Comparison of Integers is a bit confusing topic and it requires proper understanding to solve correctly. We have provided the necessary information here when comparing or ordering the integer numbers. Know various methods like comparing integers using absolute value and using number line etc. Follow all the tips given and solve the problems related to it easily. Check the below sections to know the detailed information regarding the comparison and ordering of integers.
Comparison of Integers – Introduction
Are you confused while comparing the integers? We are sure you will get clarity on things by the end of this article. Most people feel confused while comparing negative integers, but if you follow an exact procedure, then it is easy for you to solve all the problems. Two Integers are compared mostly using conditional or arithmetic methods. It is also done using the number line method. When the integers are represented on a number line, we observe that, as we are moving towards the right, the value of the number increases. In the same way, when we move towards the left, the value decreases.
The right side consists of whole numbers and the left side consists of a negative number and zero is present in the middle of the number line. Zero is less than all the positive numbers and greater than negative numbers. It is neither a positive nor a negative number. If you have to order the integer numbers from least to highest, then you would order the numbers from the right of the number line to the left.
Symbolic Representation for comparing Integers
Integers can be compared using the symbols ‘<‘, ‘>’ or ‘=’
Procedure for Comparing or Ordering of Integer Numbers
Follow the below-listed steps while comparing or ordering integer numbers. They are along the lines
- Consider, there are 2 numbers to compare. In that case, one of the numbers is greater than or less than or equal to other numbers.
- If the count of the first number is higher than the second number, then that first number is greater than the second number. The symbol ‘>’ is used to represent greater than and vice versa. The symbol ‘<‘ is used to represent less than the symbol.
- For example, consider 15 and 10 as the two integer numbers to be compared. 15 is greater than 10, as 15 has a higher count when compared to the number 10.
- Using a number line, point all the integer numbers on a number line and thus the comparison can be done easily.
Key Points to Remember while comparing Integers
Do remember the following points while ordering integers or comparing them. These help you to solve your problems easily.
- As we know, the integer is the set of whole numbers and also their opposites. In other words, Integer numbers are positive or negative whole numbers.
- Integers do not include fractions and decimals which are known as rational numbers. Integers only include whole numbers.
- Look at the integers and compare the values and then plot the integers on a number line.
- Compare the integer values and use the symbols of ‘>’,'<‘,’=’. Drawing the number line will help you to visualize the integers.
- Then, order the integer values from least to greatest.
- Arrange in order from ‘Least’ to ‘Greatest’ i.e. left to right. ‘Greatest’ to ‘Least’ is right to left.
- Consider the absolute value of the number which is the distance from the number line. Absolute values are always positive because it signifies the distance.
Comparing Integers Examples
Josh has $23, his friend Krista has $25 and another friend Mark has $8, his friend Luis has -$5, another friend Tessa has -$10. Josh wants to order and compare the amount of money they have?
First, draw the number line and make sure you include all the numbers you have to plot. Plot all the above money values on the number line.
Then, find out the number which is furthest to the left of the number line. -10 is the smallest number which means Tessa is with the least amount of money.
After -10, -5 is the second least number. Therefore, Luis has the second least amount of money. Next comes the Mark with the next least amount of money of $8. Thus the pattern follows with Josh and Krista.
This analysis will give you the numbers that are ordered from least to greatest.
Therefore, the final solution is in the order of -$10,-$5,$8,$23,$25. Thus, Tessa has less amount of money and Krista has the highest amount of money.
Choose the inequality symbol which goes in the blank to make the given statement true: -22 _____ -32
First, visualize or draw a number line. Then, plot the points of -22 and -32.
Then, determine where -22 is on the drawn number line when compared to -32. -22 will be to the right of -32.
As it is on the right side, it determines -22 is greater than -32.
The final solution is -22>-32
The inequality symbol which goes in the blank is “>”
Arrange the numbers −4, 2, 8, 9, −11, −5 in order using the number line?
First of all, draw a number line and include all the numbers in such a way that the least number -11 is included and the highest number 9 is included.
Once, you draw the number line, start plotting the numbers as per the ascending order. First, start by -11, then -5 followed by -4 and so on.
Continue by reading the points on the plotted number line from left to right which gives you the order of the numbers from least to highest.
The final solution is 11, -5, -4, 2, 8, 9.
Arrange the numbers 5, −16, 6, -12, 1, 4 in order using the number line?
First of all, draw a number line that includes all the numbers given in the above question. The least number must be greater than -16 and the highest number must be greater than 6.
Once, you start drawing the number line, make sure you arrange the numbers in ascending order. The first least number comes as -16, then -12 followed by 1 and so on.
Now, plot the numbers from left to right which you have previously arranged in order. Once you plot the numbers, you will get the list of numbers from least to highest values.
The solution is -16, -12, 1, 4, 5, 6.
Arrange the numbers −3, −2, −7, −12, −1 in order using the number line?
The first step is to draw the number line by including all the numbers that are given in the question. Make sure you draw a number line by including a few extra numbers.
Now, that you are ready with the number line, the next step is to plot the numbers on the graph. Analyze the order of the numbers from least to highest. The least number from the given series is -12. -7 is the second least number, then comes -3, and so on.
Once you are ready with the order of numbers, you can easily plot them on the number line. Plot the numbers from left to right in the order you arranged previously. After plotting the numbers, you will find the final result of numbers from least to highest values.
The final solution is -12,-7,-3,-2,-1.
Here is the detailed information about Comparison of Integers and also how to order the integers. This concept will help you throughout your integers problem-solving methods. I hope, you got clarity on how to order, compare the integers, and also how to include inequality symbols for various integer numbers. For more details regarding other mathematical topics, stay tuned to our site.