Factor A To B Answer Key

This worksheet focuses on one very important ratio-table idea: figuring out the multiplication or division factor that changes Column A into Column B. Students compare ratio pairs such as 3:5 and 12:20 or 6:4 and 18:12, then identify the factor that transforms both values in the first column into the matching values in the second. Some examples require multiplication, while others require division, so students learn to recognize both scaling up and scaling down.

For a parent, the scale factor is simply the number that tells how much the ratio changed. If 3 becomes 12, then it was multiplied by 4. Check the second value: 5 × 4 = 20. Because the same factor works for both parts, the ratios are equivalent and the factor from A to B is ×4. If 24:16 becomes 6:4, both numbers were divided by 4, so the factor is ÷4.

Learning Goals

• Find Scale Factors: Students identify the operation connecting two equivalent ratio columns.
• Scale Ratios Up: Learners recognize multiplication factors.
• Scale Ratios Down: Students recognize division factors.
• Verify Equivalent Ratios: Learners check that the same factor works for both quantities.
• Strengthen Multiplicative Reasoning: Students focus on how quantities are related rather than only on their differences.

Parent-Friendly Teaching Tips

Use this routine:

1. Compare the first number in Column A with the first number in Column B.
2. Ask what multiplication or division turns one into the other.
3. Test that same operation on the second number.
4. If it works for both, you found the factor.

For example:

Column A: 3 : 5
Column B: 12 : 20

3 × 4 = 12
5 × 4 = 20

Factor from A to B:

×4

Another example:

Column A: 24 : 16
Column B: 6 : 4

24 ÷ 4 = 6
16 ÷ 4 = 4

Factor:

÷4

Why This Worksheet Helps

• Makes Scaling Explicit: Students identify exactly how one equivalent ratio becomes another.
• Builds Strong Multiplication and Division Sense: Learners work with factors in both directions.
• Prepares for Similar Figures: Scale factors later appear in geometry, maps, and drawings.
• Supports Ratio Tables: Students become better at moving between columns.
• Encourages Checking: If the factor works for one value but not the other, something is wrong.

Classroom & Home Use

• Great for Focused Skill Practice: The worksheet isolates scale-factor reasoning.
• Helpful for Parents: The question “What changed A into B?” is easy to use at home.
• Useful for Intervention: Students who add instead of multiply can practice seeing multiplicative relationships.
• Strong for Pre-Algebra: Scale factors are an important step toward proportional equations.
• Good for Homeschooling: Families can make simple examples by multiplying or dividing both parts of any ratio.

The main value of this worksheet is that it helps students understand that equivalent ratios are connected by one consistent multiplication or division factor. Ratios, factors, multiplication, division, and proportional reasoning all work together. For parents, the best reminder is: “The same factor has to work on both numbers.”