MKMathematics Knowledge

Fractions, Decimals & Percent

Three ways to say the same thing — once you can convert freely between them, most MK problems get easier.

Formula Reference

  • Fraction → Decimal: divide numerator by denominator (3/4 = 3÷4 = 0.75)
  • Decimal → Percent: multiply by 100 (0.75 × 100 = 75%)
  • Percent → Decimal: divide by 100 (75% ÷ 100 = 0.75)
  • Adding fractions: need common denominator (1/3 + 1/4 = 4/12 + 3/12 = 7/12)
  • Multiplying fractions: straight across, then simplify (2/3 × 3/5 = 6/15 = 2/5)
  • Dividing fractions: flip the second and multiply (2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6)
  • x% of y = (x/100) × y

The big picture

Fractions, decimals, and percents are three different representations of the same underlying idea: a part of a whole. The ASVAB Math Knowledge section tests whether you can work fluently in all three forms and convert between them when needed.

This comes up more than any other single topic in MK. It also supports algebra, geometry, and percent-change problems — so getting solid here lifts your whole score.

Conversions you should know cold

Fraction Decimal Percent
1/2 0.5 50%
1/4 0.25 25%
3/4 0.75 75%
1/3 0.333... 33.3%
1/5 0.2 20%
1/8 0.125 12.5%

Memorize these. When you see 0.125 in a problem, you should immediately recognize it as 1/8 — that can save time on multi-step problems.

Fraction operations: the two rules that matter most

Adding and subtracting: You must have a common denominator. If the denominators are different, find the least common multiple, convert both fractions, then add or subtract the numerators only.

1/3 + 1/4: LCM is 12. Convert: 4/12 + 3/12 = 7/12

Dividing: Flip the second fraction (take its reciprocal), then multiply.

2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6

The "keep, change, flip" phrase helps: keep the first fraction, change division to multiplication, flip the second fraction.

Percent problems

Most percent questions are one of three types:

  1. Find the percent of a number: "What is 30% of 90?" then 0.30 x 90 = 27
  2. Find what percent one number is of another: "27 is what percent of 90?" then 27/90 = 0.30 = 30%
  3. Find the original number: "30% of what number is 27?" then 27 / 0.30 = 90

Recognize which type you have before you start calculating. The formula is always (part/whole = percent/100) — rearrange for what's missing.

Percent increase/decrease is its own thing:

% change = (new - old) / old x 100

A price going from $80 to $100 is a (100-80)/80 x 100 = 25% increase. Don't confuse the absolute dollar change ($20) with the percentage change (25%).

Practice approach

The most common errors here are mechanical — forgetting to flip, adding denominators. Slow down on setup, especially on fraction division and percent-of-a-number problems. Once the setup is right, the arithmetic is easy.

Common Pitfalls

  • Adding denominators instead of finding a common denominator (1/3 + 1/4 ≠ 2/7)
  • Forgetting to flip the divisor when dividing fractions
  • Mixing up 'percent of a number' with 'percent increase' — they use different formulas
  • Leaving an answer as an improper fraction when the choices are mixed numbers (or vice versa)

Worked Examples

Q1: What is 3/8 as a decimal?

Answer: 3 ÷ 8 = 0.375

Q2: What is 15% of 240?

Answer: (15/100) × 240 = 0.15 × 240 = 36

Q3: Simplify: (1/2) ÷ (3/4)

Answer: Flip the divisor: 1/2 × 4/3 = 4/6 = 2/3

Q4: A coat costs $80 and is marked up 25%. What is the new price?

Answer: Markup = 0.25 × 80 = $20. New price = 80 + 20 = $100. Or: 80 × 1.25 = $100

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