Arithmetic practice becomes more useful when you can explain why an answer makes sense. Fractions, ratios and percentages often describe the same quantity in different ways. Learning to move between them gives you several ways to check your work during CFAT practice.
The worked examples below are original learning exercises. Begin without a timer, write the units beside your answers and add a short practice limit once the methods feel familiar.
Find the whole before using a fraction
A supply box contains 84 items. Three-sevenths are blue. How many items are blue?
The whole is 84 items. Find one-seventh first: 84 ÷ 7 = 12. Then take three of those parts: 12 × 3 = 36 blue items. Because three-sevenths is less than one-half, the answer should be less than 42. That quick comparison supports the calculation.
For addition, the parts must be the same size. To calculate 5/12 + 1/6, rewrite 1/6 as 2/12. Now 5/12 + 2/12 = 7/12. Adding the denominators would change the size of the parts and produce the wrong result.
Keep the operation in view. Multiplication by 3/7 finds part of a quantity; adding 3/7 to another fraction combines quantities. A correct fraction rule applied to the wrong operation still gives an incorrect answer.
Separate a ratio from a share of the total
Two groups share 72 notebooks in a ratio of 5:3. How many notebooks does each group receive?
The ratio has 5 + 3 = 8 total parts. One part is 72 ÷ 8 = 9 notebooks. The first group receives 5 × 9 = 45, and the second receives 3 × 9 = 27. Check both conditions: 45 + 27 = 72, and 45:27 simplifies to 5:3.
The first group’s share of the whole is 5/8. The ratio 5:3 compares the two groups with each other. Label what the numbers represent before starting, especially when a question supplies only one group’s quantity.
Use convenient numbers for mental arithmetic
Find 15% of 260 by splitting the percentage into 10% and 5%. Ten per cent is 26. Five per cent is half of that, or 13. Together they give 39. For 25% of 260, divide by four to get 65.
Break multiplication into smaller pieces too. Calculate 18 × 24 as (20 × 24) − (2 × 24): 480 − 48 = 432. Choose a method you can track reliably. If holding several intermediate numbers causes mistakes, write them down when the practice instructions permit it.
Estimation is a check, so keep it separate from the exact answer. Sixteen per cent of 260 should be slightly greater than 39; it should not be close to 100.
Build a short repeatable drill
- Complete two fraction questions, two ratio questions and two percentage questions.
- State the whole, total ratio parts or percentage base before calculating.
- Check the answer using a second method or a rough estimate.
- Record the error’s cause: interpretation, method or arithmetic.
Tomorrow, change the values and repeat the skill that caused difficulty. Follow the current CAF application guidance and ask your recruiter which assessment instructions apply to you, including permitted aids.
Explore the CFATReady course for organised practice. Start Free Trial and choose one arithmetic skill to work on first.