Number sense means understanding what numbers mean and how they relate to each other. It's the foundation for all math work. Integers are whole numbers and their opposites: …, −3, −2, −1, 0, 1, 2, 3, … They include positive numbers, negative numbers, and zero. Rational numbers are numbers that can be written as a fraction p⁄q where p and q are integers and q ≠ 0. This includes integers (like 5 = 5⁄1), terminating decimals (like 0.25 = 1⁄4), and repeating decimals (like 0.333… = 1⁄3).
To use numbers confidently, you need to convert smoothly between fractions, decimals, and percents. Here's how: Fraction → decimal by dividing numerator by denominator. Decimal → percent by multiplying by 100 (move decimal two places right). Percent → decimal by dividing by 100 (two places left). Fraction → percent by converting to decimal first, then multiplying by 100%. These conversions let you compare values in different forms and choose the best representation for each situation.
Computations follow order of operations: brackets → exponents → multiplication/division (left to right) → addition/subtraction (left to right). This ensures everyone gets the same answer. When working with fractions, remember: addition/subtraction requires common denominators, multiplication means multiply across (numerator × numerator, denominator × denominator), and division means multiply by the reciprocal.
Equivalence is key: two numbers can look different but be equal (like 2⁄3 = 0.666… = 66.6%). Simplifying fractions by dividing top and bottom by their greatest common divisor helps you see structure clearly and compare sizes. Real-world connection: Money uses decimals, discounts use percents, and recipes use fractions — being fluent in all three forms helps you navigate everyday situations.
Conversion example 1 — fraction to decimal to percent
| Fraction | Decimal | Percent |
|---|---|---|
| 1⁄4 | 0.25 | 25% |
| 3⁄5 | 0.6 | 60% |
| 7⁄8 | 0.875 | 87.5% |
Conversion example 2 — comparing values in different forms
Which is larger: 0.7 or 5⁄8?
Operations with fractions — common denominators
Compute 2⁄3 + 1⁄4