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The Other Side of Zero - A Pinch of History

Grade 6CBSE

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

🔑Concepts

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The concept of numbers less than zero was developed to represent situations like debt, temperatures below freezing, and depths below sea level. These are called negative numbers, denoted with a minus sign (−)(-).

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The collection of numbers {…,−3,−2,−1,0,1,2,3,… }\{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\} is called the set of Integers.

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On a horizontal number line, positive integers are placed to the right of 00 and negative integers are placed to the left of 00.

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For any two integers on a number line, the integer on the right is always greater than the integer on the left. For example, 0>−10 > -1 and −2>−5-2 > -5.

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Zero (00) is an integer that is neither positive nor negative. It is smaller than every positive integer but greater than every negative integer.

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The absolute value of an integer aa, denoted by ∣a∣|a|, is its numerical value regardless of its sign. For example, ∣−7∣=7|-7| = 7 and ∣7∣=7|7| = 7.

📐Formulae

Successor of n=n+1\text{Successor of } n = n + 1

Predecessor of n=n−1\text{Predecessor of } n = n - 1

∣a∣=a if a≥0|a| = a \text{ if } a \ge 0

∣−a∣=a if a>0|-a| = a \text{ if } a > 0

💡Examples

Problem 1:

Write the following using appropriate signs: (i) A deposit of Rs 20002000 (ii) 15∘C15^{\circ}C below 0∘C0^{\circ}C.

Solution:

(i) +2000+2000 (ii) −15∘C-15^{\circ}C

Explanation:

Deposits and values above zero are represented by a positive (+)(+) sign, while withdrawals and values below zero are represented by a negative (−)(-) sign.

Problem 2:

Find the predecessor and successor of −10-10.

Solution:

Predecessor: −11-11; Successor: −9-9

Explanation:

The predecessor is found by subtracting 11: −10−1=−11-10 - 1 = -11. The successor is found by adding 11: −10+1=−9-10 + 1 = -9.

Problem 3:

Calculate the result of adding 55 and −8-8 using the number line logic.

Solution:

5+(−8)=−35 + (-8) = -3

Explanation:

Starting at 55 on the number line, moving 88 units to the left (because we are adding a negative number) brings us to −3-3.

Problem 4:

Represent the subtraction of 33 from 22 vertically.

Solution:

2−3−1\begin{array}{r} 2 \\ - 3 \\ \hline -1 \end{array}

Explanation:

When we subtract a larger number from a smaller number, the result is a negative integer.