Convert between mixed numbers and improper fractions

What you will learn

• Convert between mixed numbers and improper fractions

Models used: number sentences, stories, fraction strips.

Before you start

• Compare fractions with denominators up to 12

More than one whole

One whole and three quarters are shaded.

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

   One whole and three quarters are shaded.

   For example, one whole contains four quarters. Whole counts must be converted to part counts before they are joined.

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

   The whole is four quarters. Count those along with the three extra quarters.

   4 quarters + 3 quarters

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

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

   Seven quarters and one-and-three-quarters name the same amount.

   1 3/4 = 7/4

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

Worked example: A new example, together

Write 2 9/12 as an improper fraction.

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

   Mark each complete whole and the remaining parts separately.

   A whole contributes denominator-many fractional parts.

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

   Each whole contains 12 equal 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.

   Write 2 9/12 as an improper fraction.

   33/12

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

   Each whole contains 12 equal 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.

   2 wholes contain 24 parts; add 9 more.

   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.

   33/12 = 2 9/12.

   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.

   33 = 2 × 12 + 9.

   We found 33/12. A whole contributes denominator-many fractional parts.

Common mistakes to discuss

• Losing the whole number. Each whole contains a full set of parts. 2 1/4 is 9/4, because the two wholes are 8 quarters before the extra quarter is added.

Check your understanding

• Convert between mixed numbers and improper fractions
• connect whole counts and equal-part counts in mixed and improper fractions
• 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.