EDEXCEL GCSE FOUNDATION MATHS - What are Fractions, Decimals, and Percentages

Fractions, Decimals, and Percentages

Fractions, decimals, and percentages are all different ways to represent parts of a whole. Understanding how they relate to each other is crucial for solving many GCSE Maths problems.

Fractions

A fraction represents a part of a whole divided into equal pieces. It is written as a ratio of two numbers:

• Numerator: The top number shows how many parts we have.
• Denominator: The bottom number shows the total number of equal parts the whole is divided into.

Example: 3/4 represents 3 out of 4 equal parts.

Decimals

Decimals represent parts of a whole using place values. The decimal point separates the whole number from the fractional part.

• Whole number: The digits to the left of the decimal point represent whole numbers.
• Fractional part: The digits to the right of the decimal point represent parts of a whole. Each place value represents a power of 10.

Example: 0.75 represents 75 hundredths (7/10 + 5/100).

Percentages

A percentage is a fraction out of 100. It means "out of one hundred" and is represented by the symbol "%".

Example: 75% represents 75 out of 100, which is equivalent to 75/100.

Converting Between Fractions, Decimals, and Percentages

You can easily convert between these three forms:

Fraction to Decimal: Divide the numerator by the denominator.

Example: 3/4 = 3 ÷ 4 = 0.75

Decimal to Fraction: Write the decimal as a fraction with the denominator as a power of 10 (e.g., 10, 100, 1000). Simplify the fraction if possible.

Example: 0.75 = 75/100 = 3/4

Fraction to Percentage: Multiply the fraction by 100%.

Example: 3/4 × 100% = 75%

Decimal to Percentage: Multiply the decimal by 100%.

Example: 0.75 × 100% = 75%

Percentage to Fraction: Divide the percentage by 100 and simplify the fraction.

Example: 75% = 75/100 = 3/4

Percentage to Decimal: Divide the percentage by 100.

Example: 75% = 75/100 = 0.75

Practice Problems

1. Convert 2/5 to a decimal and a percentage.
2. Convert 0.6 to a fraction and a percentage.
3. Convert 40% to a fraction and a decimal.

Key Points

• Fractions, decimals, and percentages are all ways to represent parts of a whole.
• You can easily convert between these forms using simple calculations.
• Understanding the relationships between these forms is essential for solving many GCSE Maths problems.