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Chapter 1: Problem 11

On the number line, graph the prime numbers between 10 and \(20 .\)

Short Answer

Expert verified
The prime numbers between 10 and 20 are 11, 13, 17, and 19.

Step by step solution

01

Recognize Prime numbers

Recognize what prime numbers are. These are numbers that have only two factors, 1 and the number itself. This means they cannot be divided evenly by any other number.
02

Identify the Prime Numbers between 10 and 20

Identify these prime numbers lying between 10 and 20. The prime numbers in this interval are 11, 13, 17, and 19.
03

Plotting the prime numbers

Finally, these numbers (11, 13, 17, and 19) are plotted on a number line. To do so, draw a line and evenly space the numbers from 10 to 20. Then, mark off the numbers identified as prime numbers, and label them accordingly.

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Key Concepts

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

Understanding the Number Line
Number lines are visual tools that help us understand the placement and order of numbers. Imagine it as a horizontal line that extends infinitely in either direction. In the center is typically zero, with positive numbers increasing to the right and negative numbers increasing to the left.

Number lines are particularly helpful when learning about intervals and ranges. For instance, if tasked with plotting numbers between 10 and 20, you'd look solely at that portion of the line鈥攂etween these two points.
  • Keep the intervals evenly spaced.
  • Ensure the number line has clear, labeled markings for each integer.
  • Use arrows at both ends to indicate that the line continues indefinitely.
With a number line, you visualize concepts more clearly, making it easier to grasp where numbers belong relative to each other.
Defining Integers in the Context of Prime Numbers
Integers include all positive and negative whole numbers, along with zero. They do not have decimal points or fractions, just neat, full numbers. On the number line, integers are spaced uniformly, making it straightforward to identify them.

When discussing prime numbers, we're interested in positive integers greater than 1. A prime number is wholly divisible by only 1 and itself. For example, the integers 11, 13, 17, and 19 are prime because their only divisors are 1 and the number itself.
  • Identify integers quickly on a number line by their placement.
  • Count forwards or backwards to determine if a number is an integer.
  • Remember, integers are never fractions or decimals.
This makes the number line a great tool for identifying and understanding prime integers within a given range.
Graphing Numbers and Emphasizing Primes
Graphing numbers on a number line is a fundamental skill that aids in visualizing the relationship between numbers. It's especially useful for identifying special sets of numbers, like primes.

To graph numbers like 11, 13, 17, and 19, first draw the number line with numbers from 10 to 20. Mark your line into neat increments鈥攖his helps in placing numbers accurately. Once the line is ready, place a clear dot above or below each prime number. It鈥檚 common also to label these dots for clarity.
  • Use dots to represent specific numbers; spelling out primes keeps things clear.
  • Make sure your marks are accurately placed to avoid confusion.
  • Label every plotted number to enhance understanding.
Effective graphing not only aids in visual learning but can also strengthen mental math skills by reinforcing number positions and values on the line.

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Most popular questions from this chapter

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