Multiply Fractions | Fifth Grade

Complete Notes & Formulas

1. Multiply Two Fractions

Definition: To multiply two fractions, multiply the numerators together and multiply the denominators together. Then simplify if needed.

📐 Formula:

a/b × c/d = (a × c)/(b × d)

Multiply numerators, multiply denominators

📝 Steps:

Step 1: Multiply the numerators (top numbers)
Step 2: Multiply the denominators (bottom numbers)
Step 3: Simplify the result (divide by GCF)
Step 4: Convert to mixed number if improper

✏️ Example 1: 2/3 × 3/4

Step 1: Multiply numerators: 2 × 3 = 6

Step 2: Multiply denominators: 3 × 4 = 12

Step 3: Result: 6/12

Step 4: Simplify: 6/12 = 1/2 (divide by GCF of 6)

Answer: 1/2

✏️ Example 2: 3/5 × 2/3

(3 × 2)/(5 × 3) = 6/15 = 2/5

Answer: 2/5

2. Multiply Two Fractions: Word Problems

Definition: Apply fraction multiplication to solve real-world problems involving parts of parts.

🔑 Key Words:

"of" usually means multiply
"times" means multiply
"part of a part" requires multiplication
"fraction of a fraction" means multiply

✏️ Example 1: Garden Problem

Sarah planted flowers in 2/3 of her garden. Of the planted area, 3/4 are roses. What fraction of the entire garden has roses?

Solution:

3/4 of 2/3 = 3/4 × 2/3

(3 × 2)/(4 × 3) = 6/12 = 1/2

Answer: 1/2 of the garden

✏️ Example 2: Recipe Problem

A recipe needs 3/4 cup of sugar. If you want to make 2/3 of the recipe, how much sugar do you need?

Solution:

2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2

Answer: 1/2 cup of sugar

3. Multiply Three Fractions and Whole Numbers

Definition: When multiplying three or more fractions (including whole numbers), convert whole numbers to fractions, then multiply all numerators together and all denominators together.

📐 Formula:

a/b × c/d × e/f = (a × c × e)/(b × d × f)

Multiply all numerators, multiply all denominators

📝 Steps:

Convert whole numbers to fractions (n = n/1)
Multiply all numerators together
Multiply all denominators together
Simplify the result

✏️ Example 1: 1/2 × 2/3 × 3/4

Multiply numerators: 1 × 2 × 3 = 6

Multiply denominators: 2 × 3 × 4 = 24

Result: 6/24

Simplify: 6/24 = 1/4

Answer: 1/4

✏️ Example 2: 2 × 3/4 × 1/3

Convert whole number: 2 = 2/1

2/1 × 3/4 × 1/3

Numerators: 2 × 3 × 1 = 6

Denominators: 1 × 4 × 3 = 12

6/12 = 1/2

Answer: 1/2

4. Complete the Fraction Multiplication Sentence I (Find Missing Factor)

Definition: Find the missing fraction in a multiplication equation by working backwards (using division).

📐 Formula:

If a/b × ? = c/d, then ? = c/d ÷ a/b

✏️ Example 1: 2/3 × ___ = 1/2

Solution: Divide to find missing factor

___ = 1/2 ÷ 2/3

___ = 1/2 × 3/2 = 3/4

Check: 2/3 × 3/4 = 6/12 = 1/2 ✓

Answer: 3/4

✏️ Example 2: ___ × 3/5 = 3/10

___ = 3/10 ÷ 3/5

___ = 3/10 × 5/3 = 15/30 = 1/2

Answer: 1/2

5. Complete the Fraction Multiplication Sentence II (Multiple Missing Parts)

Definition: More complex problems with missing numerators, denominators, or multiple missing elements.

📝 Strategies:

Use cross-multiplication to find missing parts
Work with known values first
Check your answer by multiplying
Look for patterns in numerators and denominators

✏️ Example 1: 2/_ × 3/4 = 6/12

Solution: Find missing denominator

We know: 2 × 3 = 6 (numerators match)

So: ? × 4 = 12

? = 12 ÷ 4 = 3

Answer: 2/3

✏️ Example 2: _/5 × 2/3 = 4/15

Solution: Find missing numerator

We know: 5 × 3 = 15 (denominators match)

So: ? × 2 = 4

? = 4 ÷ 2 = 2

Answer: 2/5

6. Understand Fraction Multiplication and Area

Definition: Multiplying fractions can be understood through area models. The area of a rectangle with fractional dimensions is found by multiplying length × width.

📐 Area Model for Multiplication:

How It Works:

Draw a rectangle
Divide horizontally by first denominator
Shade rows according to first numerator
Divide vertically by second denominator
Shade columns according to second numerator
Count overlapping (double-shaded) sections = numerator
Total sections = denominator

Area = Length × Width

For fractional dimensions: Area = (a/b) × (c/d)

✏️ Example: Visual Model for 2/3 × 3/4

Step 1: Draw rectangle, divide into 3 rows

Step 2: Shade 2 out of 3 rows (2/3)

Step 3: Divide into 4 columns

Step 4: Shade 3 out of 4 columns (3/4)

Step 5: Count double-shaded squares: 6

Step 6: Total squares: 3 × 4 = 12

Answer: 6/12 = 1/2

7. Multiply Fractions to Find Area

Definition: Apply fraction multiplication to calculate the area of rectangles with fractional side lengths.

📐 Area Formula with Fractions:

Area = Length × Width

If Length = a/b and Width = c/d, then Area = (a × c)/(b × d)

✏️ Example 1: Rectangle Problem

A rectangle has a length of 3/4 meter and width of 2/5 meter. Find the area.

Solution:

Area = Length × Width

Area = 3/4 × 2/5

Area = (3 × 2)/(4 × 5)

Area = 6/20 = 3/10

Answer: 3/10 square meter

✏️ Example 2: Garden Area

A rectangular garden is 5/6 yard long and 2/3 yard wide. What is the area?

Solution:

Area = 5/6 × 2/3

Area = (5 × 2)/(6 × 3)

Area = 10/18 = 5/9

Answer: 5/9 square yard

💡 Key Point:

When finding area with fractional dimensions, the answer will be in square units (e.g., square meters, square feet, square yards).

Quick Reference Chart

Operation	Formula	Example
Two Fractions	a/b × c/d = (a×c)/(b×d)	2/3 × 3/4 = 6/12 = 1/2
Three Fractions	Multiply all numerators / all denominators	1/2 × 2/3 × 3/4 = 6/24 = 1/4
Area	Area = Length × Width	3/4 m × 2/5 m = 6/20 = 3/10 m²
Missing Factor	Use division to find missing	2/3 × ? = 1/2; ? = 1/2 ÷ 2/3

💡 Essential Multiplication Rules:

Multiply Straight Across

Numerator × Numerator
Denominator × Denominator

No Common Denominator Needed

Unlike addition, multiply any fractions

Simplify at the End

Reduce to lowest terms

Area Model Visual

Overlap = Product

🔑 Key Tips for Success:

Multiply numerators together, multiply denominators together
You don't need common denominators to multiply (unlike addition/subtraction)
Always simplify your final answer to lowest terms
Convert whole numbers to fractions (n = n/1) before multiplying
Use area models to visualize multiplication
When multiplying three or more fractions, multiply all numerators, then all denominators
To find missing factors, use division (work backwards)
Area of rectangle = Length × Width (even with fractions)
Remember: "of" means multiply in word problems

📚 Fifth Grade Multiply Fractions - Complete Study Guide

Master these concepts for math excellence! ✨