Understanding how to compare numbers using greater than (>), less than (<), and equal to (=) is a fundamental math skill. These symbols help us determine the relationship between two numbers and are essential for solving problems, making decisions, and understanding mathematical concepts. Let’s explore what these comparisons mean, how to use them, and provide examples to help you master this skill.

Definitions

1. Greater Than (>):
   • Used when one number is larger than another.
   • Example: 7 > 5 (7 is greater than 5).
2. Less Than (<):
   • Used when one number is smaller than another.
   • Example: 3 < 9 (3 is less than 9).
3. Equal To (=):
   • Used when two numbers are the same.
   • Example: 4 = 4 (4 is equal to 4).

Greater Than (>)

Definition

The greater than (>) symbol is used when comparing two numbers, and the first number is bigger than the second number. It tells us that one quantity is larger than the other.

Visualizing the Symbol

Imagine the symbol as the open mouth of a hungry alligator. The alligator is always looking for the bigger number to eat! The larger number is always on the side the mouth is open toward.

Example:

• 7 > 5 (7 is greater than 5)
• 20 > 10 (20 is greater than 10)
• 100 > 90 (100 is greater than 90)

How to Use Greater Than (>) in Math

1. Comparing Whole Numbers – Look at two numbers and decide which is larger.
   • Example: 15 > 9 (15 is greater than 9)
2. Using on a Number Line – Numbers increase as you move right, so a greater number will always be farther to the right.
3. Comparing Decimals and Fractions – The same concept applies! A larger decimal or fraction is greater than a smaller one.
   • Example: 0.8 > 0.5 (0.8 is greater than 0.5)

Less Than (<)

The less than symbol (<) is used in math to show that one number is smaller than another. Just like a hungry alligator always opens its mouth toward the bigger meal, the symbol’s open side faces the larger number while the pointed end points to the smaller one.

How to Use the < Symbol

• The smaller number comes before the < symbol.
• The larger number comes after the < symbol.
• Read it as “is less than.”

Example:

• 3 < 8 → “3 is less than 8”
• 10 < 15 → “10 is less than 15”

Equal To (=)

The equal sign (=) is one of the most important symbols in math. It shows that two numbers or expressions have exactly the same value.

How to Use the = Symbol

• The numbers or quantities on both sides must be identical.
• Read it as “is equal to” or “equals.”

Example:

• 5 = 5 → “5 is equal to 5”
• 3 + 2 = 5 → “3 plus 2 equals 5”

Solved exercises:

Question 1: Which number is larger, 3 or 6?

Step-by-Step Solution:

1. Look at the two numbers: 3 and 6.
2. Compare them:
   • 3 is less than 6 because it comes before 6 on the number line.
3. Write the comparison using symbols:
   • 3 < 6 (read as “3 is less than 6”).
4. Conclusion: The larger number is 6.

Answer:
3 < 6, so the bigger number is 6.

Question 2: Which number is larger, 7 or 4?

Step-by-Step Solution:

1. Look at the two numbers: 7 and 4.
2. Compare them:
   • 7 is greater than 4 because it comes after 4 on the number line.
3. Write the comparison using symbols:
   • 7 > 4 (read as “7 is greater than 4”).
4. Conclusion: The larger number is 7.

Answer:
7 > 4, so the bigger number is 7.

Question 3: Which number is larger, 9 or 9?

Step-by-Step Solution:

1. Look at the two numbers: 9 and 9.
2. Compare them:
   • Both numbers are the same, so neither is larger or smaller.
3. Write the comparison using symbols:
   • 9 = 9 (read as “9 is equal to 9”).
4. Conclusion: The two numbers are equal.

Answer:
9 = 9, so the two numbers are equal.

Exercises

This exercise tests your understanding of basic number comparisons using equality (=), less than (<), and greater than (>) symbols. Let’s analyze each statement carefully to determine whether it’s true or false.

Answer true or false to the following exercises:

a) 2=4

b) 3<9

c) 5>8

d) 3<7

e) 9>3

f) 1=6