Less Than

We compare numbers to understand which is greater, smaller, or equal. In mathematics, the less than (<) symbol is used to show which number or quantity is smaller than the other. The “<” symbol explains that the value on the left side of the sign is smaller than the value on the right side.

For example, 4 < 5 means that 4 is less than 5. Since it compares two numbers or quantities, the less than symbol is known as a binary operator because it compares two values. The other common comparison symbols are greater than (>) and equal to (=).

In mathematics, we use three main symbols to compare numbers and quantities. By using these symbols, we can easily understand which one is smaller than, greater than, or equal to another.

Let’s learn how to use the less than sign by comparing two numbers: 34 and 18.

To begin, we have to identify the place values of the given numbers. When the given numbers have the same tens digit, move on to the ones digit.

Identify which number is less than the other and use the symbol “<”. When placing the symbol, make sure the pointed end faces the smaller number and the wide-open side of the sign faces the larger number.   

Here, we can compare the tens digit of the given two numbers: 34 and 18. 

As we know, 1 is smaller than 3. 

Hence, 18 is less than 34. It can be written as 18 < 34. 

We can visually understand the less-than symbol by placing the numbers on a number line. A number line provides a clear visual that shows how values relate to each other.

Let us try to understand this with an example. 

x < 4. This inequality states that x can take any value less than 4. On a number line, we can represent this by shading the part to the left of 4, as shown in the image below.

We use the less-than-or-equal-to symbol to define a range with a maximum limit. It helps us identify how big or small a number can be.

Let us try to understand this with an example. 

x ≤ 4. This inequality states that the value is either 4 or less than 4. On a number line, we can represent this by shading the region to the left of 4 and the area where the number is present, as shown in the image below.

We use the not less than symbol (≮ ) when the quantity on the left side is not less than the quantity on the right side. This states that the amount on the left is greater than the quantity on the right.

For example, let us say that Akhtar is x years old and Akshay is y years old. Akshay is older than Akhtar, so Akshay's age is not less than Akhtar's. We can mathematically represent this as y ≮ x.

The phrase “less than” means that the value on the left side is smaller than the value on the right side. It is written using the symbol “<”. When we reverse this symbol, it becomes “>”, which symbolizes the “greater than” symbol in mathematics. “Greater than” means that the value on the left side is larger than the value on the right side and is the opposite of “less than.”

When drawing a less-than sign, the open side faces the larger number, and the pointed tip faces the smaller number. For example, 5 < 6 means five is less than 6, and 6 > 5 means six is greater than 5.

When we use the less than sign, we need to keep in mind some tricks to apply it properly. The signs of less than and greater than look similar, but have different meanings. Here are two tricks to help you remember the less than sign: the L method and the smaller mouth method.

• L method: This trick is based on the first letter of the word, “less,” and the letter L looks similar to the “<” sign. By remembering this trick, we can use the less than sign “<” correctly.

• Closed mouth method: The pointed end of “<” faces the smaller number, and the wide end faces the larger number.

• Arrow method: The symbol can be resembled with the end of an arrow. The arrow is drawn from the larger quantity towards the smaller quantity.

• Alligator Mouth: Assume the symbol as an alligator's mouth, since the alligator always eats bigger objects, the number at the open mouth side will be larger.

• Finger Trick: Extend your index finder and thumb while keeping all the fingers in a fist. The shape formed resembles a less than sign. The number at the open fingers is a larger number, whereas the number at the narrow end in smaller.
   
• Teachers can use visual supports, such as a number line, to help learners see that numbers on the left are less and those on the right are more.
   
• Parents should encourage their children to draw arrows or hops on the number line to show the movement from a smaller number to a larger one, showing that the number on the left is less.
   
• Parents can make use of everyday objects to casually ask their children to identify “Which is less?” and then connect it back to the symbol. We can use objects like items in a shopping basket, or snacks and toys.
   
• Teachers can ask learners to physically move concrete objects to match and compare ideas of 'more' and 'less'.

We often compare numbers, values, measurements and distances in our everyday life. Also, we use the less than symbol and concept to identify the lesser values among others. Here are some real-life applications of less than: 

• Shopping: Less than is used to compare the prices of different items with an estimated budget. It helps to choose and purchase affordable products from the store. For example, if an outfit costs $15, and you have $12, you can’t buy it because $12 < $15.

• Travelling: While driving, you must compare your speed with the maximum speed limit set by the authorities to ensure safety. Example: If you are driving at a speed of 45 km/h, and the speed limit is 50 km/h, then you can see that your driving speed is less than the speed limit, and you are following the traffic rules. 

• Academics: By this “less than” concept, you can evaluate academic performance and identify areas of improvement. For example, if you scored 55 marks in a subject, and the cutoff is 60. This means you scored less than the pass mark, so you need to improve your academic performance.

• Cooking: When you cook, it is important to add ingredients in the required amounts to ensure the food tastes good. Using too much or too little of an ingredient can affect the taste of the food. For example, if you add 1 teaspoon of salt to a recipe and the required amount of salt is 2 teaspoons, this means you used less than the required amount of salt. 

• Calculating Time: Less than can be used to find a duration which is shorter than a certain amount of time. Example; if a runner has to complete one round in 30 minutes, and 25 minutes have already passed, then he/she has to complete the round in less than 5 minutes., to reach the goal before the time limit.