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Number Play - Patterns of Numbers on the Number Line

Grade 6CBSE

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

🔑Concepts

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A number line is a straight line where every point corresponds to a number, and numbers are placed at equal intervals called 'unit distances'.

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On a horizontal number line, numbers increase as we move to the right and decrease as we move to the left. For any two numbers aa and bb, a>ba > b if aa is to the right of bb.

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The number 00 is the reference point. Positive numbers are to the right of 00, and negative numbers are to the left of 00.

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To add a positive number, move to the right on the number line. To subtract a positive number, move to the left.

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A number pattern on the number line is a sequence where the 'jump' or distance between consecutive numbers remains constant. For example, in the pattern 2,4,6,8,…2, 4, 6, 8, \dots, the jump is 22 units.

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The Successor of a number is the number immediately to its right (n+1n + 1), and the Predecessor is the number immediately to its left (n−1n - 1).

📐Formulae

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

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

Jump Size (d)=Term2−Term1\text{Jump Size (d)} = \text{Term}_2 - \text{Term}_1

Next Term=Current Term+Jump Size\text{Next Term} = \text{Current Term} + \text{Jump Size}

💡Examples

Problem 1:

Identify the pattern and find the next two numbers in the sequence: 3,7,11,15,…3, 7, 11, 15, \dots

Solution:

The jump size is 7−3=47 - 3 = 4. The next numbers are 15+4=1915 + 4 = 19 and 19+4=2319 + 4 = 23.

Explanation:

We observe that each number is obtained by adding 44 to the previous number. On the number line, this represents a forward jump of 44 units.

Problem 2:

Represent the operation 5−85 - 8 on the number line and find the result.

Solution:

5−8=−35 - 8 = -3

Explanation:

Start at point 55 on the number line. To subtract 88, move 88 units to the left. After moving 55 units, you reach 00, and moving 33 more units to the left brings you to −3-3.

Problem 3:

Find the predecessor of −10-10 and the successor of −1-1.

Solution:

Predecessor of −10-10 is −11-11; Successor of −1-1 is 00.

Explanation:

Using the formulas: Predecessor =−10−1=−11= -10 - 1 = -11. Successor =−1+1=0= -1 + 1 = 0. On the number line, −11-11 is one unit to the left of −10-10, and 00 is one unit to the right of −1-1.

Problem 4:

Calculate the sum using the number line: 4+37\begin{array}{r} 4 \\ + 3 \\ \hline 7 \end{array}

Solution:

4+3=74 + 3 = 7

Explanation:

Locate 44 on the number line. Move 33 units to the right (addition). The final position is 77.