CAEC Mathematics without a Calculator 2 — Questions and Answers

Question 1: What is 15% of 80?

10
12 (Correct answer)
14
16

Correct answer: 12

15% of 80 = 0.15 × 80 = 12. Or: 10% of 80 = 8; 5% of 80 = 4; total = 12.

To find 15% without a calculator, break it down: 10% of 80 = 8; 5% = half of 10% = 4; 15% = 8 + 4 = 12. Mental percentage strategies like this are essential for the non-calculator section. Percentage problems appear throughout everyday life — taxes, tips, discounts, and interest rates all require percentage calculations.

Question 2: Simplify the fraction 18/24.

3/4 (Correct answer)
2/3
6/8
9/12

Correct answer: 3/4

The GCF of 18 and 24 is 6. 18 ÷ 6 = 3; 24 ÷ 6 = 4. So 18/24 = 3/4.

To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). The GCF of 18 and 24 is 6 (because 18 = 6×3 and 24 = 6×4). Dividing both: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Note that 6/8 and 9/12 are equivalent to 3/4 but are not fully simplified.

Question 3: What is 3/4 + 2/3?

5/7
17/12 (Correct answer)
5/12
1 1/4

Correct answer: 17/12

Convert to a common denominator of 12: 3/4 = 9/12 and 2/3 = 8/12. Sum = 17/12.

To add fractions, first find the lowest common denominator (LCD). The LCD of 4 and 3 is 12. Convert: 3/4 = 9/12 and 2/3 = 8/12. Add: 9/12 + 8/12 = 17/12. This is an improper fraction; as a mixed number it equals 1 5/12. Adding fractions with different denominators is a core numeracy skill required for the non-calculator section.

Question 4: Which of the following is the correct order from least to greatest: 0.3, 1/4, 0.35, 2/5?

1/4, 0.3, 0.35, 2/5 (Correct answer)
0.3, 1/4, 0.35, 2/5
2/5, 0.35, 0.3, 1/4
1/4, 0.35, 0.3, 2/5

Correct answer: 1/4, 0.3, 0.35, 2/5

Convert all to decimals: 1/4=0.25, 0.3, 0.35, 2/5=0.40. Order: 0.25, 0.30, 0.35, 0.40 → 1/4, 0.3, 0.35, 2/5.

Convert to decimals: 1/4 = 0.25; 0.3 = 0.30; 0.35 = 0.35; 2/5 = 0.40. Ordering from least to greatest: 0.25, 0.30, 0.35, 0.40, which corresponds to 1/4, 0.3, 0.35, 2/5. Converting between fractions, decimals, and percentages and comparing them is an important skill tested on the CAEC mathematics section.

Question 5: A number increased by 40% gives 84. What is the original number?

50
56
60 (Correct answer)
48

Correct answer: 60

If x × 1.40 = 84, then x = 84 ÷ 1.40 = 60.

Let the original number be x. Increasing by 40% means multiplying by 1.40: x × 1.40 = 84. Solving: x = 84 ÷ 1.40 = 60. You can verify: 60 × 1.40 = 84. Working backwards from a percentage increase is a common type of algebraic reasoning problem on numeracy assessments.

Question 6: What is the value of the expression 5 + 3 × (8 − 2) ÷ 6?

8 (Correct answer)
3
13
16

Correct answer: 8

Following BEDMAS: brackets first (8−2=6), then 3×6=18, then 18÷6=3, then 5+3=8.

Apply BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction): Step 1 — Brackets: (8 − 2) = 6. Step 2 — Multiplication: 3 × 6 = 18. Step 3 — Division: 18 ÷ 6 = 3. Step 4 — Addition: 5 + 3 = 8. The answer is 8. BEDMAS (also known as PEMDAS in the US) determines the correct order of operations in arithmetic expressions.

CAEC Mathematics without a Calculator 2

What is 15% of 80?