grade 7 Integer & Rational Number Operations

Integer & Rational Number Operations

Addition, subtraction, multiplication, and division of integers all come down to how the signs are handled. On the number line, adding a positive moves right and adding a negative moves left, while subtracting means adding the opposite. For products and quotients, like signs give a positive and unlike signs a negative, so an even number of negatives stays positive and an odd number turns it negative. Slide the two addends and the two factors, and the arrows and the sign of the result update.

Addition & Subtraction

b-5

👀 Addition via the Number Line

①Adding a positive moves right

②Adding a negative moves left

③Subtraction = adding the opposite sign: a - b = a + (-b)

Sign Rules — Addition

Same Sign Addition

Same signs → add magnitudes, keep sign

(+3) + (+5) = +8, (-3) + (-5) = -8

Different Sign Addition

Different signs → subtract magnitudes, take sign of larger

(+3) + (-5) = -2, (-3) + (+5) = +2

💡 Converting Subtraction

①Any subtraction can be turned into addition

②a - b = a + (-b)

③Flip the sign and add

④Ex: 3 - (-5) = 3 + 5 = 8

Sign Rules — Multiplication & Division

a-3

b-4

Sign Rules for × and ÷

(+)×(+)=+, (-)×(-)=+, (+)×(-)=-

Same signs → positive; different signs → negative (same for ÷)

Work It Out

Example 1

Compute (−7) + (+3) − (−5).

Turn subtraction into addition: −(−5) = +5.

(−7) + (+3) + (+5)

Add in order.

= −4 + 5 = 1

▸ 1

Subtraction becomes addition by flipping the sign.

Example 2

Compute (−2)³ × (−3).

(−2)³ = −8 (an odd power of a negative is negative).

(−2)³ = −8

(negative) × (negative) = (positive).

(−8) × (−3) = 24

▸ 24

Do powers first; a product of two negatives is positive.

Exam Key Points

Addition Core

Same signs → sum; different signs → difference

Take the sign of the larger magnitude

Multiplication/Division Core

Even # of negatives → +, odd → -

(-1)² = 1, (-1)³ = -1

Grade-7 school exam type

Compute −2² + (−3)². (Here −2² means −(2²))

①−13

②−5

③5

④13

⑤1

▸ ③ 5

−2² is −(2²) = −4, and (−3)² is 9.

−2² = −4, (−3)² = 9

Add the two values.

−4 + 9 = 5

🎯 Exam Key Points

①Multiplying by 0 always gives 0

②Division by 0 is undefined

③Distributive: a(b+c) = ab + ac

④Power signs: (-2)² = 4, -2² = -4 (mind the parentheses!)

⑤Same sign rules apply to all rational operations

⑥Division = multiply by the reciprocal: a÷b = a×(1/b) (b≠0)

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Integers & Rational Numbers

Algebraic Expressions

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