🔢 Fractions, Decimals & Percents (Mastery)

Percent Review:
Percent means "out of 100." To find a percent of a number:
• Convert percent to decimal (divide by 100)
• Multiply by the number

Types of Percent Problems:
TypeFormulaExampleDiscountOriginal × (Percent off) = Savings20% off 50 =10 savedSale PriceOriginal - Savings50 -10 = 40 |
| **Tax** | Price × Tax rate = Tax amount |40 × 0.08 = 3.20 tax |
| **Tip** | Bill × Tip rate = Tip amount |50 × 0.15 = 7.50 tip |
| **Total with tax/tip** | Price + Tax/Tip |40 + 3.20 =43.20Percent Increase(New - Original)/Original × 100(60-50)/50 = 20%Percent Decrease(Original - New)/Original × 100(50-40)/50 = 20%

The "Keep-Change-Flip" Rule
Dividing fractions is easy with this trick:
Keep the first fraction
Change ÷ to ×
Flip the second fraction (reciprocal)
Rule: (a)/(b) ÷ (c)/(d) = (a)/(b) × (d)/(c) = (a × d)/(b × c)
Examples:
• ⅔ ÷ ⅘ = ⅔ × 5/4 = 10/12 = (5)/(6)
• ⅚ ÷ ⅓ = ⅚ × 3/1 = 15/6 = 5/2 = 2½

Dividing Mixed Numbers:
• Convert mixed numbers to improper fractions
• Use Keep-Change-Flip
• Simplify

Two Types of Decimals:
TypeDescriptionExampleTerminating DecimalEnds/stops after finite digits1/4 = 0.25Repeating DecimalDigits repeat forever1/3 = 0.333...Converting Fraction to Decimal:
Method: Divide numerator by denominator
• (1)/(4) = 1 ÷ 4 = 0.25 (terminating)
• (1)/(3) = 1 ÷ 3 = 0.333... (repeating)
• (5)/(8) = 5 ÷ 8 = 0.625 (terminating)
• (2)/(3) = 2 ÷ 3 = 0.666... (repeating)

When does a fraction terminate?
A fraction in simplest form terminates if the denominator's prime factors are only 2 and/or 5!
• (1)/(4) = 1/2² → terminates (0.25)
• 1/8 = 1/2³ → terminates (0.125)
• 3/20 = 3/(2²×5) → terminates (0.15)
• (1)/(3) = (1)/(3) → repeats (0.333...)
• 1/6 = 1/(2×3) → repeats (0.1666...)