Find a missing numerator or denominator in an equivalent fraction

What you will learn

• Find a missing numerator or denominator in an equivalent fraction

Models used: number sentences, stories, fraction strips.

Before you start

• Multiply a proper fraction by a proper or improper fraction

New cuts, same amount

Half the strip is shaded.

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

   Half the strip is shaded.

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

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

   Cut each half into two equal pieces. We now call the shaded amount two quarters.

   1/2 = 2/4

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

   1/2 = 2/4: the same length, so the same amount.

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

   Another cut makes four eighths. The coloured length never changed.

   1/2 = 2/4 = 4/8

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

   1/2 = 2/4 · 1/2 = 4/8 · 2/4 = 4/8: the same length, so the same amount.

Worked example: A new example, together

Complete the equivalent fraction: 10/12 = 30/□.

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

   Compare the chosen lengths on equal-sized wholes before comparing the written numbers.

   Multiplying or dividing both numerator and denominator by the same non-zero number preserves the fraction.

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

   Splitting each part into 3 smaller parts changes the count and total by the same factor.

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

   Complete the equivalent fraction: 10/12 = 30/□.

   36

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

   10 × 3 = 30; 12 × 3 = 36.

   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.

   30/36 and 10/12 cover the same amount. Answer: 36.

   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.

   Check the result against the question we started with.

   Cross-products agree: 30 × 12 = 10 × 36.

   We found 36. Multiplying or dividing both numerator and denominator by the same non-zero number preserves the fraction.

Common mistakes to discuss

• Adding instead of multiplying. Both numbers are multiplied or divided by the same amount. 1/2 = 4/8 because both were multiplied by 4; adding 3 to each would give 4/5, a different amount.

Check your understanding

• Find a missing numerator or denominator in an equivalent fraction
• explain equivalent fractions as different names for the same share
• check the answer against the original quantities and units

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.