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Chapter 4: Problem 10

Graph the set of prime numbers between 10 and 20 on a number line.

Short Answer

Expert verified
The prime numbers between 10 and 20 are 11, 13, 17, and 19. They have been graphed on a number line.

Step by step solution

01

Identify the Prime Numbers

Prime numbers are numbers that have only two factors: one and themselves. They start from 2. Hence, for the numbers between 10 and 20, identify the prime numbers. They are 11, 13, 17, and 19.
02

Graph the Prime Numbers on a Number Line

Draw a number line and mark the identified prime numbers (11, 13, 17, and 19) on the number line. It is crucial to ensure the line reflects the correct order and intervals of numbers from 10 to 20.

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Key Concepts

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

Number Line
A number line is an essential tool in mathematics for visualizing numbers and their relationships. Imagine it as a straight line with evenly spaced marks, each representing a number in order. Although it might seem simple, using a number line correctly can help us understand abstract mathematical concepts more clearly.
To draw a number line:
  • Start by drawing a straight line horizontally.
  • Mark equal intervals along the line to represent consecutive numbers.
  • Label these marks with their corresponding numbers.
While graphing numbers, make sure your number line covers the range needed. For the exercise, it meant stretching the line from 10 to 20. A neat and correctly spaced number line ensures accuracy when graphing your values, like prime numbers.
Prime Numbers Identification
Identifying prime numbers is like finding needles in a haystack because they occur less frequently. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it cannot be divided evenly by any other number.
For example, to determine which numbers between 10 and 20 are prime:
  • Number 11 is prime because its only divisors are 1 and 11.
  • Number 13 is prime because it can only be divided by 1 and 13.
  • Similarly, 17 and 19 are also prime as they have no divisors other than 1 and themselves.
While 12, 14, 15, 16, 18, and 20 are not, because they can each be divided evenly by numbers other than 1 and themselves. Understanding how to identify prime numbers lets you solve problems like our exercise effectively.
Mathematical Graphing
Graphing in mathematics allows us to represent numbers or equations visually. When it comes to prime numbers, plotting them on a graph helps you see their distribution. For the exercise, we used a number line, a simple graph tool, to show the prime numbers between 10 and 20.
To graph these numbers:
  • Draw a number line that spans from 10 to 20.
  • Identify the prime numbers (11, 13, 17, and 19).
  • Mark these numbers on the line with dots or vertical lines to set them apart.
Graphing prime numbers on a number line provides a visual aid that can make tricky number concepts more understandable. Once marked, you can easily see where these primes fall relative to one another, enhancing your comprehension of number theory.

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