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Number System - Integers and negative numbers

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Definition of Integers: The set of whole numbers, their opposites, and zero (..., -3, -2, -1, 0, 1, 2, 3, ...).

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The Number Line: Moving to the right increases the value, moving to the left decreases the value. Negative numbers are always less than zero and positive numbers.

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Absolute Value: The distance of a number from zero on the number line, always expressed as a positive value.

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Comparing Integers: For two negative numbers, the one with the larger absolute value is actually the smaller number (e.g., -10 < -2).

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Zero: Zero is an integer but is neither positive nor negative.

📐Formulae

Addition (Same Signs): +(a)++(b)=+(a+b)+(a) + +(b) = +(a+b) and −(a)+−(b)=−(a+b)-(a) + -(b) = -(a+b)

Addition (Different Signs): a+(−b)=a−ba + (-b) = a - b (Take the sign of the number with the larger absolute value)

Subtraction Rule: a−(−b)=a+ba - (-b) = a + b (Subtracting a negative is the same as adding a positive)

Multiplication/Division (Same Signs): (+)×(+)=(+)(+) \times (+) = (+) and (−)×(−)=(+)(-) \times (-) = (+)

Multiplication/Division (Different Signs): (+)×(−)=(−)(+) \times (-) = (-) and (−)×(+)=(−)(-) \times (+) = (-)

💡Examples

Problem 1:

Calculate: −15+9-15 + 9

Solution:

−6-6

Explanation:

Since the signs are different, find the difference between 15 and 9, which is 6. Keep the sign of the number with the larger absolute value (15), which is negative.

Problem 2:

Evaluate: 7−(−12)7 - (-12)

Solution:

1919

Explanation:

Subtracting a negative number is equivalent to adding its positive opposite. Therefore, 7+12=197 + 12 = 19.

Problem 3:

The temperature at midnight was −5∘C-5^{\circ}C. By noon, it had risen by 12∘C12^{\circ}C. What was the temperature at noon?

Solution:

7∘C7^{\circ}C

Explanation:

Starting at −5-5, rising implies addition. −5+12=7-5 + 12 = 7.

Problem 4:

Find the product of −4-4 and −8-8.

Solution:

3232

Explanation:

When multiplying two integers with the same sign (both negative), the result is always positive. 4×8=324 \times 8 = 32.

Problem 5:

Arrange the following integers in ascending order: −3,5,−10,0,2-3, 5, -10, 0, 2

Solution:

−10,−3,0,2,5-10, -3, 0, 2, 5

Explanation:

On a number line, −10-10 is furthest to the left, followed by −3-3, then 00, then the positive integers.