^numerator/_denominator

Numerator: Top number (parts you have)

Denominator: Bottom number (total parts)

Equivalent fractions have DIFFERENT numerators

and denominators but represent the SAME VALUE

Example: 1/2 = 2/4 = 3/6 = 4/8

^a/_b × ⁿ/_n = ^a×n/_b×n

Multiply both numerator and denominator by the SAME number

Divide both numerator and denominator by a COMMON FACTOR

This simplifies the fraction

A fraction is in LOWEST TERMS when the

numerator and denominator have NO common factors

other than 1 (they are relatively prime)

^a/_b ÷ ^GCF/_GCF = ^a÷GCF/_b÷GCF

Divide both by the Greatest Common Factor (GCF)

Step 1: Find the GCF of numerator and denominator

Step 2: Divide both numerator and denominator by GCF

Step 3: The result is the simplified fraction

LCD is the SMALLEST common denominator

for a set of fractions

• It's the LCM (Least Common Multiple) of denominators

• Needed for adding and subtracting fractions

Step 1: List multiples of each denominator

Step 2: Find the smallest common multiple

Step 3: That's your LCD!

If denominators are SAME:

Compare the NUMERATORS

Larger numerator = Larger fraction

Example: 5/8 > 3/8 (because 5 > 3)

If numerators are SAME:

Compare the DENOMINATORS

Smaller denominator = Larger fraction

Example: 2/3 > 2/5 (because 3 < 5)

Step 1: Find the LCD of both fractions

Step 2: Convert both fractions to LCD

Step 3: Compare numerators

a^b/_c = ^(a×c)+b/_c

Step 1: Multiply whole number × denominator

Step 2: Add the numerator

Step 3: Write result over original denominator

Step 1: Divide numerator by denominator

Step 2: Quotient = whole number

Step 3: Remainder = new numerator

Step 4: Denominator stays the same

Look at the FRACTION PART:

• If fraction ≥ 1/2 → ROUND UP

• If fraction < 1/2 → ROUND DOWN (stay same)

Compare: numerator ≥ (denominator ÷ 2)

If YES → Round up

If NO → Stay the same

Example 1: Round 7 3/4

Example 2: Round 12 1/3

Example 3: Round 9 5/8

✓ Equivalent fractions: Multiply/divide numerator AND denominator by same number

✓ Lowest terms: Divide by GCF until no common factors remain

✓ LCD is needed for adding, subtracting, and comparing fractions

✓ Same denominator: Compare numerators (larger numerator = larger fraction)

✓ Same numerator: Compare denominators (smaller denominator = larger fraction)

✓ Different numerators and denominators: Convert to LCD first

✓ Mixed to improper: Multiply, add, keep denominator

✓ Improper to mixed: Divide, quotient is whole, remainder is numerator

✓ Rounding: Compare fraction to 1/2 (numerator vs half of denominator)

✓ Always simplify your final answer to lowest terms

Equivalent Fractions:

"Whatever you do to the top, do to the bottom too!"

Simplifying:

"Find the GCF and divide it right - makes the fraction small and tight!"

Comparing Fractions:

"Same bottom? Compare the top! Same top? Smaller bottom is on top!"

Mixed to Improper:

"Multiply, add, and place - denominator stays in its space!"

Improper to Mixed:

"Divide to decide the whole, remainder's the goal!"

Rounding Mixed Numbers:

"Half or more? Raise the score! Less than half? Just laugh!"