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# Equal, Greater Than, Less Than

## What is an equality?

A relationship between two quantities or mathematical expressions that have the same value or represent distinct objects is called equality. To represent equality, we use the equal symbol or equal sign. Hence, we write two parallel horizontal symbols like “=” to show equality.

So, the equality between A and B is written as A = B which reads as A equals B or A is equal to B

## What is an inequality?

Inequality is a relationship between two numbers or algebraic expressions that are not equal. Inequalities can sometimes be presented as either question which can be solved or a statement of fact in the form of theorems. We can use four inequality terms to compare two quantities: not equal to, greater than, greater than or equal to, less than, and less than or equal to.

### Not equal to

One of the symbols we use for inequality is not equal to sign. It is used to show that one value is not equal to the other. Hence, to show a not equal to relationship, we use two horizontal lines and a slash in the middle of it.

Therefore, if two quantities A and B are not equal, it is written as A ≠ B which reads as  A is not equal to B

### Greater than

Greater than is also one of the inequalities used when a quantity is larger or bigger than the other quantity or quantities. Hence, to show that a number is greater than the other, we use two-equal length strokes that look like an acute angle going to the right.

So, to say that quantity A is greater than B, we denote it as A > B which reads as A is greater than B

### Greater than or equal to

Aside from greater than, we also use the term greater than or equal to show the relationship between two or more mathematical objects or inequalities. Greater than or equal assumes that the value of a variable can be equal to or greater than a certain number. The term “at least” means a value can be greater than or equal to. Hence, to show that a number is greater than the other, we use two-equal length strokes that looks like an acute angle going to the right and an underline under it.

Thus, to show that A is greater than B, we denote it as A ≥ B which reads as A is greater than or equal to B – which means A can be greater than B and can also be equal to B.

### Less than

When the first value is smaller than the second value, we use the term less than. Less than is used to show the relationship between a smaller and larger value. To show inequality that a number is less than the other, we use the symbol two-equal length strokes that look like an acute angle going to the left.

Hence, to show that A is less than B, we denote it as A < B which reads as A is less than B.

### Less than or equal to

Less than or equal to means that a variable is either less than or equal to the other number, expression, or term. Using the terms “at most”, “no more than”, “maximum of”, and “not exceeding” also means less than or equal to. Two-equal length strokes that look like an acute angle going to the left and an underline below it is the symbol used to show that one quantity is less than or equal to the other.

Therefore,  to show that A is less than or greater than B, we denote it as A ≤ B which reads as A is less than or equal to B.

## What are the equality and inequality symbols?

The table below summarizes all the symbols we use to show equality and inequality between two quantities.

## Why do we use equality and inequality symbols?

The use of equality and inequality symbols can help us compare numbers, state the relationship between two or more mathematical objects that we are not yet certain of and use it for mathematical equations or inequality.

### Compare numbers

One of the most important roles of using equality and inequality symbols is we get to compare two mathematical quantities. Let’s look at some of the examples below!

Using equal sign to compare mathematical objects

Example #1

In the given figure, we can see that on the left-hand side, we have two lollipops. On the right-hand side, we also have two lollipops. Since there is the same number of lollipops in the left and right-hand sign, we will use the equal sign to show equality between the two different groups of lollipops.

Using greater than or less than to compare mathematical objects

Example #1

By counting the number of cookies on both sides, we would know that the number of cookies on the left-hand side is greater than the number of cookies on the right-hand side. Hence, we use the greater than symbol to show the relationship between the cookies.

Example #2

In this second example, we can clearly see that there are more ice creams on the right-hand side than on the left-hand side. Thus, we use the less than sign to show that two is indeed less than three ice creams.

### State relationships

When there are quantities that we are not certain of, we sometimes use equality and inequality symbols to know their relationships.

Example #1

Explanation:

In the given figure, if we compare the relationship between the two dogs, we can clearly see that one is taller than the other. Hence, we can say that the dog on the right side is greater than the dog on the left side.

Example #2

\$1 = 100 cents In this example, we know that in order for us to make a dollar out of cents is by having 100 cents. Hence, we can say Example #2 Jace had 20 pens, but lost some in school. How many does he have now? Since Jace lost some of his pens, then the number of pens that he has now must be less than 20. Hence, pens < 20 Example #3 Angelina already spent \$50 and bought more clothes after. How much do you think did she spend?

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