Lesson 2 • 35 min read
Fractions & Decimals
In This Lesson
1Types of Fractions
Proper Fraction
Numerator < Denominator
Value is less than 1
Improper Fraction
Numerator ≥ Denominator
Value is 1 or greater
Mixed Number
Whole + Fraction
Combines both parts
Converting Between Forms
Improper → Mixed
Divide numerator by denominator
7/4 = 7 ÷ 4 = 1 R3 = 1³⁄₄
Mixed → Improper
(Whole × Denom) + Numer
1³⁄₄ = (1×4)+3 / 4 = 7/4
2Adding & Subtracting Fractions
Same Denominators (Easy!)
Just add/subtract the numerators, keep the denominator.
2/5 + 1/5 = (2+1)/5 = 3/5
4/7 - 2/7 = (4-2)/7 = 2/7
Different Denominators (Need LCD)
Find the LCD (Least Common Denominator) first!
Example: 1/3 + 1/4
Step 1: Find LCD of 3 and 4 = 12
Step 2: Convert: 1/3 = 4/12 and 1/4 = 3/12
Step 3: Add: 4/12 + 3/12 = 7/12
Finding LCD Methods
- Listing method: List multiples until you find common one
- Prime factorization: For larger numbers
- Quick method: If no common factors, multiply the denominators
3Multiplying Fractions
Multiply Straight Across!
No need for common denominators. Multiply numerators together, then denominators together.
a/b × c/d = (a×c)/(b×d)
Example 1:
2/3 × 4/5 = (2×4)/(3×5) = 8/15
Example 2:
3/4 × 2/7 = (3×2)/(4×7) = 6/28 = 3/14
Tip: Cross-cancel common factors before multiplying to keep numbers smaller!
4Dividing Fractions (KCF Method)
Keep - Change - Flip (KCF)
Keep the first fraction exactly as it is
Change the division sign to multiplication
Flip the second fraction (reciprocal)
Example: 2/3 ÷ 4/5
Keep: 2/3
Change: ÷ → ×
Flip: 4/5 → 5/4
2/3 × 5/4 = 10/12 = 5/6
5Decimal Conversions
Fraction → Decimal
Divide the numerator by the denominator.
1/2 = 1 ÷ 2
= 0.5
3/4 = 3 ÷ 4
= 0.75
1/8 = 1 ÷ 8
= 0.125
Decimal → Fraction
Use place value as the denominator, then simplify.
0.5 = 5/10 (tenths place) = 1/2
0.25 = 25/100 (hundredths) = 1/4
0.125 = 125/1000 (thousandths) = 1/8