Key Takeaways
- The order of operations (PEMDAS) dictates calculation sequence: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)
- To add or subtract fractions, find a common denominator first, then add or subtract the numerators
- To multiply fractions, multiply numerators together and denominators together, then simplify
- To divide fractions, multiply by the reciprocal (flip the second fraction and multiply)
- Converting fractions to decimals: divide the numerator by the denominator
- Converting decimals to percentages: multiply by 100 and add the percent sign
- Mixed numbers must be converted to improper fractions before multiplying or dividing
- Always reduce fractions to lowest terms by dividing numerator and denominator by their GCF
Basic Operations & Fractions
The HESI A2 Mathematics section tests your ability to perform fundamental calculations accurately. These skills are critical for nursing because medication dosages, IV flow rates, and patient data all require precise mathematical reasoning.
Order of Operations (PEMDAS)
When an expression contains multiple operations, follow PEMDAS:
| Step | Operation | Example |
|---|---|---|
| P | Parentheses | Solve expressions inside parentheses first |
| E | Exponents | Evaluate powers and square roots |
| M/D | Multiplication / Division | Work left to right |
| A/S | Addition / Subtraction | Work left to right |
Example: 3 + 4 x (2 + 1)^2 - 6 / 3
- Parentheses: (2 + 1) = 3
- Exponents: 3^2 = 9
- Multiplication: 4 x 9 = 36
- Division: 6 / 3 = 2
- Addition/Subtraction (left to right): 3 + 36 - 2 = 37
Fraction Operations
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator:
- Find the Least Common Denominator (LCD) of the fractions
- Convert each fraction to an equivalent fraction with the LCD
- Add or subtract the numerators
- Keep the common denominator
- Simplify (reduce) the result
Example: 2/3 + 1/4
- LCD of 3 and 4 = 12
- 2/3 = 8/12 and 1/4 = 3/12
- 8/12 + 3/12 = 11/12
Multiplying Fractions
Multiply straight across — no common denominator needed:
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Example: 3/4 x 2/5 = 6/20 = 3/10
Dividing Fractions
Multiply by the reciprocal (KCF: Keep, Change, Flip):
- Keep the first fraction as-is
- Change the division sign to multiplication
- Flip the second fraction (reciprocal)
- Multiply and simplify
Example: 3/4 / 2/5 = 3/4 x 5/2 = 15/8 = 1 7/8
Mixed Numbers
A mixed number combines a whole number and a fraction (e.g., 2 3/4).
Converting Mixed Numbers to Improper Fractions:
- Multiply the whole number by the denominator
- Add the numerator
- Place over the original denominator
Example: 2 3/4 = (2 x 4 + 3) / 4 = 11/4
Converting Improper Fractions to Mixed Numbers:
- Divide the numerator by the denominator
- The quotient is the whole number; the remainder is the new numerator
Example: 11/4 = 2 remainder 3 = 2 3/4
Decimals and Percentages
| Conversion | Method | Example |
|---|---|---|
| Fraction to Decimal | Divide numerator by denominator | 3/4 = 0.75 |
| Decimal to Percent | Multiply by 100 | 0.75 = 75% |
| Percent to Decimal | Divide by 100 | 75% = 0.75 |
| Fraction to Percent | Convert to decimal, then multiply by 100 | 3/4 = 0.75 = 75% |
| Percent to Fraction | Write over 100 and simplify | 75% = 75/100 = 3/4 |
| Decimal to Fraction | Write decimal as fraction, simplify | 0.25 = 25/100 = 1/4 |
Rounding Rules
- If the digit to the right of the rounding place is 5 or greater, round up
- If the digit is less than 5, round down
Example: Round 3.746 to the nearest tenth = 3.7 (the digit after the tenths place is 4, which is less than 5)
Solve: 2/3 + 3/4 = ?
What is 3/5 / 2/3?
Convert the fraction 7/8 to a decimal: 7/8 = _____
Type your answer below
Evaluate: 8 + 2 x 5 - 3
Convert the mixed number 3 2/5 to an improper fraction.
Arrange these fractions from smallest to largest.
Arrange the items in the correct order
What is 45% expressed as a fraction in lowest terms?