R2 · Lesson 2: Equivalent Fractions & Simplifying

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Why this matters for Grade 6: Grade 6 division of fractions (6.NS.1) requires you to find common denominators and reduce answers to lowest terms. Equivalent fractions are the engine behind all of that. If 1/2 = 2/4 = 4/8, you can always rewrite fractions in a more useful form.

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Equivalent Fractions & Simplifying

Equivalent fractions look different but represent the same amount.

Rule: Multiply (or divide) both numerator and denominator by the same number and the fraction's value doesn't change.

Example 1 — Building up: 1/2 = 2/4 = 4/8

1/2 ×2/×2 → 2/4 ×2/×2 → 4/8

1/2 — 1 out of 2 parts

2/4 — 2 out of 4 parts (same amount!)

Example 2 — Simplifying: 6/8 → 3/4
Find the Greatest Common Factor (GCF) of 6 and 8.
Factors of 6: 1, 2, 3, 6 | Factors of 8: 1, 2, 4, 8 → GCF = 2

6/8 ÷2/÷2 → 3/4

Check: 3 and 4 share no common factor bigger than 1 → simplified!

Another: 4/12 → ? GCF of 4 and 12 = 4. 4÷4 = 1, 12÷4 = 3. Answer: 1/3

Try It · Guided

Work These Together

1. Which fraction is equivalent to 1/3?

Hint

Multiply both top and bottom by 2: 1×2=2, 3×2=6. So 1/3 = 2/6.

2. Simplify 8/12 to its lowest terms. What is the simplified fraction?

Hint

GCF of 8 and 12 is 4. Divide both by 4: 8÷4=2, 12÷4=3. Answer: 2/3.

Practice · On Your Own

You Try

3. Fill in the blank: 3/4 = ?/8 (What is the missing numerator?)

Hint

To go from 4 to 8, multiply denominator by 2. Do the same to the numerator: 3×2 = 6. Answer: 6/8.

4. Simplify 10/15. What is the simplified fraction?

Hint

GCF of 10 and 15 is 5. Divide both by 5: 10÷5=2, 15÷5=3. Answer: 2/3.

5. Which pair of fractions is equivalent?

Hint

Check 3/5 and 6/10: multiply 3/5 by 2/2 → 6/10. Yes, they are equivalent!

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Exit Ticket

Show What You Know

6. Simplify 6/9 to its lowest terms.

Hint

GCF of 6 and 9 is 3. Divide both by 3: 6÷3=2, 9÷3=3. Answer: 2/3.

7. Fill in: 2/5 = ?/20 (What number goes in the blank?)

Hint

5 × 4 = 20, so multiply numerator by 4 too: 2 × 4 = 8. Answer: 8/20.

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