Key Takeaways
- PEMDAS determines the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
- When multiplying or dividing, same signs yield positive results; different signs yield negative results
- To round, look at the digit to the right: 5 or greater rounds up, less than 5 rounds down
- The distributive property: a(b + c) = ab + ac
- Estimation by rounding helps verify if calculated answers are reasonable
Whole Numbers and Basic Operations
The TEAS Mathematics section tests fundamental arithmetic skills essential for nursing calculations. This section covers whole numbers and the four basic operations: addition, subtraction, multiplication, and division.
Whole Numbers
Whole numbers are non-negative integers: 0, 1, 2, 3, 4, 5...
| Term | Definition | Example |
|---|---|---|
| Whole number | Non-negative integer | 0, 1, 42, 1000 |
| Positive integer | Whole number greater than zero | 1, 2, 3, 4 |
| Negative integer | Integer less than zero | -1, -2, -3 |
| Integer | Any positive or negative whole number | -3, -2, -1, 0, 1, 2, 3 |
Place Value
Understanding place value is crucial for working with larger numbers.
| Place | Value | Example (in 4,738) |
|---|---|---|
| Ones | 1 | 8 |
| Tens | 10 | 3 (represents 30) |
| Hundreds | 100 | 7 (represents 700) |
| Thousands | 1,000 | 4 (represents 4,000) |
Expanded form: 4,738 = 4,000 + 700 + 30 + 8
Order of Operations (PEMDAS)
When solving expressions with multiple operations, follow PEMDAS:
| Letter | Operation | Example |
|---|---|---|
| P | Parentheses | (2 + 3) = 5 |
| E | Exponents | 2² = 4 |
| M/D | Multiplication/Division (left to right) | 6 × 2 ÷ 3 = 4 |
| A/S | Addition/Subtraction (left to right) | 5 + 3 - 2 = 6 |
Example: Solve 3 + 4 × 2
- Multiply first: 4 × 2 = 8
- Then add: 3 + 8 = 11
Example: Solve (3 + 4) × 2
- Parentheses first: (3 + 4) = 7
- Then multiply: 7 × 2 = 14
Properties of Operations
| Property | Definition | Example |
|---|---|---|
| Commutative | Order doesn't matter | 3 + 5 = 5 + 3 |
| Associative | Grouping doesn't matter | (2 + 3) + 4 = 2 + (3 + 4) |
| Distributive | Multiply across addition | 2(3 + 4) = 2(3) + 2(4) = 14 |
| Identity | Adding 0 or multiplying by 1 | 5 + 0 = 5; 5 × 1 = 5 |
| Zero property | Multiplying by 0 | 5 × 0 = 0 |
Working with Negative Numbers
Rules for Addition:
- Same signs: Add and keep the sign
- Different signs: Subtract and use the sign of the larger absolute value
Rules for Subtraction:
- Change subtraction to addition of the opposite
- Example: 5 - (-3) = 5 + 3 = 8
Rules for Multiplication/Division:
- Same signs: Result is positive
- Different signs: Result is negative
| Operation | Example | Result |
|---|---|---|
| Positive × Positive | 3 × 4 | 12 |
| Negative × Negative | (-3) × (-4) | 12 |
| Positive × Negative | 3 × (-4) | -12 |
| Negative × Positive | (-3) × 4 | -12 |
Rounding Whole Numbers
Steps to Round:
- Identify the place value to round to
- Look at the digit to the right
- If it's 5 or greater, round up; if less than 5, round down
- Replace all digits to the right with zeros
Example: Round 4,738 to the nearest hundred
- Hundreds digit: 7
- Digit to the right: 3 (less than 5)
- Round down: 4,700
Estimation
Estimation involves rounding before calculating to get an approximate answer quickly.
Example: Estimate 487 + 312
- Round: 500 + 300
- Estimate: 800
- Actual: 799
This is useful for checking if your calculated answer is reasonable.
Solve: 12 + 3 × 4 - 2
What is the result of (-5) × (-3)?
Round 3,847 to the nearest hundred.