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The Other Side of Zero - Bela’s Building of Fun

Grade 6CBSE

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

🔑Concepts

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Integers are a collection of whole numbers and their negatives. The set is represented as Z={…,−3,−2,−1,0,1,2,3,… }Z = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}.

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

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A number is greater than any number to its left. For example, 0>−10 > -1 and −2>−10-2 > -10.

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The successor of an integer is found by adding 11 to it. The successor of −5-5 is −5+1=−4-5 + 1 = -4.

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The predecessor of an integer is found by subtracting 11 from it. The predecessor of −5-5 is −5−1=−6-5 - 1 = -6.

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The absolute value of an integer aa is its numerical value regardless of its sign, denoted by ∣a∣|a|. For example, ∣−10∣=10|-10| = 10 and ∣10∣=10|10| = 10.

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When adding two integers with the same sign, we add their absolute values and keep the common sign. Example: (−2)+(−3)=−5(-2) + (-3) = -5.

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When adding two integers with different signs, we find the difference between their absolute values and use the sign of the integer with the greater absolute value. Example: (−8)+5=−3(-8) + 5 = -3.

📐Formulae

Successor=n+1Successor = n + 1

Predecessor=n−1Predecessor = 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

a−b=a+(−b)a - b = a + (-b)

💡Examples

Problem 1:

Bela is on the 2nd2^{nd} floor of the basement (Floor −2-2). She takes the lift and goes up 55 floors. Which floor is she on now?

Solution:

She is on Floor 33.

Explanation:

Starting point is −2-2. Moving 'up' means addition. So, we calculate (−2)+5(-2) + 5. Since the signs are different, we subtract the absolute values: 5−2=35 - 2 = 3. The sign of the larger absolute value (∣5∣|5|) is positive, so the result is 33.

Problem 2:

Find the sum of −120-120 and −80-80.

Solution:

−200-200

Explanation:

Both numbers have the same sign (negative). We add their absolute values: 120+80=200120 + 80 = 200. We then attach the common negative sign to get −200-200.

Problem 3:

Calculate the difference: 150−75150 - 75.

Solution:

150−7575\begin{array}{r} 150 \\ - 75 \\ \hline 75 \end{array}

Explanation:

This is a standard subtraction of two positive integers where the result is 7575.

Problem 4:

Arrange the following integers in ascending order: −5,2,0,−8,3-5, 2, 0, -8, 3.

Solution:

−8,−5,0,2,3-8, -5, 0, 2, 3

Explanation:

On a number line, −8-8 is furthest to the left, followed by −5-5, then 00, then 22, and finally 33 is furthest to the right.