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Chapter 1: Problem 5

Use a number line to represent each sum or difference. $$6-11$$

Short Answer

Expert verified
Draw a number line with numbers from 0 to 11. Locate 6 and 11 as points A and B on the number line. To subtract 11 from 6, draw an arrow from point B (11) to point A (6). Count the units between A and B, which is 5 units. Since 11 is greater than 6, the result will be negative. Thus, \(6 - 11 = -5\).

Step by step solution

01

Draw a number line

To represent the subtraction on a number line, first, we need to draw a number line with numbers from at least 0 to 11 (or even more if you prefer) in equal intervals.
02

Locate 6 and 11 on the number line

Now, we will locate the numbers 6 and 11 on the number line. Mark 6 and 11 on the number line as points A and B respectively. These are the two numbers we are working with in this subtraction problem.
03

Represent the subtraction on the number line

Next, we will represent the subtraction process using arrows. To subtract 11 from 6, draw an arrow from point B (11) to point A (6). We are essentially visualizing the distance between these two numbers on the number line.
04

Calculate the difference using the number line

Finally, count the units between the two numbers (A and B). In this case, the distance between point A (6) and point B (11) on the number line is 5 units. Since we are subtracting a larger number from a smaller one, the result will be a negative number. Therefore, the answer to this subtraction problem is -5. So, \(6 - 11 = -5\).

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Key Concepts

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

Subtraction Made Simple
Subtraction is one of the basic operations in mathematics where one number is taken away from another. Think of it as figuring out what's left after removing a certain amount. For example, when you subtract 11 from 6, you end up with the remainder, or difference. In this case, subtracting involves counting the steps backward on a number line.

The initial number represents where you start, and the second number tells you how many steps you need to move in the opposite direction. This backward movement on the number line is a straightforward way to visually grasp subtraction. The result tells us how far and in what direction we moved, giving us the subtraction outcome.
Understanding Negative Numbers
Negative numbers are numbers less than zero. They are used to represent values below a starting point on a number line or below zero in general terms. When we subtract a larger number from a smaller one, as in the case of 6 - 11, we end up with a negative result. This is because the larger number "overpowers" the smaller one, leaving us in the negative side of the number line.

Think about the weather: if it falls below zero, the temperature is negative. Negative numbers follow the same concept. They communicate a deficit or decrease, helping us better understand scenarios less than zero by encasing them in mathematical form.
The Importance of Visual Representation
Visual representations like number lines make abstract math concepts tangible. By visualizing the subtraction on a number line, we can see the relationship between numbers more clearly. Here鈥檚 why it helps:
  • Number lines provide a clear path from one number to another, showing the direct relationship in subtraction.
  • They make it easier to plot and track movements, especially when dealing with negative numbers.
  • Visual aids can simplify the process, turning a complex problem into a simple path with steps.

When you draw the numbers and see the direct movement, it reinforces understanding, making subtraction especially involving negative numbers more intuitive.
The Basics of Basic Arithmetic
Basic arithmetic includes addition, subtraction, multiplication, and division. These operations are the foundation of all mathematical calculations, crucial for problem-solving in everyday scenarios. Subtraction is a vital component, and understanding its function helps form a comprehensive understanding of mathematics.

Arithmetic allows us to:
  • Break down larger math problems into smaller, more manageable parts.
  • Build critical thinking and analytical skills through practice.
  • Address real-world issues such as budgeting, measuring, and planning.
The arithmetic operations work synergistically, so grasping subtraction also aids in understanding how these operations interact and depend on each other.

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Most popular questions from this chapter

Write a mathematical expression for each and simplify. The sum of \(-21\) and 13.

Write an expression for each and simplify. Answer the question with a complete sentence. During one offensive drive in the first quarter of Super Bowl XXXVIII, the New England Patriots ran for 7 yd, gained 4 yd on a pass play, gained 1 yd on a running play, gained another 6 yd on a pass by Tom Brady, then lost 10 yd on a running play. What was the Patriots' net yardage on this offensive drive?

Write a mathematical expression for each and simplify. Twice the difference of \(-5\) and \(-15\)

Determine whether each statement is true or false. For any real numbers \(a\) and \(b\).

Applications of Perimeter, Area, and Volume: Use 3.14 for \(\pi\) and include the correct units. A pile of sand is in the shape of a right circular cone. The radius of the base is \(2 \mathrm{ft}\), and the pile is \(6 \mathrm{ft}\) high. Find the volume of sand in the pile.
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