🔗 3C | Equivalent & Comparing Ratios Study Guide

Unit 3: Ratios & Proportions • Lesson 3.3 • Standard: 6.AT.3a

📘 Key Vocabulary

Equivalent Ratio — two ratios that have the same value when simplified. Example: 2:3 and 4:6 are equivalent. (razón equivalente)
Proportion — an equation that shows two ratios are equal. Example: 2/3 = 4/6. (proporción)
Scale Factor — the number you multiply both parts of a ratio by to get an equivalent ratio. (factor de escala)
Cross Multiply — a method to check if two ratios are equivalent or to solve for a missing number. (multiplicar en cruz)
Simplify — to reduce a ratio to its smallest whole numbers by dividing by the GCF. (simplificar)

🖼️ Visual Example — Equivalent Ratios

Are 3:4 and 9:12 equivalent?

Method 1 — Scale Factor:
3 × 3 = 9   and   4 × 3 = 12   ✓ Same multiplier = equivalent!

Method 2 — Cross Multiply:
3 × 12 = 36   and   4 × 9 = 36   ✓ Cross products are equal = equivalent!

Are 2:5 and 3:8 equivalent?

Cross Multiply:
2 × 8 = 16   and   5 × 3 = 15   ✗ 16 ≠ 15, so they are NOT equivalent.

🔢 Step-by-Step

Finding Equivalent Ratios

  1. 1 Multiply both parts of the ratio by the same number.
  2. 2 Or divide both parts by their GCF to simplify.
4 : 10 → ÷ 2 → 2 : 5 (simplified)
2 : 5 → × 3 → 6 : 15 (equivalent)
2 : 5 → × 4 → 8 : 20 (equivalent)

Comparing Ratios with Cross Multiplication

  1. 1 Write both ratios as fractions: ab and cd
  2. 2 Cross multiply: a × d and b × c
  3. 3 If the cross products are equal, the ratios are equivalent.
  4. 4 If the cross products are not equal, the ratios are NOT equivalent.
Compare: 35 and 610

3 × 10 = 30    5 × 6 = 30
30 = 30 ✓ → They are equivalent!

Solving for a Missing Value

  1. 1 Set up the proportion: ab = c?
  2. 2 Cross multiply: a × ? = b × c
  3. 3 Divide to solve for the missing number.
34 = 9?

3 × ? = 4 × 9 = 36
? = 36 ÷ 3 = 12

📐 Formula Box

Equivalent Ratios: Multiply or divide BOTH parts by the same number
Cross Multiply: If ab = cd then a × d = b × c
Solving: ab = cd → a × d = b × c → solve for the unknown

⚠️ Watch Out!

✏️ Practice Problems

1. Are 4:6 and 10:15 equivalent ratios? Type "yes" or "no".

2. Find the missing number: 58 = 15?

3. Write an equivalent ratio for 6:9 by simplifying. Use a colon (example: 2:3).

4. Find the missing number: ?12 = 34