The greater than less than calculator displays the result whether the first number is less than or greater than the second number. STUDYQUERIES’s online greater than less than calculator tool makes calculations easier and faster, and it compares numbers in a fraction of a second.
How to Use Greater Than Less Than Calculator?
To use the greater than less than calculator, follow these steps:
- Step 1: Input two numbers in the respective input fields “Number 1” and “Number 2”
- Step 2: Compare the numbers by clicking the “Compare” button
- Step 3: The result will now be displayed in the output field, indicating whether the first number is greater or smaller than the second number
Greater Than Less Than Calculator
What Is Greater Than Less Than Sign And Calculator?
To compare two numbers, greater than and less than symbols are used. When a number is bigger than or smaller than another number, greater than less than symbols are used. If the first number is greater than the second number, greater than symbol \(\pmb{\color{red}{{”\gt”}}}\) is used. If the first number is less than the second number, less than symbol \(\pmb{\color{red}{{”\lt”}}}\) is used. Mathematics is a language that has its own rules and formulas.
Mathematical symbols are unique to all fields, and they are universally accepted. Using mathematical symbols requires less space and time. It allows individuals to communicate information visually. In this article, we will cover the definition of greater than and less than symbols, their symbols, and some examples of how to compare two numbers by using less than and greater than signs.
Greater Than and Less Than Symbols Definition
Greater than and less than symbols denote an inequality between two values. The symbol used to denote greater than is \(\pmb{\color{red}{{”\gt”}}}\) and for less than is \(\pmb{\color{red}{{”\lt”}}}\).
Greater Than Sign
In math, a greater than symbol is placed between two values when the first number is greater than the second number.
For example \(10 \gt 5\). Here 10 is greater than 5.
In inequality, the greater than symbol is always pointed to the greater value, and the symbol consists of two equal-length strokes that connect at an acute angle at the right. \(\pmb{\color{red}{{”\gt”}}}\).
Less Than Sign
A less-than symbol is also placed between two numbers if the first number is less than the second.
An example for less than the inequality symbol is \(5 \lt 10\). It means that 5 is less than 10.
In inequality, less than symbol points to the smaller value where the two equal length strokes connect at an acute angle at the left \(\pmb{\color{red}{{”\lt”}}}\).
The greater than less than symbol reduces the time complexity and makes understanding easy for the reader.
Equal To Sign
When two numbers or values are equal, the ‘equal to’ sign indicates that they are equal. It contradicts both the greater than and less than signs. Even in terms of writing the equations, we use equal to sign. It is denoted by \(\color{red}{{\mathbf{”=”}}}\).
Example: If \(a \color{red}{=} 10\) and \(b \color{red}{=} 10\), then \(a \color{red}{=} b\).
Trick to Remember Greater Than Less Than Sign
Three methods are generally used to remember greater than and less than symbols. These are:
Alligator Method
It is easiest to memorize the greater than and less than signs by picturing them as alligators (or crocodiles) with fish on either side. Alligators always try to eat the most number of fish, so whatever number the mouth is open towards is the number they are looking for.
The alligator’s mouth is open toward the 4, so even if we weren’t sure that 4 is a bigger number than 3, then \(\pmb{\color{red}{{\gt}}}\) sign would tell us. All inequality signs give us the relationship between the first number and the second, beginning with the first number, so \(4\ \pmb{\color{red}{{\gt}}}\ 3\) translates to \(\pmb{\color{red}{4\ is\ greater\ than\ 3.}}\)
This also works the other way around. If you see \(5\ \pmb{\color{red}{{\lt}}}\ 8\), imagine the \((\pmb{\color{red}{{\lt}}})\) sign as a little alligator mouth about to chomp down on some fish.
The mouth is pointed at the 8, which means that 8 is more than 5. The sign always tells us the relationship between the first number and the second, so \(5\ \pmb{\color{red}{{\lt}}}\ 8\) can be translated to \(\pmb{\color{red}{5\ is\ less\ than\ 8}}.\)
When you’re working with inequalities, you can even draw little eyes on the symbols to help you remember which one means what. If you are having trouble remembering these, don’t be afraid to get a little creative until you have them down.
L Method
This method is pretty simple—\(\color{red}{“less\ than”}\) starts with a letter \(\color{red}{L}\), so the symbol that looks most like an \(\color{red}{L}\) is the one that means \(\color{red}{“less\ than.”}\)
\(\color{red}{\lt}\) looks more like an \(\color{red}{L}\) than \(\color{red}{\gt}\), so \(\color{red}{\lt}\) means \(\color{red}{“less\ than.”}\) Because \(\color{red}{\gt}\) doesn’t look like an \(\color{red}{L}\), it can’t be \(\color{red}{“less\ than.”}\)
Equal Sign Method
Once you’ve mastered the \(\color{red}{Alligator}\) or \(\color{red}{L\ method}\), the other symbols are easy! \(\color{red}{Greater\ than\ or\ equal\ to}\) and \(\color{red}{less\ than\ or\ equal\ to}\) are just the applicable symbol with half an equal sign under them.
