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Number System - Negative numbers in context

Grade 5IGCSE

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

🔑Concepts

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Definition: Negative numbers are values less than zero, indicated by a minus sign (-).

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Number Line: On a horizontal number line, negative numbers are located to the left of zero. As you move further left, the value decreases.

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Zero: Zero is neither positive nor negative; it acts as the origin or neutral point.

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Comparing and Ordering: A number is smaller if it is further to the left on the number line (e.g., -10 is smaller than -2).

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Real-world Contexts: Common uses include temperature (below freezing), elevation (below sea level), and finance (debts or bank overdrafts).

📐Formulae

New Temperature=Original Temperature±Change\text{New Temperature} = \text{Original Temperature} \pm \text{Change}

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

Moving Right on Number Line→Addition (+)\text{Moving Right on Number Line} \rightarrow \text{Addition (+)}

Moving Left on Number Line→Subtraction (-)\text{Moving Left on Number Line} \rightarrow \text{Subtraction (-)}

💡Examples

Problem 1:

The temperature in London is 5∘C5^{\circ}C. Overnight, it drops by 8∘C8^{\circ}C. What is the new temperature?

Solution:

−3∘C-3^{\circ}C

Explanation:

Start at 5 on the number line and move 8 units to the left. 5−5=05 - 5 = 0, and then moving 3 more units left reaches −3-3.

Problem 2:

Arrange these numbers in ascending order (smallest to largest): 2,−5,0,−1,42, -5, 0, -1, 4.

Solution:

−5,−1,0,2,4-5, -1, 0, 2, 4

Explanation:

In negative numbers, the larger the digit following the minus sign, the smaller the value. Therefore, −5-5 is the smallest.

Problem 3:

A diver is at 1515 meters below sea level. She swims up 77 meters. What is her new position relative to sea level?

Solution:

−8-8 meters

Explanation:

Sea level is 00. Being below sea level is represented by negative numbers, so the diver starts at −15-15. Swimming up is addition: −15+7=−8-15 + 7 = -8.