Number and Algebra makes up 40 to 50 percent of the LANTITE numeracy component. Within that domain, fractions, decimals, and percentages appear repeatedly across both the calculator and non-calculator sections. If you are losing marks on numeracy, this is the most likely place to recover them.
The Non-Calculator Section: What ACER Says
The numeracy component has two sections. Section 1 is 52 questions with an online calculator. Section 2 is 13 questions with no calculator. ACER states the non-calculator section covers common numbers, fractions, and percentages, involves a small number of steps, and uses familiar and routine operations only. You cannot return to Section 1 once you proceed. That means Section 2 demands mental fluency, not complex multi-step reasoning.
The practical implication: you need to know your common equivalences cold. Do not rely on deriving them under time pressure.
Common Equivalences to Memorise
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/3 | 0.333... | approx. 33.3% |
| 2/3 | 0.666... | approx. 66.7% |
| 1/10 | 0.1 | 10% |
Core Operations You Need to Execute Reliably
Finding X% of a value. Multiply the value by the decimal form of the percentage. To find 35% of 240: 0.35 x 240 = 84. Without a calculator, break it apart. 10% of 240 is 24. 30% is 72. 5% is 12. Total: 84.
Expressing one quantity as a percentage of another. Divide the part by the whole, then multiply by 100. A student scores 42 out of 60: (42 / 60) x 100 = 70%. This appears in school contexts as test results, attendance figures, or class composition questions.
Percentage increase and decrease. Increase: new value = original x (1 + rate). Decrease: new value = original x (1 - rate). A school supply budget of $800 is cut by 15%: 800 x 0.85 = $680. Percentage change between two values: (change / original) x 100.
Weighted percentages across tasks. This appears frequently in school contexts. A student completes three assignments worth 30%, 30%, and 40% of the total grade. You multiply each score by its weight, then sum. Score of 70 on the 40% task contributes 0.40 x 70 = 28 points toward the final grade. Add the weighted contributions to get the overall result.
Converting Between Forms
To convert a fraction to a percentage: divide numerator by denominator, multiply by 100. To convert a percentage to a decimal: divide by 100 (move decimal point two places left). To convert a decimal to a fraction: write it over the appropriate power of 10 and simplify. These conversions appear in both sections. In Section 2 they will involve common values only, which is why the equivalence table above is worth committing to memory.
School Context Examples
- Test scores: 18 out of 25 correct. (18/25) x 100 = 72%.
- Class proportions: 9 of 30 students have a reading intervention. 9/30 = 0.3 = 30%.
- Budget allocations: A classroom budget of $400 allocates 25% to resources. 0.25 x 400 = $100.
- Grade thresholds: A pass requires 65%. A student scores 52 out of 80. (52/80) x 100 = 65%. Exactly passing.
Non-Calculator Strategy
Use the scratch paper provided. Write out your working steps. The non-calculator section is designed for small number of steps, so if you find yourself doing long multi-stage arithmetic, re-read the question. A common mistake is overcomplicating what is actually a one-step conversion. Break percentages into 10% chunks when direct multiplication is awkward. Know that 1/3 is approximately 33% and 2/3 is approximately 67%, since these are recurring decimals and ACER will use them with rounded or approximate answers.
The pass standard for LANTITE is the 70th percentile of the Australian adult population, validated against the OECD PIAAC. Fractions and percentages are everyday numeracy. The expectation is that you can apply them accurately in practical, school-relevant contexts without a calculator when the numbers are straightforward.
See how you go on the real question types
Our numeracy practice tests include fractions, percentages, and weighted grade problems in school-realistic contexts. Work through them now to find where your gaps are before test day.
Test yourself nowAll facts on this page are sourced directly from teacheredtest.acer.edu.au. For the latest information, always refer to the ACER website.