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The Other Side of Zero - Integers in Other Places

Grade 6CBSE

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

🔑Concepts

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Integers are a collection of numbers that include positive natural numbers (1,2,3,…1, 2, 3, \dots), negative numbers (…,−3,−2,−1\dots, -3, -2, -1), and zero (00).

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On a number line, zero is the origin. Positive integers lie to the right of zero, and negative integers lie to the left of zero.

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The Successor of an integer is the number immediately to its right on the number line, calculated as n+1n + 1.

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The Predecessor of an integer is the number immediately to its left on the number line, calculated as n−1n - 1.

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Comparison: Every positive integer is greater than every negative integer. Zero is greater than every negative integer but smaller than every positive integer.

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Additive Inverse: Two integers whose sum is 00 are called additive inverses of each other. For any integer aa, its additive inverse is −a-a.

📐Formulae

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

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

a+(−a)=0a + (-a) = 0

a−b=a+(−b)a - b = a + (-b), where (−b)(-b) is the additive inverse of bb.

💡Examples

Problem 1:

Find the predecessor and successor of −8-8.

Solution:

Successor: −8+1=−7-8 + 1 = -7. Predecessor: −8−1=−9-8 - 1 = -9.

Explanation:

To find the successor, we move one unit to the right on the number line (add 11). To find the predecessor, we move one unit to the left (subtract 11).

Problem 2:

Calculate: (−12)+(−5)+20(-12) + (-5) + 20.

Solution:

(−12)+(−5)=−17(-12) + (-5) = -17 Then, −17+20=3-17 + 20 = 3

Explanation:

First, add the two negative integers by summing their absolute values and keeping the negative sign. Then, add the result to the positive integer by finding the difference and using the sign of the larger absolute value.

Problem 3:

Perform the subtraction: 50−(−25)50 - (-25).

Solution:

Subtracting a negative number is equivalent to adding its additive inverse: 50+25=7550 + 25 = 75 50+2575\begin{array}{r} 50 \\ +25 \\ \hline 75 \end{array}

Explanation:

According to the rule a−(−b)=a+ba - (-b) = a + b, we change the sign of the subtrahend and add it to the minuend.

Problem 4:

Compare the following using >> or <<: −100-100 and −50-50.

Solution:

−100<−50-100 < -50

Explanation:

On the number line, −50-50 is to the right of −100-100. In negative numbers, the number with the smaller absolute value is actually the larger number.