In a written aptitude exercise, arithmetic becomes easier when you decide what the numbers represent before calculating. Label the units, identify the whole and estimate the answer’s size. These three habits help you catch a neat-looking answer that solves the wrong problem.
OFAI lists mathematical reasoning among its FACT subjects. Your own assessment’s coverage and calculator rules come from its current instructions. The examples below are original classroom exercises about supplies and distances, rather than operational firefighting calculations.
Share a total using ratios
Exercise: a fictional study group sorts 35 cards into blue and red piles in the ratio 3:2. How many cards belong in each pile?
The ratio has five equal parts altogether: 3 + 2 = 5. Each part contains 35 ÷ 5 = 7 cards. Blue receives 3 × 7 = 21 cards, and red receives 2 × 7 = 14. Check both conditions: 21 + 14 = 35, and 21:14 simplifies to 3:2.
A common mistake is dividing 35 by 3. That treats the blue share as the entire total. Write “total parts” above the addition before you divide. If the question instead gives the blue pile as 21 cards, one part is 21 ÷ 3 = 7, so the red pile is still 14.
Convert units before combining quantities
Exercise: a fictional walking route has one section of 2.4 kilometres and another of 650 metres. Find the combined distance in kilometres.
Convert 2.4 kilometres to 2,400 metres, then add 650 metres to obtain 3,050 metres. Convert back to get 3.05 kilometres. Alternatively, convert 650 metres to 0.65 kilometres and add 2.4 + 0.65. Both methods should agree.
The NIST metric-prefix reference gives kilo as one thousand and centi as one hundredth. Keep the unit beside each line of working. A length conversion does not automatically give an area conversion: a square metre contains 100 × 100 = 10,000 square centimetres.
Find the percentage’s starting whole
Exercise: a box contains 24 notebooks, and 18 have been handed out. What percentage has been distributed?
The whole is the original 24 notebooks. Calculate 18 ÷ 24 × 100 = 75%. Six remain, which is 6 ÷ 24 × 100 = 25%. The two percentages add to 100%, providing a useful check.
Now change the wording: “The group needs 20% more than its current 30 notebooks.” Twenty percent of 30 is 6, so the new total is 36. Notice the difference between the increase, six notebooks, and the resulting total, 36. Underline which quantity the question requests.
Check the method with a fresh example
Try sharing 48 cards in a 5:3 ratio before reading the answer. Eight parts make six cards per part, so the piles are 30 and 18. Their sum is 48, and their ratio reduces to 5:3.
When reviewing a mistake, identify whether the problem began with interpretation, units or calculation. Correct that step and attempt a different question. Remembering the answer to a repeated item is less useful than being able to explain why a new solution works.
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