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OCR GCSE Maths (Higher) Study Notes

1.4.1 Understanding and Usage of Fractions, Decimals, and Percentages

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.

Fractions illustration
  • Proper Fractions: Where the numerator is smaller than the denominator, e.g., 34\frac{3}{4}.
Proper Fraction illustration

Image courtesy of BYJUS

  • Improper Fractions: Where the numerator exceeds or equals the denominator, e.g., 53\frac{5}{3}.
Improper Fraction illustration

Image courtesy of Twinkl

Improper fractions can transform into mixed numbers, blending whole numbers with fractions, like 1231\frac{2}{3}.

Example: Converting Improper Fractions to Mixed Numbers

Question: Convert 114\frac{11}{4} into a mixed number.

Solution:

1. Divide 11 by 4: 11÷4=211 \div 4 = 2 with a remainder of 3.

2. Express as a mixed number: 2342\frac{3}{4}.

Thus, 114\frac{11}{4} converts to 2342\frac{3}{4}.

Decimals

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

Fractions to Decimals

Image courtesy of Cuemath

Example: Converting Fractions to Decimals

Question: Convert 38\frac{3}{8} to decimal.

Solution:

38=0.375\frac{3}{8} = 0.375


Percentages

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

Decimal to Percent

Example: Converting Decimals to Percentages

Question: Convert 0.2 to a percentage.

Solution:

0.2×100=20%0.2 \times 100 = 20\%

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%=0.220\% = 0.2.

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

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

Final price: £40.

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