Fractions

Fractions are essential for nursing calculations, including medication dosages and IV flow rates. The TEAS tests your ability to work with fractions in various forms.

Fraction Basics

A fraction represents part of a whole, written as:

numerator / denominator

Converting Between Improper Fractions and Mixed Numbers

Improper → Mixed:

1. Divide numerator by denominator
2. The quotient is the whole number
3. The remainder is the new numerator

Example: Convert 11/4 to a mixed number

• 11 ÷ 4 = 2 remainder 3
• Answer: 2¾

Mixed → Improper:

1. Multiply whole number by denominator
2. Add the numerator
3. Put the result over the original denominator

Example: Convert 2¾ to an improper fraction

• (2 × 4) + 3 = 11
• Answer: 11/4

Equivalent Fractions

Fractions that represent the same value:

Create equivalent fractions: Multiply or divide both numerator and denominator by the same number.

Example: 1/2 = 2/4 = 3/6 = 4/8 = 50/100

Simplifying Fractions

Simplify by dividing both numerator and denominator by their greatest common factor (GCF).

Example: Simplify 12/16

• GCF of 12 and 16 is 4
• 12 ÷ 4 = 3
• 16 ÷ 4 = 4
• Answer: ¾

Adding and Subtracting Fractions

Same denominator: Add/subtract numerators; keep denominator.

• 3/8 + 2/8 = 5/8

Different denominators: Find a common denominator first.

1. Find the least common denominator (LCD)
2. Convert each fraction
3. Add or subtract numerators
4. Simplify if needed

Example: 1/3 + 1/4

• LCD of 3 and 4 is 12
• 1/3 = 4/12
• 1/4 = 3/12
• 4/12 + 3/12 = 7/12

Multiplying Fractions

Multiply numerators, multiply denominators, then simplify.

Example: 2/3 × 3/4

• Numerators: 2 × 3 = 6
• Denominators: 3 × 4 = 12
• Result: 6/12 = 1/2

Tip: Cross-cancel before multiplying to simplify:

• 2/3 × 3/4 → 2/1 × 1/4 = 2/4 = 1/2

Dividing Fractions

Multiply by the reciprocal (flip the second fraction).

Example: 2/3 ÷ 1/4

• Flip: 1/4 → 4/1
• Multiply: 2/3 × 4/1 = 8/3 = 2⅔

Comparing Fractions

Method 1: Convert to same denominator

• Compare 3/4 and 5/6
• 3/4 = 9/12
• 5/6 = 10/12
• 9/12 < 10/12, so 3/4 < 5/6

Method 2: Cross-multiply

• Compare 3/4 and 5/6
• 3 × 6 = 18 and 4 × 5 = 20
• 18 < 20, so 3/4 < 5/6

Fractions in Healthcare