Mastering Fractions, Decimals, and Percentages
Understanding the Connections and Solving Problems Year 11 Mathematics
Understanding Fractions
A fraction represents part of a whole Written as numerator/denominator (e.g., 3/4) Real-life examples: pizza slices, class attendance, money portions Key skills: simplifying fractions and converting improper to mixed numbers
Understanding Decimals
Decimals are another way to express parts of a whole Based on powers of 10 (tenths, hundredths, thousandths) Converting: Divide numerator by denominator (3/4 = 0.75) Rounding: to nearest tenth, hundredth, or whole number
Understanding Percentages
Percentage means 'per hundred' or 'out of 100' Converting fractions: multiply by 100 (3/4 × 100 = 75%) Converting decimals: multiply by 100 (0.75 × 100 = 75%) Real applications: discounts, tax rates, test scores, interest rates
The Connection Triangle
Real-Life Word Problems
Problem 1: Sarah scored 18 out of 24 on her test. Express as fraction, decimal, and percentage. Problem 2: A shirt costs $80. With a 25% discount, what's the sale price? Problem 3: 0.6 of the class plays sport. If there are 30 students, how many play sport? Convert your answers into all three forms where possible!
Quick Conversion Reference
{"left":"Common Fractions to Remember:\n1/2 = 0.5 = 50%\n1/4 = 0.25 = 25%\n3/4 = 0.75 = 75%\n1/5 = 0.2 = 20%","right":"Conversion Tips:\nFraction → Decimal: Divide top by bottom\nDecimal → Percentage: Multiply by 100\nPercentage → Fraction: Put over 100, simplify\nAlways check if fractions can be simplified!"}
Challenge Problems
Challenge 1: A recipe calls for 2¾ cups of flour. How much is this as a decimal and percentage of 4 cups? Challenge 2: In a sale, prices are reduced by 35%. If a jacket originally costs $120, what's the new price? Challenge 3: 7/8 of a pizza was eaten. What percentage remains? Express as decimal too. Work in pairs - explain your working to your partner!
Quick Check Understanding
Which is larger: 3/5 or 62%? Convert 0.45 to a percentage and simplified fraction If 40% of students walk to school, what fraction walk to school? A test score of 17/20 equals what percentage?
Key Takeaways
"Master these three number forms to handle real-life mathematics with confidence!" • Fractions, decimals, and percentages are different ways to express the same value • Practice converting between forms until it becomes automatic • Look for these concepts everywhere: shopping, cooking, sports, and academics • Remember: understanding these connections makes complex problems much easier!