Expressing Quantities as Fractions for the TMUA

Expressing One Quantity as a Fraction

One quantity can be expressed as a fraction of another by following the rule that $\frac{x}{y}$ represents $x$ expressed as a fraction of $y$. This process is common in university admission tests to evaluate your ability to compare magnitudes and manage unit conversions.

To perform this calculation correctly, both quantities must be in the same units. This normally involves identifying the two measures and converting the larger unit into the smaller of the two units. This approach is preferred as it usually prevents the introduction of decimals within your fraction.

Fractions Less Than 1

A fraction is less than 1 when the first quantity ($x$) is smaller than the second quantity ($y$).

Worked Example: Fraction Less Than 1

Express $200\text{ g}$ as a fraction of $1\text{ kg}$.

1. First, observe that the quantities are provided in different units: grams ($\text{g}$) and kilograms ($\text{kg}$).
2. Convert the $1\text{ kg}$ into grams to match the first quantity: $1\text{ kg} = 1000\text{ g}$.
3. Write the first quantity over the second: $\frac{200}{1000}$.
4. Simplify the fraction by dividing both parts by their highest common factor, 200: $\frac{200 \div 200}{1000 \div 200} = \frac{1}{5}$.

Fractions Greater Than 1

A fraction is greater than 1 when the first quantity ($x$) is larger than the second quantity ($y$). In these cases, the result is an improper fraction.

Worked Example: Fraction Greater Than 1

Express $1\text{ litre}$ as a fraction of $450\text{ ml}$.

1. Start by ensuring both quantities are written in the same units. We convert the litre to millilitres: $1\text{ litre} = 1000\text{ ml}$.
2. Express the first quantity ($1000\text{ ml}$) as a fraction of the second ($450\text{ ml}$): $\frac{1000}{450}$.
3. Simplify the fraction. Dividing both by 10 gives $\frac{100}{45}$.
4. Further simplify by dividing both by 5: $\frac{20}{9}$.
5. This improper fraction can also be expressed as the mixed number $2\frac{2}{9}$.