How to Subtract Fractions with Unlike Denominators - Maths with Mum - Free Printable

Let's solve the problem step by step.

We are given the expression:

$$
5\frac{1}{4} - 2\frac{2}{3}
$$

Step 1: Convert mixed numbers to improper fractions

#### Convert $5\frac{1}{4}$:
- Multiply the whole number by the denominator: $5 \times 4 = 20$
- Add the numerator: $20 + 1 = 21$
- So, $5\frac{1}{4} = \frac{21}{4}$

#### Convert $2\frac{2}{3}$:
- Multiply the whole number by the denominator: $2 \times 3 = 6$
- Add the numerator: $6 + 2 = 8$
- So, $2\frac{2}{3} = \frac{8}{3}$

Now the expression becomes:

$$
\frac{21}{4} - \frac{8}{3}
$$

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Step 2: Find a common denominator

The denominators are 4 and 3. The least common denominator (LCD) is 12.

Convert both fractions to have denominator 12:

- $\frac{21}{4} = \frac{21 \times 3}{4 \times 3} = \frac{63}{12}$
- $\frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12}$

Now subtract:

$$
\frac{63}{12} - \frac{32}{12} = \frac{31}{12}
$$

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Step 3: Simplify (if needed)

$\frac{31}{12}$ is an improper fraction. Convert it to a mixed number:

- Divide 31 by 12: $12 \times 2 = 24$, remainder $7$
- So, $\frac{31}{12} = 2\frac{7}{12}$

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✔ Final Answer:

$$
\boxed{2\frac{7}{12}}
$$

This is the result of $5\frac{1}{4} - 2\frac{2}{3}$.