Mastering Arithmetic for GCSE Success
Introduction
Arithmetic forms the foundation of GCSE Maths, covering everything from basic calculations to real-life applications. These skills are critical for understanding advanced topics like algebra, geometry, and statistics.
In this article, we’ll focus on:
- Fractions, Decimals, and Percentages.
- Simplifying and calculating accurately.
- Real-life applications of arithmetic.
Fractions: Simplifying and Calculating
Fractions represent a part of a whole and are crucial for GCSE success.
Simplifying Fractions
To simplify fractions:
- Divide the numerator and denominator by their highest common factor (HCF).
Example: Simplify 
.
- HCF of 18 and 24 is 6.
![\[ \frac{18 \div 6}{24 \div 6} = \frac{3}{4}. \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-4aa0749ee5503c52d488e66c733c0d91_l3.png "Rendered by QuickLaTeX.com")
Adding and Subtracting Fractions
Fractions must have the same denominator.
Example: 
- Find a common denominator:
. - Rewrite fractions:
.
.
.Multiplying and Dividing Fractions
- Multiply: Multiply the numerators and denominators directly.
- Divide: Multiply by the reciprocal of the second fraction.
Example:
![\[ \frac{2}{5} \div \frac{3}{4} = \frac{2}{5} \times \frac{4}{3} = \frac{8}{15}. \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-1e35225365c6e6cfedb3bb38abe73bfe_l3.png "Rendered by QuickLaTeX.com")
Decimals: Converting and Calculating
Converting Fractions to Decimals
- Divide the numerator by the denominator.
Example: Convert 
to a decimal:
![\[ 7 \div 8 = 0.875. \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-c8ffbee094dbf3456e8b57d50645b8d1_l3.png "Rendered by QuickLaTeX.com")
Rounding Decimals
- Round to a specified number of decimal places or significant figures.
Example: Round 3.4567 to 2 decimal places: 3.46.
Percentages: Finding Parts and Whole
Finding Percentages of a Number
Example: Find 20% of 80.
- Convert to a decimal:
. - Multiply:
.
.
.Finding the Whole Given a Percentage
Example: 25% of a number is 50. What is the number?
- Rewrite as an equation:
. - Solve:
.
.
.Real-Life Applications
- Money Problems: Working out discounts, VAT, and interest.
- Measurements: Scaling recipes or resizing shapes.
Practice Question
Question: A coat is discounted by 15%, reducing the price to £85. What was the original price?
Solution:
- Let the original price be
. - Equation:
. - Simplify:
. - Solve:
.
.
.
.
.Answer: The original price was £100.
Conclusion
Mastering arithmetic is essential for GCSE Maths and beyond. Practice simplifying fractions, calculating percentages, and applying these skills to real-life scenarios to build confidence.
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