For example, \(\color{red}{4\ or\ 3 \ge 1}\) shows us a greater sign over half an equal sign, meaning that \(\color{red}{4\ or\ 3\ are\ greater\ than\ or\ equal\ to\ 1.}\)
It works the other way, too. \(\color{red}{1 \le 2\ or\ 3}\) shows us a less than sign over half of an equal sign, so we know it means that \(\color{red}{1\ is\ less\ than\ or\ equal\ to\ 2\ or\ 3.}\)
The \(\color{red}{does\ not\ equal}\) sign is even easier! It’s just an equal sign crossed out. If you see an equal sign crossed out, it means that the equal sign doesn’t apply—thus, \(\color{red}{2 \neq 3}\) means that \(\color{red}{2\ does\ not\ equal\ 3.}\)
Applications of Greater Than Less Than Symbols in Algebra
Mathematical problems rarely end inequality, as we all know. It should sometimes have inequalities, such as greater than and less than signs. A mathematical expression can be used to express the statement.
For example, \(\color{red}{x}\) is the number of students in a class. If there are more than 45 students in a class, and again 5 more students join in your class, then there are more than 50 students in a class. This statement is mathematically expressed as $$\color{red}{x+5 \gt 45}$$
Solving inequalities is similar to solving equations in mathematics. Always keep the inequalities direction in mind when dealing with inequality problems. Tricks may not affect the direction of inequalities in a problem. There it is.
- Divide or multiply the inequalities on both sides by the same positive number
- By adding or subtracting the same number from both sides of the inequality expression
Greater Than and Less Than Symbols Examples
Some of the examples of greater than symbol are as follows
- \(4 \gt 1\) means 4 is greater than 1.
- \(2^5 > 2^3\): \(2^5\) can be written as \(2 \times 2 \times 2 \times 2 \times 2 =32\) and \(2^3\) can be written as \(2 \times 2 \times 2 =8\). So \(32 \gt 8\) .Therefore \(2^5\ is\ greater\ than\ 2^3\)
- \(\frac{10}{2} \gt \frac{6}{3}\): \(\frac{10}{2}\) equals to \(5\) and \(\frac{6}{3}\) equals to \(2\). So that, \(5 \gt 2\) which implies that \(\frac{10}{2}\) is greater than \(\frac{6}{3}\).
- \(5\frac{1}{2} \gt 2\frac{2}{3}\): In the mixed fractions, first convert into the fraction so that it becomes \(\frac{11}{2} \gt \frac{8}{3}\) which equals to \(5.5 \gt 2.7\).
- \(0.1 \gt 0.01\): In number system, which consists of decimal numbers where the value \(0.1\) is greater than \(0.01\)
- \(1 \gt -2\): Here \(1\) is a positive integer and \(-2\) is a negative integer. We know that the always positive integer is greater than the negative integer. So that \(1\) is greater than \(-2\).
- \(-2 \gt -5\): Consider the negative integers, in which the smallest number has a greater value than the largest number. So we conclude that \(-2\) is greater than \(-5\).
Word Problems on Greater than and Less than Symbols
$$\pmb{\color{red}{Dizzy\ has\ fifteen\ bananas\ and\ Mansi\ has\ nineteen\ bananas.\ Find\ out\ who\ has\ more\ bananas.}}$$
Given, Dizzy has 15 bananas.
Mansi has 19 bananas.
so, 19 is greater than 15, \(19 \gt 15\)
Therefore Mansi has more bananas than Dizzy.
$$\pmb{\color{red}{Dizzy\ sleeps\ for\ forty\ minutes\ and\ Mansi\ sleeps\ for\ fifty\ minutes\ every\ day\ in\ the\ afternoon.}}$$
$$\pmb{\color{red}{Find\ out\ who\ sleeps\ for\ less\ time.}}$$
Given, Dizzy sleeps for 40 minutes
Mansi sleeps for 50 minutes
We know that 40 minutes is less than 50 minutes, so we can write it as \(40 \lt 50\)
As a result, Dizzy sleeps less.
FAQs
How do you use greater than less than?
A greater than or less than symbol is used when a number is bigger or smaller than another number. If the first number is greater than the second number, the greater than symbol (>) is used. The less than symbol (<) is used if the first number is less than the second number.
How do you remember greater than less than?
Imagine the greater than and less than signs as little alligators (or crocodiles), with the numbers on either side representing the amount of fish. The alligator always eats the largest number of fish, so whichever number the mouth is open toward is the largest number.
What does ≥ mean?
greater than or equal to
What does ≤ mean?
a ≤ b means “a is less than or equal to b”
What are the <> symbols called?
<> is called an angle bracket or the chevron. Old French originally meant rafter and was likely derived from the Latin term caper, meaning goat.