Comparing Numbers to 100: Detailed Exercises and Solutions

Master comparing numbers up to 100: greater than (>), less than (<), equal to (=) with these 5 detailed exercises including methods, rules, and visual aids.

Solution: Exercises 1 to 3
1 Comparing tens and ones
Exercise 1
Compare 47 and 39 using >, <, or =
Which number is greater?
Definition:

Comparing numbers: Determine which number is larger, smaller, or if they are equal by comparing digits from left to right (highest place value first)

Comparison method:
  1. Compare the tens digits first
  2. If tens are equal, compare the ones digits
  3. Use comparison symbols: > (greater than), < (less than), = (equal to)
Number 47
Tens: 4
Ones: 7
Number 39
Tens: 3
Ones: 9
Step 1: Compare tens digits

47 has 4 tens, 39 has 3 tens

Since 4 > 3, then 47 > 39

Step 2: Confirm with number line visualization
39
39
47
47
Step 3: Write the comparison

47 comes after 39 on the number line, so 47 is greater

47 > 39
Final answer:

47 > 39

Applied rules:

• Place Value Rule: Compare digits starting from the highest place value

• Number Line Rule: Numbers to the right are greater than numbers to the left

• Symbol Rule: > means "greater than", < means "less than"

2 Equal numbers
Exercise 2
Compare 64 and 64 using >, <, or =
Are these numbers equal?
Definition:

Equal numbers: Two numbers that have the same value in all place positions

Number 64
Tens: 6
Ones: 4
Number 64
Tens: 6
Ones: 4
Step 1: Compare tens digits

Both numbers have 6 tens

Step 2: Compare ones digits

Both numbers have 4 ones

Step 3: Conclusion

Since all digits match, the numbers are equal

64 = 64
Final answer:

64 = 64

Applied rules:

• Equality Rule: If all corresponding digits are the same, the numbers are equal

• Reflexive Property: Any number equals itself

• Comparison Logic: Only proceed to next place value if previous digits are equal

3 Same tens, different ones
Exercise 3
Compare 58 and 53 using >, <, or =
Which number is greater?
Definition:

Same tens comparison: When tens digits are equal, compare ones digits to determine which number is greater

Number 58
Tens: 5
Ones: 8
Number 53
Tens: 5
Ones: 3
Step 1: Compare tens digits

Both numbers have 5 tens

Since tens are equal, we move to ones

Step 2: Compare ones digits

58 has 8 ones, 53 has 3 ones

Since 8 > 3, then 58 > 53

Step 3: Number line confirmation
53
53
58
58
58 > 53
Final answer:

58 > 53

Applied rules:

• Tens-First Rule: Always compare tens before ones when comparing two-digit numbers

• Ones-Fallback Rule: When tens are equal, ones determine the greater number

• Sequential Comparison: Move from left to right (highest to lowest place value)

Rules and methods, laws,...
47 > 39
Greater Than
Greater Than
>
Point opens toward larger number
Less Than
<
Point opens toward smaller number
Equal To
=
Numbers have same value
Key definitions:

Place Value: The value of a digit based on its position (tens, ones)

Comparison: Determining the relationship between two numbers

Number Line: Visual representation showing numbers in order

Complete methodology:
  1. Identify place values: Separate tens and ones digits
  2. Compare from left: Start with tens, then ones if needed
  3. Select symbol: Use >, <, or = based on comparison
  4. Verify: Check using number line or counting
Tip 1: Remember: the "mouth" of the symbol always opens toward the larger number.
Tip 2: When comparing, always start with the largest place value (tens in two-digit numbers).
Tip 3: If tens are equal, only then compare the ones digits.
Tip 4: Use number lines to visualize comparisons when in doubt.
Common errors: Forgetting to compare place values in order, confusing the direction of symbols, misreading numbers.
Memory aid: Think of the symbol as an alligator's mouth that wants to eat the bigger number.
Rules to know by heart:

• Place Value Order: Tens > Ones

• Comparison Sequence: Left to right (highest to lowest place value)

• Symbol Direction: > means "greater than", < means "less than"

• Equality Check: Numbers are equal only if all corresponding digits match

Solution: Exercises 4 to 5
4 Comparing with zero ones
Exercise 4
Compare 70 and 68 using >, <, or =
Which number is greater?
Definition:

Numbers ending in zero: Numbers like 70 have 0 in the ones place, which affects comparison

Number 70
Tens: 7
Ones: 0
Number 68
Tens: 6
Ones: 8
Step 1: Compare tens digits

70 has 7 tens, 68 has 6 tens

Since 7 > 6, then 70 > 68

Step 2: Note about ones digits

Even though 70 has 0 ones and 68 has 8 ones, the tens comparison determines the outcome

Step 3: Number line confirmation
68
68
70
70
70 > 68
Final answer:

70 > 68

Applied rules:

