DepEd MELC reviewer for Grade 7 Mathematics, Quarter 1. Study the rules, worked formulas, and exam hacks below.
Sets and the Real Number System
A set is a well-defined collection of objects called elements. Numbers are organized into the real number system.
| Set | Examples |
|---|---|
| Natural / Counting | 1, 2, 3, โฆ |
| Whole | 0, 1, 2, 3, โฆ |
| Integers | โฆโ2, โ1, 0, 1, 2โฆ |
| Rational | fractions, decimals that terminate/repeat |
| Irrational | ฯ, โ2 (non-repeating) |
Set operations: union (โช) = all elements in either set; intersection (โฉ) = elements in both.
Operations on Integers
Integers include negative numbers. Follow the sign rules:
| Operation | Rule | Example |
|---|---|---|
| Same signs (+) | Add, keep the sign | โ4 + (โ3) = โ7 |
| Different signs | Subtract, keep sign of larger | โ7 + 4 = โ3 |
| Multiply / Divide same signs | Answer is positive | (โ6)(โ2)=12 |
| Multiply / Divide diff signs | Answer is negative | (โ6)(2)=โ12 |
Two negatives multiplied/divided give a POSITIVE. For addition, think of money: negative = debt, positive = cash.
Absolute Value
The absolute value |a| is the distance of a number from zero โ always non-negative.
|โ8| is 8, not โ8. Absolute value can never be negative.
Worked Example
Simplify: โ5 + 8 โ (โ3).
Subtracting a negative is the same as adding a positive.
Before your test, make sure you can confidently do each of the following:
- Explain and apply Sets and the Real Number System.
- Explain and apply Operations on Integers.
- Explain and apply Absolute Value.
- Explain and apply Worked Example.
Re-read any section above where you hesitate, then try the worked example again without looking.