Primary 4 maths · Fractions · About 10 minutes
Represent mixed numbers and improper fractions
Mark each complete whole and the remaining parts separately.
Start the interactive lesson →Practise: Mixed-number bakery
What you will learn
- Represent mixed numbers and improper fractions
Models used: number sentences, stories, fraction strips.
Before you start
More than one whole
One whole and three quarters are shaded.
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.
The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.
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.
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.
What did the picture help us see?
Seven quarters and one-and-three-quarters name the same amount.
Worked example: A new example, together
Write 23/8 as a mixed number in simplest form.
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.
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
Each whole contains 8 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 23/8 as a mixed number in simplest form.
2 7/8
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
2 wholes contain 16 parts; add 7 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.
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
23/8 = 2 7/8.
The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.
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.
23 = 2 × 8 + 7.
We found 2 7/8. 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
- Represent 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.
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