Fractions and Percentages Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) PDF Download

Equivalence, comparing and ordering fractions

• The objective is to recognize proper fractions as fractions less than a whole.
• Identify when fractions are equivalent.
• Compare and order fractions based on their size.
• Proper fractions are fractions where the numerator is less than the denominator, e.g., 3/4.
• Equivalent fractions have the same value despite different numerators and denominators, e.g., 3/6 = 1/2.
• Caution is needed when comparing fractions across different wholes, e.g., 3/6 of Pie A may not equal 1/2 of Pie B if the pies differ in size.
• To compare or order fractions, convert them to equivalent fractions with a common denominator, e.g., for 1/2, 5/8, 3/8, 3/4, rewrite with denominator 8: 1/2 = 4/8, 5/8 = 5/8, 3/8 = 3/8, 3/4 = 6/8, then order as 3/8, 4/8, 5/8, 6/8.
• Methods to find equivalent fractions include:
  • Dividing rectangles to visualize equivalence, e.g., 1/2 = 4/8, 3/4 = 6/8.
  • Using a number line to locate fractions, e.g., marking 1/8, 2/8, 3/8, ..., 8/8.
  • Using a fraction wall to compare fractions visually, showing 1/2, 1/4, 1/8 divisions.
• Previous learning in Stages 2 and 3 covered equivalent fractions for halves, quarters, fifths, and tenths, now extended to other proper fractions.

Percentages

• The objective is to understand a percentage as the number of parts out of 100.
• Use the percentage symbol (%) correctly.
• Percentage and percent refer to parts per hundred, denoted by %, e.g., 25% means 25 out of 100.
• Percentages are commonly seen in everyday contexts, such as:
  • Food labels, e.g., a burger containing 19% fat or 30% saturates of an adult’s reference intake.
  • Shop sales, where discounts are expressed as percentages.
• To calculate a percentage, determine the portion relative to 100, e.g., for a dress with 50% cotton and 25% wool:
  • % silk = 100 - 50 - 25 = 25%.
  • Alternatively, 50 + 25 = 75, then 100 - 75 = 25%.
• Percentages can be converted to fractions, e.g., 25% = 25/100 = 1/4.
• Fractions can be converted to percentages, e.g., 3/4 = 75/100 = 75%, 1/4 = 25/100 = 25%, 1/2 = 50/100 = 50%.