Fractions, decimals and percentages: the NZ numeracy essentials

One idea, three forms

Fractions, decimals, and percentages aren’t three separate topics — they’re three ways of expressing the same underlying idea: a part of a whole. The moment that clicks, the whole strand becomes much easier to navigate.

One half. 0.5. 50%. Same thing, different form.

The LNAAT numeracy requirement — the maths competence assessment for primary ITE applicants in New Zealand — tests this strand in multiple ways and at a level calibrated to approximately NCEA Level 2. That means you’re expected to work with fractions, decimals, and percentages fluently and in real-world contexts, not just convert between them on a worksheet.

The conversions you need to know cold

Being able to convert quickly — without having to think too hard — saves time and reduces errors on test day. These are worth memorising:

1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75%
1/5 = 0.2 = 20%
1/10 = 0.1 = 10%
1/3 ≈ 0.333… ≈ 33.3%
2/3 ≈ 0.667… ≈ 66.7%

Beyond memorising these benchmarks, make sure you understand the method: to convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. The benchmark conversions flow from those rules — they’re not arbitrary facts.

Working with fractions

Adding and subtracting

You can only add or subtract fractions directly when the denominators are the same. If they’re different, find a common denominator first, then add or subtract the numerators.

For example: 1/3 + 1/4. The lowest common denominator is 12. So: 4/12 + 3/12 = 7/12.

Multiplying fractions

Multiply numerator × numerator and denominator × denominator. Then simplify. For example: 2/3 × 3/5 = 6/15 = 2/5.

Dividing fractions

Flip the second fraction and multiply. For example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Finding a fraction of a quantity

This appears often in real-world contexts: “3/5 of the class passed the test — if there are 30 students, how many passed?” Multiply the quantity by the fraction: 30 × 3/5 = 18.

Working with percentages

Finding a percentage of a quantity

Convert the percentage to a decimal and multiply. 15% of $240: 0.15 × 240 = $36.

Percentage increase and decrease

These appear frequently in real-world LNAAT contexts — salary increases, price reductions, GST. The method:

Increase by 20%: multiply by 1.20
Decrease by 15%: multiply by 0.85

Finding what percentage one number is of another

Divide the part by the whole, then multiply by 100. For example: 18 out of 30 → 18/30 × 100 = 60%.

Finding the original value after a percentage change

This is trickier: if a price after a 20% increase is $180, what was the original? Divide by 1.20: $180 ÷ 1.20 = $150. Don’t fall into the trap of subtracting 20% from $180 — that gives you the wrong answer.

In context: what LNAAT questions look like

The LNAAT doesn’t ask “what is 3/4 of 80?” in isolation. It wraps questions in real situations. You might see:

A timetable where you need to work out what fraction of the school day is allocated to a subject
A budget breakdown where you calculate the percentage spent on a category
A scenario involving a price reduction or a pay increase
A data table where you interpret proportions across groups

The maths is the same — but reading the context carefully is what gets you to the right calculation in the first place. Practise with questions that are embedded in scenarios, not just bare calculations.

Common errors to watch for

Confusing “percent of” with “percent more than.” A 20% increase on $100 is $120, not $20.
Forgetting to simplify fractions. The answer 6/15 and 2/5 are both correct, but you may need the simplified form.
Division errors when finding an original value. Always divide by (1 + rate) for an increase, not subtract the percentage from the final value.
Mixing up fractions and ratios. A ratio of 3:2 means 3/5 of the total is one part — not 3/2.

Practise this topic well

Fractions, decimals, and percentages are one of the highest-yield topics in the LNAAT numeracy requirement. Time spent here pays off across the test — they connect to proportions, ratios, data interpretation, and more.

The free SN Academy diagnostic will show you specifically where your gaps are in this strand, so you can focus your practice where it counts.

— The people of SN Academy