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Maths for SG Primary Schools

Primary 5 Foundation maths · Fractions · About 12 minutes

Multiply a proper fraction by a proper or improper fraction

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, fraction strips.

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 11/8 × 3/4.

  1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    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.

  2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    A fraction of an amount means divide by 8, then take 11 of those parts.

    The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

    Find 11/8 × 3/4.

    33/32

  3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    A fraction of an amount means divide by 8, then take 11 of those parts.

    The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

  4. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    Multiply numerators and denominators: (11 × 3)/(8 × 4).

    The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

  5. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    The amount is 33/32.

    The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

  6. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

    Check the result against the question we started with.

    The selected amount divided by 0.75 equals 11/8.

    We found 33/32. A fraction of a amount scales that quantity by the fraction.

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.

Try this lesson →

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