing sneakers. What is the ratio of students wearing sneakers to total students?

Solution

  1. Identify quantities: sneakers = 12, total = 28
  2. Write ratio: 12:28
  3. Simplify: GCF of 12 and 28 is 4. So 12/4 = 3 and 28/4 = 7
  4. Answer: The ratio is 3:7

Practice

Try these problems. Use the hint button if you need help!

Question 1 Part-to-Part

A pet store has 15 dogs and 10 cats. What is the ratio of dogs to cats in simplest form?

Find the GCF of 15 and 10. Both numbers are divisible by 5.
Question 2 Part-to-Whole

Out of 24 cupcakes, 8 have chocolate frosting. What is the ratio of chocolate cupcakes to all cupcakes?

The GCF of 8 and 24 is 8. Divide both numbers by 8.
Question 3 Equivalent Ratios

Which ratio is equivalent to 4:6?

Simplify 4:6 first by dividing both by 2. Then see which answer matches.
Question 4 Word Problem

For every 5 blue marbles, there are 3 red marbles. If there are 20 blue marbles, how many red marbles are there?

Set up equivalent ratios: 5:3 = 20:? Think: 5 times what equals 20?

Check Your Understanding

Complete this 10-question quiz to test your ratio skills!

Ratio Practice Quiz

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Next Steps

Key Takeaways

  • Always read carefully to identify the order of quantities
  • Simplify ratios by dividing both numbers by the GCF
  • For equivalent ratios, multiply or divide both parts by the same number
  • Check your answer by making sure it makes sense in context
  • Review any problems you found challenging
  • Practice finding equivalent ratios with larger numbers
  • Move on to Review Mistakes to learn from common errors