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Chapter 1: Problem 67

On a number line, what number is 3 units to the left of \(7 ?\)

Short Answer

Expert verified
4

Step by step solution

01

Understand the Problem

Identify the starting point on the number line, which is the number 7.
02

Determine the Direction

Since the task requires moving to the left, this means the movement will be towards smaller numbers on the number line.
03

Calculate the Movement

Subtract the number of units to move from the starting point. In this case, move 3 units to the left of 7: \[ 7 - 3 = 4 \]
04

Identify the Result

The result of moving 3 units to the left of 7 on the number line is 4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Number Line
The number line is a visual representation that helps us understand the concept of numbers and their order. It consists of a straight, horizontal line with numbers placed at equal intervals along its length. Typically, positive numbers are placed to the right of zero, and negative numbers to the left. Using a number line simplifies various mathematical operations and makes abstract concepts more tangible. For example, to solve problems involving addition and subtraction, we can visualize the movement of points along the line. This makes understanding arithmetic operations more intuitive, especially for beginners.
The Concept of Subtraction
Subtraction is one of the basic arithmetic operations where we find the difference between two numbers. In simpler terms, it is the process of taking one number away from another. In mathematical notation, if we have a number 'a' and we subtract 'b' from it, the result is written as \( a - b = c \). Subtraction can also be visualized on a number line, where moving to the left from a starting point represents this operation. For instance, if we start at 7 and need to subtract 3, we move 3 units to the left to land on 4.
Movement on the Number Line
Visualizing arithmetic operations on a number line can be very helpful. When it comes to subtraction, the direction of movement matters a lot. Moving to the left signifies subtracting values, while moving to the right indicates adding values.

Let's take the example from the original exercise: Finding the number 3 units to the left of 7 on the number line. You start at the number 7, then move 3 units to the left. Each unit you move leftwards takes you to a smaller number.

Step-by-Step:
  • Start at 7 on the number line.
  • Move 1 unit to the left: land on 6.
  • Move another unit to the left: land on 5.
  • Move one more unit to the left: land on 4.
After this process, you've moved 3 units to the left and landed on 4. Thus, the solution to the problem is 4.

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