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:

1. Fractions, Decimals, and Percentages.
2. Simplifying and calculating accurately.
3. Real-life applications of arithmetic.

1. Fractions: Simplifying and Calculating

Fractions represent a part of a whole and are crucial for GCSE success.

Simplifying Fractions

To simplify fractions:

1. Divide the numerator and denominator by their highest common factor (HCF).

Example: Simplify .

• HCF of 18 and 24 is 6.

Adding and Subtracting Fractions

Fractions must have the same denominator.

Example:

1. Find a common denominator: .
2. Rewrite fractions: .

Multiplying and Dividing Fractions

• Multiply: Multiply the numerators and denominators directly.
• Divide: Multiply by the reciprocal of the second fraction.

Example:

2. Decimals: Converting and Calculating

Converting Fractions to Decimals

• Divide the numerator by the denominator.

Example: Convert to a decimal:

Rounding Decimals

• Round to a specified number of decimal places or significant figures.

Example: Round 3.4567 to 2 decimal places: 3.46.

3. Percentages: Finding Parts and Whole

Finding Percentages of a Number

Example: Find 20% of 80.

1. Convert to a decimal: .
2. Multiply: .

Finding the Whole Given a Percentage

Example: 25% of a number is 50. What is the number?

1. Rewrite as an equation: .
2. Solve: .

4. 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:

1. Let the original price be .
2. Equation: .
3. Simplify: .
4. 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.