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Year 5 Maths Fractions

Improper fractions to mixed numerals

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Theory

To change an improper fraction such as \(\dfrac{14}{3}\) into a mixed numeral, find how many wholes it makes and what is left over. Divide the numerator by the denominator: \(14 \div 3 = 4 \text{ r } 2\), so \(\dfrac{14}{3} = 4\dfrac{2}{3}\). This Year 5 maths page shows the method with diagrams, whole-number answers and simplifying the fraction part.

Every \(3\) thirds make \(1\) whole. In \(\dfrac{14}{3}\) there are four groups of \(3\) thirds (\(12\) thirds) and \(2\) thirds left over: \(4\dfrac{2}{3}\).

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

If there is no remainder, the fraction is a whole number: \(\dfrac{15}{5} = 3\).

If the fraction part can be simplified, do it: \(\dfrac{26}{4} = 6\dfrac{2}{4} = 6\dfrac{1}{2}\).

Fourteen thirds as bars Five bars, each cut into 3 equal parts. The first four bars are fully shaded and the fifth has 2 of its 3 parts shaded: 14 thirds make 4 wholes and 2 thirds. 1 whole 1 whole 1 whole 1 whole 23
\(\dfrac{14}{3}\): \(4\) full wholes and \(2\) thirds, so \(4\dfrac{2}{3}\).
14 divided by 3 Short division: 3 into 14 goes 4 times with remainder 2, shown as 4 and 2 thirds. 3 141 423
\(14 \div 3 = 4 \text{ r } 2\), so \(\dfrac{14}{3} = 4\dfrac{2}{3}\).

Divide the numerator by the denominator:

\[ \dfrac{14}{3} \to 14 \div 3 = 4 \text{ r } 2 \to 4\dfrac{2}{3} \]
14/3→14÷3=4 r 2→42/3
\[ \dfrac{15}{5} = 3 \]
15/5=3
\[ \dfrac{26}{4} = 6\dfrac{2}{4} = 6\dfrac{1}{2} \]
26/4=62/4=61/2
Quotient, remainder, same denominator. The quotient is the whole number; the remainder sits on top; the denominator does not change.
Check by changing back. \(4\dfrac{2}{3} = \dfrac{4 \times 3 + 2}{3} = \dfrac{14}{3}\).

How to change an improper fraction to a mixed numeral

  1. Divide the numerator by the denominator.
  2. Write the quotient as the whole number.
  3. Write the remainder over the same denominator.
  4. Simplify the fraction part if you can.
Example 1 — From a diagram
Use the first diagram. Write \(\dfrac{14}{3}\) as a mixed numeral.
Solution
\(14 \div 3\)\(=\)\(4 \text{ r } 2\)
14/3=42/3

\(\dfrac{14}{3} = 4\dfrac{2}{3}\).

Example 2 — Quarters
Write \(\dfrac{17}{4}\) as a mixed numeral.
Solution
\(17 \div 4\)\(=\)\(4 \text{ r } 1\)
17/4=41/4

\(4\dfrac{1}{4}\).

Example 3 — Whole-number part and remainder
Consider \(\dfrac{29}{6}\).
(i) What is the whole-number part?
(ii) What is the new numerator?
(iii) Write the mixed numeral.
Solution
\(29 \div 6\)\(=\)\(4 \text{ r } 5\)
29/6=45/6

(i) \(4\)
(ii) \(5\)
(iii) \(4\dfrac{5}{6}\)

Example 4 — A whole number
Write \(\dfrac{15}{5}\) as a whole number.
Solution
\(15 \div 5\)\(=\)\(3\)
15/5=3

\(\dfrac{15}{5} = 3\).

Example 5 — Simplify the fraction part
Write \(\dfrac{26}{4}\) as a mixed numeral in simplest form.
Solution
\(26 \div 4\)\(=\)\(6 \text{ r } 2\)
\(\dfrac{2}{4}\)\(=\)\(\dfrac{1}{2}\)
26/4=61/2

\(6\dfrac{2}{4} = 6\dfrac{1}{2}\).

Example 6 — Several at once
Write each as a mixed numeral.
(i) \(\dfrac{23}{5}\)
(ii) \(\dfrac{11}{2}\)
(iii) \(\dfrac{22}{6}\)
Solution
\(23 \div 5\)\(=\)\(4 \text{ r } 3\)
\(11 \div 2\)\(=\)\(5 \text{ r } 1\)
\(22 \div 6\)\(=\)\(3 \text{ r } 4\)
23/5=43/5,11/2=51/2,22/6=32/3

(i) \(4\dfrac{3}{5}\)
(ii) \(5\dfrac{1}{2}\)
(iii) \(3\dfrac{4}{6} = 3\dfrac{2}{3}\)

Example 7 — In context
A jug holds \(\dfrac{21}{8}\) litres of water. Write this as a mixed numeral.
Solution
\(21 \div 8\)\(=\)\(2 \text{ r } 5\)
21/8=25/8

\(2\dfrac{5}{8}\) litres.

Example 8 — Find the mistake
Max wrote \(\dfrac{18}{5} = 5\dfrac{3}{5}\), using the denominator as the whole number. Fix it.
Solution
\(18 \div 5\)\(=\)\(3 \text{ r } 3\)
18/5=33/5

The whole number is the quotient, \(3\), not the denominator. \(\dfrac{18}{5} = 3\dfrac{3}{5}\).

Common pitfalls

Using the denominator as the whole number. Divide to find the whole number: \(\dfrac{18}{5} = 3\dfrac{3}{5}\), not \(5\dfrac{3}{5}\).
Changing the denominator. The remainder goes over the same denominator: \(\dfrac{29}{6} = 4\dfrac{5}{6}\).
Writing the remainder as the whole number. The quotient is the whole number; the remainder is the new numerator.
Leaving the fraction part unsimplified. When asked for simplest form, \(6\dfrac{2}{4}\) becomes \(6\dfrac{1}{2}\).

Frequently asked questions

How do you change an improper fraction to a mixed numeral?

Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: \(\dfrac{17}{4} = 4\dfrac{1}{4}\).

What if there is no remainder?

The answer is a whole number: \(\dfrac{15}{5} = 3\).

Does the denominator change?

No. The parts are the same size, so the denominator stays the same.

How can you check your answer?

Change it back: \(4\dfrac{1}{4} = \dfrac{4 \times 4 + 1}{4} = \dfrac{17}{4}\).

When should you simplify?

When the fraction part has a common factor, such as \(3\dfrac{4}{6} = 3\dfrac{2}{3}\).

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