2B Divide Fractions Study Guide

📘 Key Vocabulary

Reciprocal — the "flipped" version of a fraction. The reciprocal of ab is ba. (recíproco)

Keep-Change-Flip — the method for dividing fractions: Keep the first fraction, Change ÷ to ×, Flip the second fraction. (mantener-cambiar-voltear)

Quotient — the answer to a division problem. (cociente)

Numerator — the top number in a fraction. (numerador)

Denominator — the bottom number in a fraction. (denominador)

🔄 Visual Example — Keep-Change-Flip

KEEP	CHANGE	FLIP
Keep the first fraction the same	Change the ÷ sign to ×	Flip the second fraction (find its reciprocal)
34	÷ → ×	12 → 21

34 ÷ 12 = 34 × 21 = 64 = 32 = 1½

🔢 Step-by-Step

1 Keep the first fraction exactly as it is.
2 Change the division sign (÷) to a multiplication sign (×).
3 Flip the second fraction (swap the numerator and denominator).
4 Multiply straight across: numerator × numerator, denominator × denominator.
5 Simplify your answer. Convert improper fractions to mixed numbers.

Dividing with Mixed Numbers

Example: 2⅓ ÷ 14

Step 1: Convert 2⅓ to improper: 2 × 3 + 1 = 7 → 73

Step 2: Keep-Change-Flip: 73 × 41

Step 3: Multiply: 283 = 9⅓

Dividing a Whole Number by a Fraction

Example: 4 ÷ 25

Write 4 as 41, then Keep-Change-Flip:

41 × 52 = 202 = 10

📐 Formula Box

ab ÷ cd = ab × dc

Reciprocal of cd is dc

⚠️ Watch Out!

Only flip the SECOND fraction! The most common mistake is flipping the first fraction or flipping both.
Remember to simplify your answer. Always check if the numerator and denominator share a common factor.
Convert mixed numbers to improper fractions BEFORE doing Keep-Change-Flip.
A whole number as a fraction: Write it over 1. For example, 4 = 41.

✏️ Practice Problems

Write fractions as a/b. Write mixed numbers as: whole a/b (example: 1 1/2). Write whole numbers as just the number.

1. 34 ÷ 12 = ?

2. 56 ÷ 23 = ?

3. 2⅓ ÷ 14 = ?

4. 4 ÷ 25 = ?

➗ 2B | Divide Fractions Study Guide