Operations with negative numbers, absolute value and rationals
Master integers and their extension to rational numbers: adding and subtracting with signs, multiplying and dividing negatives, absolute value, order of operations, powers with negative bases, negative exponents and square roots. Every answer includes a step-by-step explanation.
Integers are the positive numbers, the negative numbers and zero (…-2, -1, 0, 1, 2…). They appear whenever a subtraction gives less than zero: temperatures below zero, debts, basement floors. Rational numbers extend them by adding fractions and decimals, that is, any number that can be written as a fraction.
The main challenge is operating with signs: remembering that minus times minus is plus, respecting the order of operations, and handling absolute value, powers with a negative base, negative exponents and square roots. They are the foundation of algebra and of almost everything that follows in Secondary and Sixth Form.
Practise operations with negatives and rationals with the exam below, with a reasoned explanation after each answer so no doubts remain.
Mathematics · Secondary
The exam systematically reinforces: (−)×(−)=+, (−)×(+)=−. After several repetitions with context the rule sticks without rote memorisation.
Brackets first, then powers, then multiplication/division, finally addition/subtraction. The exam includes expressions with multiple operations to practise the correct order.
From integers to rationals: negative fractions, negative exponents (2⁻³=1/8) and exact square roots (√144=12).
"A Year 7 student who thought 4−(−6)=−2 learns that subtracting a negative equals adding: 4+6=10."
Tricks and techniques to master this topic faster:
Subtracting a negative: 5−(−3) = 5+3 = 8. "Minus negative = positive".
Absolute value: always positive. |−7|=7, |+7|=7.
Power with negative base: (−2)²=4 (positive), (−2)³=−8 (negative). Check if the exponent is even or odd.
Negative exponent: a⁻ⁿ = 1/aⁿ. For example, 2⁻³ = 1/2³ = 1/8.
If you are studying Integers and Rational Numbers — Maths Exam, these curriculum topics complement each other:
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