Greater Than, Less Than, and Equal

For Elementary Students

The Three Comparison Symbols

When we compare numbers, we use special symbols to show which is bigger, smaller, or if they're the same!

Think about it like this: These symbols are like arrows that point to relationships between numbers!

The Symbols

Greater Than >

10 > 4
(10 is greater than 4)

Less Than <

4 < 10
(4 is less than 10)

Equal To =

5 = 5
(5 equals 5)

The Alligator Trick!

Memory trick: Think of the symbol as an alligator's mouth 🐊

The alligator is hungry and always wants to eat the bigger number, so its mouth opens toward the bigger number!

  8   >   3
  ↑       ↑
bigger  smaller

The mouth opens toward 8 (the bigger meal!)

Another way to see it:

  3   <   8
  ↑       ↑
smaller bigger

The mouth opens toward 8!

Both 8 > 3 and 3 < 8 say the same thing — just from different sides!

Using the Symbols

Example 1: Compare 15 and 9

• 15 is bigger, so: 15 > 9 OR 9 < 15

Example 2: Compare 6 and 6

• They're the same, so: 6 = 6

Example 3: Compare 4 and 12

• 4 is smaller, so: 4 < 12 OR 12 > 4

Important Rules

❌ Never use > or < when numbers are equal!

• 7 < 7 is WRONG
• 7 = 7 is RIGHT ✓

✓ The symbols always tell the truth!

• If 5 > 2 is true, then 2 < 5 is also true

Comparing with Pictures

Which has more? 7 apples or 5 apples?

7 apples: 🍎🍎🍎🍎🍎🍎🍎
5 apples: 🍎🍎🍎🍎🍎

Answer: 7 > 5 (7 is greater than 5)

True or False?

Sometimes you need to check if a comparison is true or false.

Example: Is 9 > 12 true or false?

• 9 is NOT bigger than 12
• Answer: False ❌

Example: Is 15 < 20 true or false?

• 15 IS smaller than 20
• Answer: True ✓

For Junior High Students

The Three Symbols

There are three symbols for comparing values:

Key concept: These symbols create mathematical statements that are either true or false.

The Alligator Rule

Think of the symbol as an alligator's mouth — it always opens toward the bigger number because the alligator is hungry and wants the bigger meal!

• 8 > 3 — the mouth opens toward 8
• 3 < 8 — the mouth opens toward 8

Both statements say the same thing, just from different sides.

Tip: The pointed end of < or > always points to the smaller number.

Comparing Single Numbers

Rules:

• If a is larger than b, then a > b
• If a is smaller than b, then a < b
• If a and b are the same, then a = b

Examples:

• 25 > 18 (25 is greater than 18)
• 7 < 100 (7 is less than 100)
• 50 = 50 (50 equals 50)

Important: The symbols < and > mean strictly less or greater. If two values are the same, only = is correct.

Comparing Expressions

You can compare not just single numbers, but entire expressions. Evaluate each side first, then compare.

Example: Is 4 + 5 greater than, less than, or equal to 3 + 7?

Step 1: Evaluate left side

• 4 + 5 = 9

Step 2: Evaluate right side

• 3 + 7 = 10

Step 3: Compare

• 9 < 10

Answer: 4 + 5 < 3 + 7

Another example: 12 − 5 ___ 3 + 4

• Left: 12 − 5 = 7
• Right: 3 + 4 = 7
• Answer: 12 − 5 = 3 + 4 (both equal 7)

True or False Statements

A comparison statement is either true or false.

Examples:

• 15 > 12 → True (15 is indeed greater than 12)
• 6 + 2 = 9 → False (because 6 + 2 = 8, not 9)
• 20 < 20 → False (they are equal, not less than)
• 30 ≥ 30 → True (using ≥ means "greater than or equal to")

Important: When checking true/false:

1. Calculate/simplify both sides
2. Check if the comparison is accurate
3. Answer true or false

Chaining Comparisons

You can chain comparisons to show order:

• 2 < 5 < 9 means "2 is less than 5, and 5 is less than 9"
• 100 > 50 > 10 means "100 is greater than 50, and 50 is greater than 10"

Example: Which statement correctly orders these numbers: 3, 7, 1?

From smallest to largest: 1 < 3 < 7 ✓

From largest to smallest: 7 > 3 > 1 ✓

Additional Comparison Symbols

You may also see:

Examples:

• x ≥ 10 means "x is 10 or larger"
• y ≤ 5 means "y is 5 or smaller"
• a ≠ b means "a and b are different"

Solving Simple Inequalities

Sometimes you need to find what makes a comparison true.

Example: What number makes 5 + ___ > 12 true?

Method:

• Need: 5 + n > 12
• Try 7: 5 + 7 = 12 (not greater, equal) ✗
• Try 8: 5 + 8 = 13 (13 > 12) ✓

Answer: Any number greater than 7 works!

Real-Life Uses

Shopping: "Is $25 > $30?" → No, so I have enough money!

Temperature: "Is 85°F < 90°F?" → Yes, so today is cooler than yesterday.

Scores: "My score (45) = your score (45)" → We tied!

Speed limits: "Is 55 mph > 65 mph speed limit?" → No, I'm within the limit.

Common Mistakes

Mistake 1: Confusing the direction

❌ 15 < 8 (wrong direction!) ✓ 15 > 8

Tip: Remember the alligator eats the bigger number!

Mistake 2: Using wrong symbol for equal values

❌ 10 > 10 or 10 < 10 ✓ 10 = 10

Mistake 3: Not calculating expressions first

❌ Comparing 3 + 4 to 2 + 5 without evaluating ✓ Evaluate first: 7 = 7

Practice