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Maths for SG Primary Schools

Primary 6 maths · Ratio, rate & percentage · About 12 minutes

Connect ratios and fractions

Keep the quantity labels in order. Distinguish one part from the sum of all ratio parts.

Start the interactive lesson →Open practice activity

What you will learn

Models used: number sentences, stories, diagrams.

Before you start

Which whole does the fraction mean?

Red to blue is 2 to 3. Red has two units; blue has three.

  1. All the small boxes represent equally sized units, even when they belong to different rows.

    Red to blue is 2 to 3. Red has two units; blue has three.

    The counts of equal units describe the comparison. Their actual size comes from a given quantity or total.

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

    For the fraction that is red, the whole includes both colours: five units.

    2 + 3 = 5 units

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

    1/51/51/51/51/52/5

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

    Two of all five units are red. Red is two fifths of the total.

    red : blue = 2 : 3; red / total = 2/5

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

    1/51/51/51/51/52/5
What did the picture help us see?

Two of all five units are red. Red is two fifths of the total.

Worked example: A new example, together

Red:blue:green = 1:4:4. What fraction of all counters is red?

  1. All the small boxes represent equally sized units, even when they belong to different rows.

    Keep the quantity labels in order. Distinguish one part from the sum of all ratio parts.

    A fraction of the total uses all ratio units in its denominator.

  2. All the small boxes represent equally sized units, even when they belong to different rows.

    All ratio units: 1 + 4 + 4 = 9.

    One unit must have the same value in every row. That lets us compare amounts by counting their units.

    Red:blue:green = 1:4:4. What fraction of all counters is red?

    1/9

  3. All the small boxes represent equally sized units, even when they belong to different rows.

    All ratio units: 1 + 4 + 4 = 9.

    One unit must have the same value in every row. That lets us compare amounts by counting their units.

  4. All the small boxes represent equally sized units, even when they belong to different rows.

    Red has 1 units.

    One unit must have the same value in every row. That lets us compare amounts by counting their units.

  5. All the small boxes represent equally sized units, even when they belong to different rows.

    The fraction is 1/9 = 1/9.

    One unit must have the same value in every row. That lets us compare amounts by counting their units.

  6. All the small boxes represent equally sized units, even when they belong to different rows.

    Check the result against the question we started with.

    Red has 1 of the 9 total units.

    We found 1/9. A fraction of the total uses all ratio units in its denominator.

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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