• Place Value Hierarchy: Tens place has higher value than ones place

• Zero in Ones: Zero in ones place doesn't make the number smaller than one with higher tens

• Early Determination: Stop comparing once you find unequal digits

5 Comparing consecutive numbers
Exercise 5
Compare 92 and 95 using >, <, or =
Which number is greater?
Definition:

Consecutive numbers: Numbers that follow each other in counting order, differ by 1 in the ones place

Number 92
Tens: 9
Ones: 2
Number 95
Tens: 9
Ones: 5
Step 1: Compare tens digits

Both numbers have 9 tens

Since tens are equal, we move to ones

Step 2: Compare ones digits

92 has 2 ones, 95 has 5 ones

Since 2 < 5, then 92 < 95

Step 3: Counting verification

Counting sequence: 92, 93, 94, 95

Since 92 comes before 95, 92 < 95

92 < 95
Final answer:

92 < 95

Applied rules:

• Sequential Order: Numbers increase as we count forward

• Same Tens Rule: When tens are equal, ones determine the relationship

• Counting Verification: Use counting sequence to confirm comparisons

Detailed Guide: Comparison Methods and Techniques
47 > 39 because 4 > 3 in tens place
Comparison Process
Key definitions:

Place Value: The value of a digit depends on its position (tens, ones)

Comparison Symbols: > (greater than), < (less than), = (equal to)

Digit Position: Leftmost digits have higher place value than rightmost

Complete methodology:
  1. Separate digits: Identify tens and ones in each number
  2. Start left: Compare digits in the highest place value position
  3. Move right: Only compare lower place values if higher ones are equal
  4. Apply symbol: Use appropriate comparison symbol
  5. Verify: Check with number line or counting
Tip 1: Always compare place values from left to right (highest to lowest).
Tip 2: The "alligator mouth" always opens toward the larger number.
Tip 3: When tens are equal, focus only on ones digits.
Tip 4: Use a number line to visualize if you're unsure about the relationship.
Common errors: Comparing ones before tens, confusing symbol directions, misreading numbers with zeros.
Exam preparation: Practice with various combinations of tens and ones, memorize comparison symbols, use number lines.
Rules to know by heart:

• Place Value Priority: Tens > Ones in importance for comparison

• Left-to-Right Rule: Compare from highest to lowest place value

• Symbol Direction: > means "greater than", < means "less than"

• Equality Condition: All corresponding digits must match for equality

• Early Exit: Stop comparing once you find unequal digits

Questions & Answers

Question: I always get confused about which way the greater than and less than symbols go. How can I remember which is which?

Answer: Great question! Here are several memory aids:

  • Alligator Method: Imagine the symbol as an alligator's mouth that always wants to eat the bigger number: 5 > 3 (mouth opens toward 5) and 2 < 7 (mouth opens toward 7)
  • Arrow Method: The symbol points to the smaller number: 8 > 3 (point goes to 3) and 1 < 9 (point goes to 1)
  • Big Side Small Side: The big open side faces the larger number, the small pointed side faces the smaller number

Practice with this: In 45 > 32, the open side (>) faces 45 because 45 is larger than 32.

Visual trick: Draw the symbols and always write them with the wider opening facing the larger number.

Question: Why do we compare the tens first and then the ones? Why can't we compare the ones first?

Answer: We compare from left to right (highest to lowest place value) because of the way our number system works:

  • Place Value System: In 47, the 4 represents 40 (4 tens), while the 7 represents only 7 ones. So 40 is much more significant than 7.
  • Efficiency: If the tens are different, we don't need to look at the ones. For example, 63 vs 49: since 6 > 4 in tens, we know 63 > 49 without even checking the ones.
  • Logical Order: We always organize things from most important to least important, just like alphabetical order starts with the first letter.

Think of it like comparing heights: if person A is taller in their feet measurement, they're likely taller overall, regardless of inches.

Example: 71 vs 69 - Since 7 > 6 in tens, 71 > 69. The ones (1 vs 9) don't change this because 70 is already much larger than 60.

Question: What happens when I have numbers like 50 and 48? Doesn't the 0 in 50 make it smaller than 48?

Answer: This is a common misconception! The 0 in 50 doesn't make it smaller than 48. Let me explain why:

  • Place Value: In 50, the 5 represents 5 tens (which is 50), and the 0 represents 0 ones. So 50 = 50 + 0 = 50
  • Comparison: 50 has 5 tens, while 48 has 4 tens. Since 5 > 4, then 50 > 48
  • Value Understanding: The 0 in ones place doesn't subtract from the value; it just means there are no extra ones beyond the tens

Think of it this way: 50 is five groups of ten, while 48 is four groups of ten plus eight more. Five groups of ten (50) is definitely more than four groups of ten plus eight (48).

The key rule: Place value matters more than individual digit values. Tens place has higher value than ones place, so 5 tens (50) beats 4 tens (40) even with 0 ones.