3.2 Fractions

Fractions on the TEAS

Fractions appear throughout the Numbers and Algebra portion of the ATI TEAS 7, and they reappear inside dosage, measurement, and data questions. A fraction represents part of a whole and is written as a numerator over a denominator. The denominator names how many equal parts make a whole; the numerator counts how many of those parts you have. Because the provided calculator handles decimals more easily than fractions, knowing the hand methods below keeps you accurate when answer choices are written in fraction form.

Types of Fractions

Converting Between Improper Fractions and Mixed Numbers

Improper → Mixed: divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

Worked Example: Convert 11/4. 11 ÷ 4 = 2 remainder 3, so 11/4 = 2¾.

Mixed → Improper: multiply the whole number by the denominator, add the numerator, and keep the denominator.

Worked Example: Convert 3¾. (3 × 4) + 3 = 15, so 3¾ = 15/4.

You will almost always convert mixed numbers to improper fractions before multiplying or dividing — it is the single most common setup error on fraction questions.

Equivalent Fractions and Simplifying

Two fractions are equivalent if they name the same value. Multiply or divide the top and bottom by the same nonzero number to generate equivalents: 1/2 = 2/4 = 3/6 = 4/8 = 50/100.

To simplify (reduce) a fraction, divide the numerator and denominator by their greatest common factor (GCF).

Worked Example: Simplify 12/16. The GCF of 12 and 16 is 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4, so 12/16 = ¾. TEAS answer keys expect fully reduced fractions, so always make this last move.

Adding and Subtracting Fractions

Same denominator: add or subtract the numerators and keep the denominator. 3/8 + 2/8 = 5/8.

Different denominators: find the least common denominator (LCD) — the smallest common multiple of the denominators — rewrite each fraction, then combine.

1. Find the LCD.
2. Rewrite each fraction with that denominator.
3. Add or subtract the numerators.
4. Simplify if possible.

Worked Example: Compute 1/3 + 1/4. The LCD of 3 and 4 is 12. Rewrite: 1/3 = 4/12 and 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12 (already in lowest terms).

Worked Example (mixed numbers): Compute 2½ + 1¾. Convert to improper: 5/2 + 7/4. LCD is 4: 5/2 = 10/4. Add: 10/4 + 7/4 = 17/4 = 4¼.

Multiplying Fractions

Multiply numerators together and denominators together, then simplify. You do not need a common denominator.

Worked Example: 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = ½.

Cross-cancel before multiplying to keep numbers small: in 2/3 × 3/4 the 3s cancel, leaving 2/1 × 1/4 = 2/4 = ½. A whole number multiplies as if it sits over 1: 5 × 2/3 = 5/1 × 2/3 = 10/3 = 3⅓.

Dividing Fractions

Use keep–change–flip: keep the first fraction, change ÷ to ×, and flip the second fraction to its reciprocal.

Worked Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2⅔.

Worked Example (mixed): 2½ ÷ ¾. Convert: 5/2 ÷ 3/4 = 5/2 × 4/3 = 20/6 = 3⅓.

Comparing Fractions

Common-denominator method: rewrite both with the same denominator and compare numerators. To compare 3/4 and 5/6, use 12ths: 3/4 = 9/12 and 5/6 = 10/12, so 3/4 < 5/6.

Cross-multiply method: multiply each numerator by the other denominator. For 3/4 and 5/6: 3 × 6 = 18 versus 4 × 5 = 20; since 18 < 20, 3/4 < 5/6.

Fractions in Healthcare

These contexts are why the TEAS emphasizes fractions: a nurse who reduces 12/16 to ¾ or correctly halves a dose protects patient safety, and the exam mirrors that reasoning.