Rational Applications

Grade 7 · ratios · 92 practice problems · read aloud

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What is a Ratio? 🤔

A ratio is a way to compare two or more quantities. It shows the relative size of one thing to another. We use ratios all the time in real life—like in recipes (2 cups flour to 1 cup sugar), maps (1 inch represents 10 miles), and comparing speeds (miles per hour).

How to Solve Ratio Problems

  1. Identify the quantities being compared.
  2. Write the ratio using a colon (:) or as a fraction.
  3. Simplify the ratio by dividing both numbers by their greatest common factor (GCF).
  4. Use the ratio to find missing values by setting up equivalent ratios (proportions).

Worked Examples

Example 1: Simplifying a Ratio

In a classroom, there are 12 girls and 16 boys. What is the ratio of girls to boys in simplest form?

Step 1: Write the ratio → 12:16
Step 2: Find the GCF of 12 and 16 → 4
Step 3: Divide both sides by 4 → 12÷4 : 16÷4
Answer: 3:4

Example 2: Using a Ratio to Find a Quantity

The ratio of red to blue marbles is 3:5. If there are 18 red marbles, how many blue marbles are there?

Step 1: Set up equivalent fractions → 3/5 = 18/x
Step 2: Cross-multiply → 3 × x = 18 × 5
Step 3: Solve → 3x = 90 → x = 30
Answer: There are 30 blue marbles.

Common Mistakes to Avoid ⚠️

Writing ratios in the wrong order: The ratio of A to B is A:B, not B:A. Pay close attention to the wording!

Forgetting to simplify: Always reduce ratios to their simplest form, just like fractions.

Mixing units: If a ratio compares inches to feet, convert to the same unit before writing the ratio.

Tips & Tricks

Word clue: "For every..." or "per..." often indicates a ratio.

Double-check: After finding an answer, see if it makes sense. If the ratio is 3:4, the first quantity should be a bit smaller than the second.

Fraction friend: Remember that a ratio can be written as a fraction. What you know about simplifying fractions applies to ratios too!

How to Practice

  • Look for ratios in your daily life—in cooking, shopping, or sports statistics.
  • Solve at least 3 ratio problems each day for a week.
  • Create your own ratio problems and solve them.
  • Practice with online games or worksheets that focus on ratios and proportions.

Practice problems

6 of the 92, worked through step by step — try them before opening the answer.

1 (3/4 + 2/3) × 24 = ?

Hint: First find a common denominator to add the fractions, then multiply the result by the whole number.

Show the answer

Answer: 34

  1. Find a common denominator for 3/4 and 2/3. The denominators are 4 and 3. The least common denominator is 12.
  2. Convert each fraction to have a denominator of 12. For 3/4: Multiply numerator and denominator by 3. This gives (3 * 3)/(4 * 3) = 9/12. For 2/3: Multiply numerator and denominator by 4. This gives (2 * 4)/(3 * 4) = 8/12.
  3. Add the fractions. Now we have 9/12 + 8/12 = (9 + 8)/12 = 17/12.
  4. Multiply the result by 24. So the problem is now (17/12) * 24.
  5. Perform the multiplication. Multiplying a fraction by a whole number: (17/12) * 24 = (17 * 24) / 12.
  6. Simplify before multiplying. Notice that 24 divided by 12 is 2. So we can simplify: (17 * 24) / 12 = 17 * (24 / 12) = 17 * 2.
  7. Final multiplication. 17 * 2 = 34. Therefore,

First, we need to calculate the expression inside the parentheses: 3/4 + 2/3. the correct answer is 34.

2 (3/4 + 2/3) × 36 = ?

Hint: First find a common denominator to add the fractions, then multiply the result by the whole number

Show the answer

Answer: 51

  1. Add the fractions 3/4 + 2/3
  2. Find a common denominator of 12
  3. Convert 3/4 to 9/12 and 2/3 to 8/12
  4. Add the fractions: 9/12 + 8/12 = 17/12
  5. Multiply the result by 36: 17/12 × 36
  6. Simplify: 17 × 36/12 = 17 × 3 = 51

The answer is 51.

3 (-3/4 + 2/3) × 12 = ?

Hint: First find a common denominator to combine the fractions inside the parentheses, then multiply the result by the whole number.

Show the answer

Answer: -1

  1. Find a common denominator for -3/4 and 2/3. The least common denominator is 12.
  2. Convert -3/4 to -9/12 (multiply numerator and denominator by 3).
  3. Convert 2/3 to 8/12 (multiply numerator and denominator by 4).
  4. Add the fractions: -9/12 + 8/12 = -1/12.
  5. Multiply the result by 12: (-1/12) × 12 = -12/12 = -1.

The answer is -1.

4 (-3/4 + 2/3) × (-12) = ?

Hint: First find a common denominator to combine the fractions inside the parentheses, then multiply the result by the negative number, remembering the rules for multiplying positive and negative numbers.

Show the answer

Answer: 1

  1. Find a common denominator for -3/4 and 2/3. The least common denominator is 12.
  2. Convert -3/4 to -9/12 and 2/3 to 8/12.
  3. Add the fractions: -9/12 + 8/12 = -1/12.
  4. Multiply the result by -12: (-1/12) × (-12) = 12/12 = 1.

The answer is 1.

5 (-3/4 + 2/3) × (-24) = ?

Hint: First find a common denominator to combine the fractions inside the parentheses, then multiply the result by the negative number outside.

Show the answer

Answer: 2

  1. Find a common denominator for -3/4 and 2/3. The least common denominator is 12.
  2. Convert -3/4 to -9/12 (multiply numerator and denominator by 3).
  3. Convert 2/3 to 8/12 (multiply numerator and denominator by 4).
  4. Add the fractions: -9/12 + 8/12 = -1/12.
  5. Multiply the result by -24: (-1/12) × (-24) = 24/12.
  6. Simplify 24/12 = 2.

The answer is 2.

6 (-5/6 + 3/4) × (-36) = ?

Hint: First combine the fractions inside the parentheses by finding a common denominator. Then multiply the result by the negative number outside. Pay close attention to the signs.

Show the answer

Answer: 3

  1. Find a common denominator for -5/6 and 3/4. The least common denominator is 12.
  2. Convert -5/6 to -10/12 (multiply numerator and denominator by 2).
  3. Convert 3/4 to 9/12 (multiply numerator and denominator by 3).
  4. Add the fractions: -10/12 + 9/12 = -1/12.
  5. Multiply the result by -36: (-1/12) × (-36) = 36/12.
  6. Simplify 36/12 = 3.

The answer is 3.

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