Number and Place Value - Negative numbers in real-world contexts

Grade 4IGCSE

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

🔑Concepts

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Negative numbers are values less than zero, often represented with a minus (-) sign.

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The Number Line: Positive numbers are to the right of zero; negative numbers are to the left of zero.

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Zero as a Reference Point: In real-world contexts, zero represents a specific state like freezing point (0°C) or sea level (0m).

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Comparing Magnitudes: A larger negative number (e.g., -10) is actually 'smaller' or 'colder' than a smaller negative number (e.g., -2) because it is further from zero on the left.

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Real-world application: Temperature (above/below freezing), Altitude (above/below sea level), and Finance (credit/debt).

📐Formulae

\text{Difference} = \text{Higher Value} - \text{Lower Value}

\text{Distance from zero} = |n|

\text{Final Temperature} = \text{Starting Temp} + \text{Rise}

\text{Final Temperature} = \text{Starting Temp} - \text{Fall}

💡Examples

Problem 1:

At 6:00 AM, the temperature in London was -4°C. By noon, the temperature had risen by 9°C. What was the temperature at noon?

Solution:

5°C

Explanation:

Start at -4 on the number line. Moving 'up' or 'rising' means adding. -4 + 4 takes you to 0. You still have 5 more degrees to add (9 - 4 = 5). Therefore, 0 + 5 = 5°C.

Problem 2:

A diver is at 15 meters below sea level (-15m). A bird is flying at 12 meters above sea level (+12m). What is the vertical distance between the diver and the bird?

Solution:

27 meters

Explanation:

To find the distance between a negative and a positive number, add their distances from zero. The diver is 15m from zero, and the bird is 12m from zero. 15 + 12 = 27 meters.

Problem 3:

Which temperature is colder: -12°C or -8°C?

Solution:

-12°C

Explanation:

On a number line, -12 is further to the left of zero than -8. In terms of temperature, the further a number is below zero, the colder it is.