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Maths for SG Primary Schools

Primary 5 maths · Fractions · About 12 minutes

Multiply fractions by fractions

Identify the amount that acts as the whole, then one part, then the selected parts.

Start the interactive lesson →Open practice activity

What you will learn

Models used: number sentences, stories, diagrams.

Before you start

A part of a part

The orange part is three quarters of a sheet.

  1. The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.

    The orange part is three quarters of a sheet.

    The denominator determines one part’s size. The numerator tells us how many of those parts to take.

    3 of 4 columns

  2. The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.

    We only want two thirds of that orange part. Split it into three equal rows and keep two.

    Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.

    Take 2 of the 3 rows

  3. The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.

    The overlap covers 6 of 12 equal pieces. That is half of the original sheet.

    2/3 × 3/4 = 6/12 = 1/2

    The overlap counts the parts we kept. Count it against every equal part in the original whole, not just the originally shaded part.

    6 of 12 equal pieces
What did the picture help us see?

The overlap covers 6 of 12 equal pieces. That is half of the original sheet.

Worked example: A new example, together

Find 2/5 × 2/4.

Take 2 of the 5 rows

  1. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    Identify the amount that acts as the whole, then one part, then the selected parts.

    A fraction of a amount scales that quantity by the fraction.

    Take 2 of the 5 rows

  2. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    A fraction of an amount means divide by 5, then take 2 of those parts.

    Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.

    Take 2 of the 5 rows
    Find 2/5 × 2/4.

    1/5

  3. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    A fraction of an amount means divide by 5, then take 2 of those parts.

    Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.

    Take 2 of the 5 rows

  4. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    Multiply numerators and denominators: (2 × 2)/(5 × 4).

    Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.

    Take 2 of the 5 rows

  5. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    The amount is 1/5.

    Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.

    Take 2 of the 5 rows

  6. The whole rectangle has 5 equal rows and 4 equal columns. We are finding 2/5 of 2/4.

    Check the result against the question we started with.

    The selected amount divided by 0.5 equals 2/5.

    We found 1/5. A fraction of a amount scales that quantity by the fraction.

    Take 2 of the 5 rows

Common mistakes to discuss

Check your understanding

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.

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