✖️ 2A | Multiply Fractions Study Guide

Unit 2: Fractions & Decimals • Lessons 2.1–2.2 • Standard: 6.NOS.1

📘 Key Vocabulary

Numerator — the top number in a fraction; it tells how many parts you have. (numerador)
Denominator — the bottom number in a fraction; it tells how many equal parts make the whole. (denominador)
Fraction — a number that represents part of a whole, written as numerator/denominator. (fracción)
Mixed Number — a whole number and a fraction together (example: 1½). (número mixto)
Improper Fraction — a fraction where the numerator is bigger than the denominator (example: 7/4). (fracción impropia)
Simplify — to reduce a fraction to its lowest terms by dividing numerator and denominator by their GCF. (simplificar)

🖼️ Visual Example

Multiplying fractions means finding a part of a part.

Example: 23 × 45 means "2/3 of 4/5"

Imagine a rectangle split into 5 columns. Shade 4 columns (4/5).
Now split those into 3 rows. Shade 2 rows (2/3).
The overlap = 8 out of 15 small squares = 8/15

🔢 Step-by-Step

Multiplying Simple Fractions

  1. 1 Multiply the numerators (top × top).
  2. 2 Multiply the denominators (bottom × bottom).
  3. 3 Simplify the answer if possible.
23 × 45 = 2 × 43 × 5 = 815

Multiplying with Mixed Numbers

  1. 1 Convert mixed numbers to improper fractions first.
  2. 2 Multiply numerators, then denominators.
  3. 3 Simplify and convert back to a mixed number if needed.
Convert 1½ to improper: 1 × 2 + 1 = 3 → 32

32 × 23 = 66 = 1

📐 Formula Box

ab × cd = a × cb × d
Mixed to Improper: whole × denominator + numerator = new numerator

⚠️ Watch Out!

✏️ Practice Problems

Write fractions as a/b (example: 8/15). Write mixed numbers as whole and fraction (example: 1 1/2).

1. 23 × 45 = ?

2. 34 × 27 = ?

3. 1½ × 23 = ?

4. 2¼ × 1⅓ = ?