Private: Selective School Placement Test Preparation Book

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2. Number Line and Whole Number Operations Using a Number Line

Private: Selective School Placement Test Preparation Book Whole Numbers 2. Number Line and Whole Number Operations Using a Number Line

. Introduction to Number Lines

A number line is a straight line with numbers placed at equal intervals along its length. It extends infinitely in both directions.

  • Left side: Smaller numbers or negative numbers (if included)
  • Right side: Larger numbers or positive numbers

Key Points:

  • Zero (0) is the center of the number line (if considering positive and negative numbers), but for whole numbers, we start from 0 and move right.
  • The number line helps in visualizing operations such as addition, subtraction, multiplication, and division.

2. Whole Numbers on a Number Line

Whole numbers are non-negative integers: 0, 1, 2, 3, and so on. To represent whole numbers on a number line:

  • Place each whole number at a specific, equal distance from the previous one.

Example:

Represent 0, 1, 2, 3, and 4 on a number line:

3. Basic Operations on a Number Line

3.1. Addition of Whole Numbers

Addition means moving right on the number line.

Example: 2 + 3

  • Start at 2 on the number line.
  • Move 3 steps to the right.
  • You land at 5.
Addition Using Number Line
Addition Using Number Line

3.2. Subtraction of Whole Numbers

Subtraction means moving left on the number line.

Example: 5 − 3

  • Start at 5 on the number line.
  • Move 3 steps to the left.
  • You land at 2.
Subtraction Using Number Line
Subtraction Using Number Line

4. Advanced Whole Number Operations Using a Number Line

4.1. Multiplication on a Number Line

Multiplication can be seen as repeated addition.

Example: 2 × 3

  • Start at 0.
  • Make 2 jumps of 3 steps each to the right.
  • You land at 6.
Multiplication Using Number Line
Multiplication Using Number Line

4.2. Division on a Number Line

Division can be viewed as repeated subtraction or splitting into equal parts.

Example: 8 ÷ 2

  • Start at 8.
  • Move 2 steps to the left repeatedly until you reach 0.
  • You can make exactly 4 steps, so 8 ÷ 2 = 4
Division Using Number Line
Division Using Number Line

5. Complex Scenario: Mixed Operations on a Number Line

When dealing with multiple operations (addition, subtraction, multiplication, and division), use the BODMAS rule:

  • Brackets
  • Orders (powers and roots)
  • Division
  • Multiplication
  • Addition
  • Subtraction

Example: Solve 3 + 4 × 2 − 5 using a number line.

  1. First, handle multiplication: 4 × 2 = 8
  2. Then, addition: 3 + 8 = 11.
  3. Finally, subtraction: 11 − 5 = 6 .

Visualize on a number line:

  • Start at 3, jump 8 steps right to reach 11, then move 5 steps left to land at 6.

6. Introducing Negative Numbers for Advanced Scenarios

In more advanced scenarios, negative numbers can be introduced:

  • Addition of a negative number means moving left.
  • Subtraction of a negative number means moving right.

7. Logical Challenges and Scenarios

7.1. Temperature Change

If the temperature is 5°C and it drops by 7°C, what is the new temperature? Use a number line with negative numbers.

7.2. Time on a Clock

If it’s 3 PM and you need to add 9 hours, where will the time be on a 12-hour clock?

8. Practice Questions

  1. Represent 4 + 6 on a number line.
  2. Solve 10 − 7 using a number line.
  3. Visualize 3 × 5 on a number line.
  4. Show 12 ÷ 4 on a number line.
  5. Solve 5 + 8 − 3 using the number line.
  6. Use a number line to solve 9 × 2 − 7.
  7. Visualize and solve 24 ÷ 6 + 5 on a number line.
  8. Apply a number line to 15 + 3 × 4 − 8.
  9. Solve 7 + 3 × (10 − 8) using a number line.
  10. Represent 18 ÷ 2 + 4 − 5 on a number line.

9. Practice Question Solutions

  1. 4 + 6 = 10
    • Start at 4, move 6 steps to the right. Result: 10.
  2. 10 − 7 = 3
    • Start at 10, move 7 steps to the left. Result: 3.
  3. 3 × 5 = 15
    • Start at 0, make 3 jumps of 5 steps. Result: 15.
  4. 12 ÷ 4 = 3
    • Start at 12, make 4 jumps of 3 steps to the left. Result: 3.
  5. 5 + 8 − 3 = 10
    • Start at 5, move 8 steps right (to 13), then 3 steps left. Result: 10.
  6. 9 × 2 − 7 = 11
    • Start at 0, make 9 jumps of 2 steps to reach 18, then move 7 steps left. Result: 11.
  7. 24 ÷ 6 + 5 = 9
    • Start at 24, make 6 jumps of 4 steps to reach 4, then move 5 steps right. Result: 9.
  8. 15 + 3 × 4 − 8 = 19
    • Start at 15, make 3 jumps of 4 steps to reach 27, then move 8 steps left. Result: 19.
  9. 7 + 3 × (10 − 8) = 13
    • Start at 7, solve the brackets first 10−8=210 – 8 = 210−8=2, then multiply by 3, move 6 steps right. Result: 13.
  10. 18 ÷ 2 + 4 − 5 = 8
    • Start at 18, make 2 jumps of 9 steps to reach 9, move 4 steps right, and then 5 steps left. Result: 8.

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