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Sec 1 Integers and Negative Numbers | Number Lines, Operations and Sign Control

Secondary 1 Integers and Negative Numbers is the first major bridge from Primary arithmetic into Secondary Mathematics. Positive and negative integers are not difficult because the numbers are large; they are difficult because pupils must separate direction, order and operation. A minus sign can mean a negative number, subtraction, or the opposite of a quantity.

Students searching for Sec 1 integers, negative numbers, integer operations, number line or Secondary 1 Mathematics often memorise sign rules before understanding what the signs represent. That works until a question combines several operations. The durable method is locate → interpret → operate → estimate → check.

This page is the canonical Integers owner under the Secondary Mathematics Topic Library. It is also a prerequisite for Algebraic Expressions and Linear Equations.

Quick answer: the six integer ideas

  • Positive integers: numbers greater than zero.
  • Negative integers: numbers less than zero.
  • Zero: neither positive nor negative.
  • Opposites: +a and −a are equally far from zero.
  • Absolute value: distance from zero, ignoring direction.
  • Order: farther right on the number line means greater.

Number-line meaning

The number line prevents many sign mistakes. Moving right increases value; moving left decreases value. Therefore −2 is greater than −7 because −2 lies farther right.

The phrase “more negative” means smaller, not larger in magnitude.

Addition: combine signed movement

Same signs

Add the magnitudes and keep the sign. Example: −4 + (−7) = −11.

Different signs

Subtract the smaller magnitude from the larger magnitude and keep the sign of the larger magnitude. Example: −9 + 5 = −4.

A number-line interpretation is even safer: start at −9 and move 5 steps right.

Subtraction: change it into addition of the opposite

a − b = a + (−b).

Example: 6 − (−3) = 6 + 3 = 9.

The two minus signs have different jobs: the first means subtraction; the second belongs to the negative number.

Multiplication and division signs

  • positive × positive = positive
  • negative × negative = positive
  • positive × negative = negative
  • negative × positive = negative

The same sign rules apply to division.

A useful principle is: an even number of negative factors gives a positive product; an odd number gives a negative product.

Worked example: multi-step operation

Evaluate: −6 + 4 × (−3).

Order of operations first: 4 × (−3) = −12.

Then −6 + (−12) = −18.

Do not add −6 + 4 before multiplying.

Absolute value

|−8| = 8 because −8 is eight units from zero.

Absolute value is distance, not “make the number positive” as a memorised trick. That meaning becomes important later in coordinate geometry and algebra.

Temperature and elevation

Integers model real direction.

Example: Temperature rises from −5°C to 3°C. Change = 3 − (−5) = 8°C.

The final temperature is 3°C; the change is +8°C. These are different quantities.

Debt and credit

A bank balance of −$30 can represent owing $30. Depositing $50 changes the balance to +$20. The context makes sign meaning concrete.

Ordering negatives

To arrange −3, 5, −9, 0 and 2 from smallest to largest:

−9, −3, 0, 2, 5.

Among negatives, the number with larger absolute value is smaller.

Brackets protect meaning

Write negative values in brackets when substituting or multiplying:

3(−4) = −12, not 3−4.

This habit becomes essential in algebra.

Common integer errors

  • treats −8 as greater than −3 because 8 > 3
  • forgets order of operations
  • confuses subtracting a negative with subtracting a positive
  • drops brackets around substituted negative numbers
  • applies multiplication sign rules to addition
  • finds final value when the question asks for change

The integer error check

  1. What does each minus sign mean?
  2. Which operation happens first?
  3. What sign should the answer roughly have?
  4. Can a number-line check confirm the direction?
  5. If multiplying/dividing, how many negative factors are there?

Transfer into algebra

Integer fluency becomes algebra fluency. A student who cannot calculate −7 + 12 reliably will struggle with 3x − 7 = 12. A student who mishandles −(−4) will struggle when substituting negative values into expressions.

This is why the Secondary Mathematics library treats integers as a dependency, not an isolated first chapter.

Practice

Practice 1

Question: −7 + 12

Answer: 5

Practice 2

Question: 4 − (−9)

Answer: 13

Practice 3

Question: −6 × 7

Answer: −42

Practice 4

Question: −36 ÷ (−4)

Answer: 9

Practice 5

Question: −5 + 3 × (−2)

Answer: −11

Practice 6

Question: Temperature from −8°C to 4°C

Answer: rise of 12°C

Frequently asked questions

Why is −2 greater than −7?

Because −2 lies farther right on the number line.

Why does subtracting a negative become addition?

Subtracting a quantity means adding its opposite. The opposite of −3 is +3.

Do multiplication sign rules work for addition?

No. Addition with different signs requires comparing magnitudes.

Why are brackets important?

They show that the negative sign belongs to the value, especially during substitution and multiplication.

Where does this sit in Atlas?

This is the canonical Sec 1 Integers owner under Secondary Mathematics Topic Library.

The final Integers rule

Treat signs as meaning, not decoration. Use the number line for direction, brackets for negative values, and operation order for calculation. Reliable integer control is one of the foundations of Secondary algebra.

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