📝 Types of Models:

• Area Model: Rectangles divided into parts
• Number Line Model: Showing jumps along a line
• Set Model: Groups of objects
• Circle/Fraction Bar Model: Visual fractions
• Array Model: Rows and columns

🔑 Key Concept:

4 × 2/3 means "4 groups of 2/3"

📝 Steps to Complete Equation:

1. Look at the model shown
2. Count how many groups are shaded
3. Count total shaded parts (numerator)
4. Identify the denominator (parts in each whole)
5. Write as a fraction or mixed number

✏️ Example: 3 × 2/5

📝 Steps Using Number Lines:

1. Draw a number line starting at 0
2. Mark equal intervals based on the denominator
3. Make jumps equal to the fraction size
4. Count how many jumps (equal to whole number)
5. Where you land is the answer

✏️ Example: 4 × 1/3

🔑 Pattern of Multiples:

💡 Finding Missing Numbers:

If ___ × 3/4 = 9/4, find the missing number:

Divide: 9 ÷ 3 = 3

Answer: 3

📝 Array Model Steps:

1. Create rows equal to the whole number
2. Divide each row by the denominator
3. Shade parts according to the numerator in each row
4. Count total shaded parts
5. Write as a fraction with same denominator

✏️ Example: 3 × 2/5 using array

📐 Formula:

Fraction × Whole Number = (Numerator × Whole Number) / Denominator

✏️ Example: Find 2/3 of 12

📝 Area Model Steps:

1. Draw a rectangle (unit whole)
2. Divide vertically for first denominator
3. Shade columns for first numerator (1 column)
4. Divide horizontally for second denominator
5. Shade rows for second numerator (1 row)
6. Count the overlapping shaded region

Formula: 1/a × 1/b = 1/(a × b)

✏️ Example: 1/3 × 1/4

📐 General Formula:

a/b × c/d = (a × c)/(b × d)

Multiply numerators, multiply denominators

✏️ Example: 2/3 × 3/4 using area model

📝 Steps for Fractions > 1:

1. Convert mixed numbers to improper fractions (if needed)
2. Draw multiple rectangles for wholes
3. Apply area model technique
4. Count all overlapping shaded regions
5. Convert back to mixed number if needed

✏️ Example: 1 1/2 × 2/3

💡 Key Concepts to Remember:

🔑 Key Tips for Success:

• When multiplying by a whole number, multiply only the numerator
• For fraction × fraction, multiply numerators together and denominators together
• Use visual models to understand what multiplication means
• The word "of" in word problems often means multiply (1/2 of 12 = 1/2 × 12)
• Always simplify your final answer to lowest terms
• Convert improper fractions to mixed numbers when appropriate
• Practice with different models to build deep understanding