Key Exam Secret
Fractions, decimals, and percentages are just three different ways of showing the exact same number! For instance: $\frac{1}{2} = 0.5 = 50\%$. Knowing the common conversion table by heart saves crucial minutes during the Grade 7 exam.
Table of Contents
1. Types of Fractions & Simplifying
- Proper Fraction: Numerator is smaller than denominator (e.g., $\frac{3}{5}$).
- Improper Fraction: Numerator is greater than or equal to denominator (e.g., $\frac{7}{4}$).
- Mixed Number: A whole number combined with a proper fraction (e.g., $1\frac{3}{4}$).
To reduce a fraction to its lowest terms, divide both numerator and denominator by their Highest Common Factor (HCF). For example: $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$.
2. Operations on Fractions
Addition & Subtraction (Same Denominator vs LCM)
Find the Lowest Common Multiple (LCM) of the denominators before adding or subtracting:
$$\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$$
Multiplication of Fractions
Multiply numerators together and denominators together, simplifying before multiplying:
$$\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 4}{8 \times 9} = \frac{12}{72} = \frac{1}{6}$$
Division of Fractions ("Keep, Change, Flip")
$$\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$$
3. Decimals: Place Value & Arithmetic
In decimal numbers, the point separates whole units from fractional parts (tenths, hundredths, thousandths):
- $0.7 = \frac{7}{10}$ (seven tenths)
- $0.05 = \frac{5}{100} = \frac{1}{20}$ (five hundredths)
- $0.125 = \frac{125}{1000} = \frac{1}{8}$ (one hundred and twenty-five thousandths)
4. The Master Equivalence Table
Memorize these high-frequency Grade 7 conversions:
| Fraction | Decimal | Percentage |
|---|---|---|
| $\frac{1}{2}$ | $0.5$ | $50\%$ |
| $\frac{1}{4}$ | $0.25$ | $25\%$ |
| $\frac{3}{4}$ | $0.75$ | $75\%$ |
| $\frac{1}{5}$ | $0.2$ | $20\%$ |
| $\frac{2}{5}$ | $0.4$ | $40\%$ |
| $\frac{1}{10}$ | $0.1$ | $10\%$ |
| $\frac{1}{8}$ | $0.125$ | $12.5\%$ |
5. Zambian Currency Word Problems
Solution:
Discount $= 15\% \times \text{K}240 = \frac{15}{100} \times 240 = \text{K}36$.
Amount Paid $= \text{K}240 - \text{K}36 = \text{K}204$.
Solution:
$\text{Profit} = \text{Selling Price} - \text{Cost Price} = 180 - 150 = \text{K}30$.
$\text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\% = \frac{30}{150} \times 100\% = \frac{1}{5} \times 100\% = 20\%$.
Parent Math Practice at Home
Practice percentages during grocery shopping. Ask your child: "If this loaf of bread costs K20 and VAT is 16%, how many Ngwee is that?" Practical shopping math eliminates abstract confusion.