Fractions — Deep Dive Learning

What is a fraction?

• A fraction is a part of a whole.
• A fraction has a top number (numerator) and a bottom number (denominator).
• Example: ½ means 1 part out of 2 equal parts.
• We use fractions for cooking, time, money and sharing.
• Common fractions: ½, ¼, ¾, ⅓

Understanding Halves

• ½ means split into 2 equal parts and take 1.
• ½ of 10 = 5
• ½ of £20 = £10
• Half an hour = 30 minutes.
• Half is the same as 50%.

Understanding Quarters

• ¼ means split into 4 equal parts and take 1.
• ¼ of 20 = 5
• ¼ of £40 = £10
• ¾ means take 3 out of 4 parts.
• ¾ of 20 = 15

Fractions in cooking

• Recipes often use fractions.
• ½ a cup of sugar means half a cup.
• ¼ teaspoon of salt means a quarter teaspoon.
• If a recipe serves 4 and you need 2 portions, use half of everything.

Worked Examples

Practice Problems

• What is ½ of 18?
  Hint: Divide 18 by 2.
  Answer: 9
• What is ¼ of 32?
  Hint: Divide 32 by 4.
  Answer: 8
• A recipe needs ¾ of 12 eggs. How many eggs?
  Hint: Divide by 4, then multiply by 3.
  Answer: 9

Common Mistakes to Avoid

• Mistake: Adding numerators and denominators: 1/3 + 1/4 = 2/7
  Correction: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
  Why: You must find a common denominator first, then add the numerators only.
• Mistake: Thinking 1/3 is bigger than 1/2
  Correction: 1/2 is bigger because 2 parts are larger than 3 parts
  Why: The bigger the denominator, the smaller each piece. Think of cutting a pizza into more slices.
• Mistake: Saying half of 1/4 is 1/2
  Correction: Half of 1/4 is 1/8
  Why: Halving a fraction means doubling the denominator: 1/4 ÷ 2 = 1/8.