Proportional Tables

Grade 7 · ratios · 100 practice problems · read aloud

🔊 Listen to this explanation

Proportional Tables: Understanding Ratios

🧠 What is a Proportional Table?

A proportional table shows equivalent ratios. If two quantities are proportional, they change at the same rate. This is super useful for solving real-world problems like scaling recipes, calculating unit prices, and converting measurements!

📝 How to Solve Proportional Tables

  1. Identify the Constant of Proportionality: Find the number you multiply by to get from the top row to the bottom row (or vice versa).
  2. Check for Consistency: Make sure the same multiplier works for every pair of numbers in the table.
  3. Find Missing Values: Use the constant of proportionality to calculate any unknown numbers.

🔍 Worked Examples

Example 1: The Constant Multiplier

Find the missing value (?) in the table.

Boxes257?
Apples6152136

Step 1: Find the multiplier: 6 ÷ 2 = 3. So, Apples = Boxes × 3.

Step 2: Check: 5 × 3 = 15 ✓, 7 × 3 = 21 ✓.

Step 3: Find the missing value: 36 ÷ 3 = 12. The missing value is 12.

Example 2: Using Unit Rate

If 4 bags of chips cost $12, how much do 7 bags cost?

Step 1: Find the cost of 1 bag (unit rate): $12 ÷ 4 = $3 per bag.

Step 2: Multiply by the number of bags: 7 × $3 = $21.

Answer: 7 bags cost $21.

⚠️ Common Mistakes to Avoid

  • Adding instead of multiplying: Don't just add the same number to get from one row to the next. Look for multiplication!
  • Inconsistent ratios: If the multiplier isn't the same for every pair, the table is not proportional.
  • Mixing up rows: Be careful which number you're dividing. Always do: (Bottom Value) ÷ (Top Value) to find the constant.

💡 Tips & Tricks

  • The 1-Trick: Always try to find the value for 1 unit first. This "unit rate" makes everything easier!
  • Cross-Multiplication Check: For any two ratios in the table, a/b = c/d. You can check with cross-multiplication: a × d = b × c.
  • Look for Patterns: See if you can simplify the numbers. A ratio of 6:2 is the same as 3:1.

🎯 How to Practice

  • Create your own proportional tables for real-life situations (e.g., miles run vs. calories burned).
  • Use online math games that focus on ratios and proportions.
  • Practice with worksheets that have missing values in different spots (not just the end).
  • Explain the steps to a friend or family member – teaching is a great way to learn!

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 If y = 3x + 2, find y when x = 5

Hint: Substitute the given value into the equation and perform the operations in the correct order.

Show the answer

Answer: 17

  1. Substitute x = 5 into the equation. y = 3(5) + 2
  2. Perform the multiplication first (order of operations). 3 times 5 is 15, so: y = 15 + 2
  3. Perform the addition. 15 + 2 = 17
  4. Write the final answer. y = 17 So when x = 5, y = 17.

We are given the equation: y = 3x + 2 We are told to find y when x = 5.

2 If y = 3x, what is y when x = 7?

Hint: In a proportional relationship, the output value equals the input multiplied by the constant of proportionality. For example, if y = 2x, then when x = 5, y would be 10.

Show the answer

Answer: 21

  1. Substitute the value of x into the equation. Since y = 3x and x = 7, we replace x with 7: y = 3 * 7
  2. Multiply 3 by 7. 3 * 7 = 21
  3. State the value of y. Therefore, y = 21 Final answer: 21

We are given the equation: y = 3x We are also told: x = 7

3 If y = 3x + 7, find y when x = 12

Hint: Substitute the given value into the equation and follow the order of operations

Show the answer

Answer: 43

  1. Start with the equation y = 3x + 7
  2. Substitute x = 12 into the equation: y = 3(12) + 7
  3. Multiply first: 3 × 12 = 36
  4. Add 7 to 36: 36 + 7 = 43
  5. Therefore, y = 43

The answer is 43.

4 If y = 2.5x + 7, find y when x = 12

Hint: Substitute the given x-value into the equation and follow the order of operations

Show the answer

Answer: 37

  1. Start with the equation y = 2.5x + 7
  2. Substitute x = 12 into the equation: y = 2.5(12) + 7
  3. Multiply first: 2.5 × 12 = 30
  4. Add 7: 30 + 7 = 37
  5. Therefore, y = 37 when x = 12

The answer is 37.

5 If y = 2.5x, find y when x = 12 = ?

Hint: This involves multiplying a decimal by a whole number. Remember that multiplying by 2.5 is the same as multiplying by 5/2.

Show the answer

Answer: 30

  1. The equation is y = 2.5x
  2. Substitute x = 12 into the equation: y = 2.5 × 12
  3. Calculate 2.5 × 12 = 30
  4. Therefore, y = 30 when x = 12

The answer is 30.

6 If y = 2.5x, what is y when x = 16?

Hint: Remember that multiplying by a decimal is the same as multiplying by a fraction. For example, if y = 1.5x and x = 10, you would multiply 1.5 × 10.

Show the answer

Answer: 40

  1. The equation is y = 2.5x
  2. Substitute x = 16 into the equation: y = 2.5 × 16
  3. Multiply 2.5 × 16: 2.5 × 10 = 25 and 2.5 × 6 = 15
  4. Add the results: 25 + 15 = 40
  5. Therefore, y = 40 when x = 16

The answer is 40.

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