Fractions, Decimals, and Percentages: Practice Questions & Explanations

To add fractions with different denominators, find the common denominator. Least common multiple of 4 and 3 is 12. Convert: 3/4 = 9/12 (multiply by 3/3), 1/3 = 4/12 (multiply by 4/4). Add: 9/12 + 4/12 = 13/12. The answer is 13/12 or 1 1/12 as a mixed number. Common mistakes: adding numerators and denominators directly (3+1)/(4+3) = 4/7 — wrong. Adding without common denominator is invalid. Quick check: 3/4 is 0.75 and 1/3 is about 0.33, so the sum should be about 1.08. 13/12 ≈ 1.083 ✓. The ASVAB tests fundamentals of fractions: adding, subtracting, multiplying, dividing. Remember: multiply fractions straight across (numerator × numerator, denominator × denominator), divide by multiplying by the reciprocal.

Percent of a number = (percent ÷ 100) × number. 15% of 80 = 0.15 × 80 = 12. Three methods to solve percent problems: (1) Convert percent to decimal and multiply: 15% = 0.15; 0.15 × 80 = 12. (2) Use the fraction equivalent: 15% = 15/100; (15/100) × 80 = 1200/100 = 12. (3) Set up proportion: 15/100 = x/80; cross-multiply: 100x = 1200; x = 12. Useful percent shortcuts to memorize: 10% = move decimal point one place left (10% of 80 = 8); 1% = move decimal two places left; 25% = ÷ 4; 50% = ÷ 2; 75% = (number × 3) ÷ 4. For 15%: take 10% (which is 8) and add half of that (4) = 12. Practice mental math with percentages — it saves time on the ASVAB.

Two ways to solve: (1) Calculate the discount, then subtract: 20% of $50 = 0.20 × $50 = $10 discount; $50 - $10 = $40 sale price. (2) Calculate the percent remaining and multiply: 100% - 20% = 80% remaining; 80% of $50 = 0.80 × $50 = $40 sale price. Method 2 is often faster on the ASVAB. Be careful with percent problems: '20% off' and '20% of' are different. '20% off' means subtract 20%; '20% of' means just calculate that percentage. Multi-step problems may involve discount then tax: $40 (sale price) + 8% tax = $40 × 1.08 = $43.20. Or sequential discounts: 20% off then 10% off is NOT 30% off — apply each successively: $50 × 0.80 × 0.90 = $36. The ASVAB often includes problems with sequential percentages, which trip up test-takers who try to combine them incorrectly.

0.375 = 375/1000. Simplify by dividing both by greatest common factor. 375 ÷ 125 = 3; 1000 ÷ 125 = 8. So 0.375 = 3/8. Common decimal-fraction equivalents to memorize: 0.5 = 1/2; 0.25 = 1/4; 0.75 = 3/4; 0.125 = 1/8; 0.375 = 3/8; 0.625 = 5/8; 0.875 = 7/8; 0.333... = 1/3; 0.666... = 2/3; 0.1 = 1/10; 0.2 = 1/5; 0.4 = 2/5; 0.6 = 3/5; 0.8 = 4/5. Knowing these saves time on the ASVAB. To convert decimal to fraction: write decimal over its place value (0.375 has thousandths place, so 375/1000), then simplify. To convert fraction to decimal: divide numerator by denominator (3/8 = 3 ÷ 8 = 0.375). Percent conversion: percentage to decimal = move decimal two places left (25% = 0.25); decimal to percent = move two places right (0.375 = 37.5%).

Multiply as if integers: 25 × 4 = 100. Then count decimal places in the original numbers: 2.5 has 1 decimal place; 0.4 has 1 decimal place. Total decimal places: 2. Place the decimal in the answer: 1.00 or 1.0. So 2.5 × 0.4 = 1.0. Quick check: 2.5 is between 2 and 3; 0.4 is less than half. So the answer should be a bit less than half of 2.5, which is about 1.25 — close to 1.0 ✓. Common decimal multiplication mistakes: misplacing the decimal point, or just guessing. The method 'count total decimal places in inputs, put that many in the answer' always works. Another approach: convert to fractions. 2.5 = 5/2; 0.4 = 2/5; (5/2) × (2/5) = 10/10 = 1. Note: when multiplying by a number less than 1, the result is smaller than the original; when multiplying by a number greater than 1, the result is larger.

15% of 240 = 0.15 × 240 = 36. Convert percent to decimal (÷100) then multiply. A fast mental route: 10% of 240 is 24, and 5% is half of that, 12, so 15% = 24 + 12 = 36. The distractor 24 is 10%, 30 is 12.5% and 40 is roughly 16.7% — the test often offers a nearby percentage as a wrong answer, so check your work against the easy 10% benchmark.

3/8 × 16 = 48/8 = 6 gallons. 'Of' means multiply when it follows a fraction. One route: 16 ÷ 8 = 2 gallons per eighth, and 3 eighths = 6 gallons. The distractor 8 is half the can (4/8), 4 is a quarter (2/8) and 5 is 5/16 — none match 3/8. Note the question asks how much was used, not how much is left (which would be 10 gallons).

The 12 gallons removed represents the difference between 3/4 and 1/2 of the tank: 3/4 − 1/2 = 3/4 − 2/4 = 1/4. So 1/4 of the tank = 12 gallons. Total capacity = 12 × 4 = 48 gallons. ASVAB Arithmetic Reasoning tests fraction word problems. Strategy: find what fraction of the whole the known amount represents (here, 1/4 = 12 gallons), then scale up to the whole (multiply by 4). Check: 3/4 of 48 = 36; 1/2 of 48 = 24; 36 − 24 = 12. ✓

To find a fraction of a fraction, multiply them: 3/4 × 2/3 = (3 × 2)/(4 × 3) = 6/12 = 1/2 cup. The word 'of' between fractions means multiply. Multiply the numerators (3 × 2 = 6) and the denominators (4 × 3 = 12), then reduce 6/12 to 1/2. A useful shortcut is to cancel before multiplying: the 3 in the numerator and the 3 in the denominator cancel, leaving 1/4 × 2/1 = 2/4 = 1/2. Fraction-of-a-quantity problems appear often in arithmetic reasoning, and the reliable method is to multiply and then reduce.

To convert a fraction to a decimal, divide the numerator by the denominator: 7 ÷ 8 = 0.875. You can do this by long division, or by recognizing common conversions (1/8 = 0.125, so 7/8 = 7 × 0.125 = 0.875). Fraction-to-decimal conversions appear in arithmetic reasoning when comparing values or computing with money and measurements. Memorizing the eighths (0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875) is especially handy. The exact decimal value of 7/8 is 0.875.