EDEXCEL GCSE FOUNDATION MATHS - What is Expressing as a Fraction or Percentage

Expressing as a Fraction or Percentage

Understanding Fractions and Percentages

• Fractions: Represent parts of a whole. They have a numerator (top number) and a denominator (bottom number). For example, 1/2 represents one out of two equal parts.

• Percentages: Represent parts of a whole out of 100. They are denoted by the symbol “%”. For example, 50% means 50 out of 100.

Converting Between Fractions and Percentages

1. Fraction to Percentage: * Divide the numerator by the denominator. * Multiply the result by 100. * Add the percentage symbol (%).

Example: Convert 3/4 to a percentage: * 3 ÷ 4 = 0.75 * 0.75 × 100 = 75 * Therefore, 3/4 is equal to 75%.

1. Percentage to Fraction: * Divide the percentage by 100. * Simplify the fraction to its lowest terms.

Example: Convert 60% to a fraction: * 60 ÷ 100 = 0.6 * 0.6 can be written as 6/10 * Simplifying the fraction gives us 3/5

Expressing Quantities as Fractions and Percentages

1. Expressing a Quantity as a Fraction: * Identify the whole. * Determine the part you want to express as a fraction. * Write the part as the numerator and the whole as the denominator.

Example: In a class of 20 students, 12 are girls. Express the number of girls as a fraction of the class. * The whole is 20 students. * The part is 12 girls. * The fraction is 12/20, which can be simplified to 3/5.

1. Expressing a Quantity as a Percentage: * Convert the fraction to a percentage (as explained above).

Example: Using the previous example, express the number of girls as a percentage of the class. * We know that the fraction is 3/5. * 3 ÷ 5 = 0.6 * 0.6 × 100 = 60 * Therefore, 60% of the class are girls.

Important Notes:

• Always simplify fractions to their lowest terms.
• Remember that a percentage represents a fraction out of 100.
• When expressing quantities as fractions or percentages, make sure you are comparing them to the correct whole.

Practice Problems:

1. Convert the following fractions to percentages: * 1/2 * 2/5 * 3/8

2. Convert the following percentages to fractions: * 25% * 70% * 125%

3. In a bag of 30 marbles, 15 are blue. Express the number of blue marbles as a fraction and a percentage of the total marbles.

These exercises will help you solidify your understanding of expressing quantities as fractions and percentages.