Exploring fractions, decimals, and percentages reveals their interconnectedness and utility in maths and real-life scenarios. This section aims to solidify your understanding, offering step-by-step calculations and examples to navigate through these concepts effectively.

Proper and Improper Fractions

Fractions express parts of a whole, defined by a numerator and a denominator.

• Proper Fractions: Where the numerator is smaller than the denominator, e.g., $\frac{3}{4}$.

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• Improper Fractions: Where the numerator exceeds or equals the denominator, e.g., $\frac{5}{3}$.

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Improper fractions can transform into mixed numbers, blending whole numbers with fractions, like $1\frac{2}{3}$.

Example: Converting Improper Fractions to Mixed Numbers

Question: Convert $\frac{11}{4}$ into a mixed number.

Solution:

1. Divide 11 by 4: $11 \div 4 = 2$ with a remainder of 3.

2. Express as a mixed number: $2\frac{3}{4}$.

Thus, $\frac{11}{4}$ converts to $2\frac{3}{4}$.

Decimals

Decimals offer another perspective for representing fractions, delineating the whole from the fractional part via a decimal point.

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Example: Converting Fractions to Decimals

Question: Convert $\frac{3}{8}$ to decimal.

Solution:

Percentages

Percentages frame fractions out of 100, simplifying comparisons and proportions.

Example: Converting Decimals to Percentages

Question: Convert 0.2 to a percentage.

Solution:

Applying Concepts

Applying these conversions is crucial across financial calculations, measurements, and data analysis.

Real-life Application: Calculating Discounts

Scenario: A 20% discount on a £50 jacket. What's the final price?

Solution:

1. Convert 20% to decimal: $20\% = 0.2$.

2. Calculate discount: $£50 \times 0.2 = £10$.

3. Deduct discount from original price: $£50 - £10 = £40$.

Final price: £40.