Proportion Proof Answer Key

This worksheet asks students to decide whether each pair of ratios forms a true proportion. Students write True if the two ratios are equivalent and False if they are not. Problems include statements such as 2:3 = 8:12, 3:5 = 12:25, and 4:7 = 12:21. Students can check the relationship by simplifying, using scale factors, or comparing cross products.

For a parent, the main idea is that a proportion is only true when the two ratios represent the same relationship. If 2:3 becomes 8:12, both numbers were multiplied by 4, so the statement is true. But if 3:5 becomes 12:25, the first number was multiplied by 4 while the second was multiplied by 5, so the ratios are not equivalent and the proportion is false.

Learning Goals

• Verify Proportions: Students determine whether two ratios are truly equivalent.
• Use Scale Factors: Learners check whether both terms changed by the same factor.
• Simplify Ratios: Students reduce ratios when that is the easiest method.
• Use Cross Products When Helpful: Learners can compare diagonal products to verify equality.
• Strengthen Mathematical Proof: Students make a True or False decision based on evidence.

Parent-Friendly Teaching Tips

Students can use whichever checking method feels easiest.

Method 1: Scale factor

2:3 = 8:12

2 × 4 = 8
3 × 4 = 12

True.

Method 2: Simplify

12:21

Divide by 3:

4:7

So 4:7 = 12:21 is True.

Method 3: Cross multiply

3/5 = 12/25

3 × 25 = 75
5 × 12 = 60

The cross products are not equal, so the statement is False.

Why This Worksheet Helps

• Builds Verification Skills: Students learn to check a relationship instead of assuming it is correct.
• Encourages Multiple Strategies: Scale factors, simplification, and cross products can all be useful.
• Strengthens Ratio Sense: Learners become better at recognizing equivalent and non-equivalent ratios.
• Prepares for Algebra: Checking whether two expressions are equal is a key mathematical habit.
• Supports Error Detection: Students learn to find exactly where a proportional relationship breaks.

The main value of this worksheet is that students learn that a proportion must be proved by equivalence, not accepted because the numbers merely look related. For parents, the best question is: “Can you show that both ratios describe the same relationship?”