Solved Exercises on Comparing Numbers Using Place Value in Grade 1

Master comparing numbers: tens and ones comparison, greater than less than symbols, place value charts through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Compare tens and ones
Exercise 1
Compare 23 and 32 using place value
Which number is greater?
Definition:

Place value: In a 2-digit number, the left digit is the tens place and the right digit is the ones place

Comparison method:
  1. Compare the tens digits first
  2. If tens are equal, compare the ones digits
  3. Use > (greater than), < (less than), or = (equal to)
Number 1
23
Number 2
32
Comparison
23 < 32
Step 1: Identify place values in 23

Tens digit: 2, Ones digit: 3

Tens: 2
Ones: 3
Step 2: Identify place values in 32

Tens digit: 3, Ones digit: 2

Tens: 3
Ones: 2
Step 3: Compare tens digits

2 tens vs 3 tens → 2 < 3, so 23 < 32

23 < 32
Final answer:

32 is greater than 23 because 3 tens is more than 2 tens

Applied rules:

• Place value rule: Tens place has more value than ones place

• Comparison rule: Compare from left to right (highest place value first)

• Symbol usage: 23 < 32 means "23 is less than 32"

2 Equal tens comparison
Exercise 2
Compare 45 and 48 using place value
Which number is greater?
Definition:

Equal tens: When tens digits are the same, compare ones digits

Number 1
45
Number 2
48
Comparison
45 < 48
Step 1: Compare tens digits

Both numbers have 4 tens: 45 has 4 tens, 48 has 4 tens

Tens: 4
Ones: 5
Tens: 4
Ones: 8
Step 2: Since tens are equal, compare ones

5 ones vs 8 ones → 5 < 8

Step 3: Make final comparison

Since tens are equal and 5 < 8, then 45 < 48

45 < 48
Final answer:

48 is greater than 45 because when tens are equal, we compare ones: 8 > 5

Applied rules:

• Equal tens rule: When tens are equal, compare ones digits

• Sequential comparison: Go from highest to lowest place value

• Digit comparison: Compare individual digits at each place value

3 Greater than comparison
Exercise 3
Compare 67 and 59 using place value
Which number is greater?
Definition:

Greater than: The number with higher place value digits is greater

Number 1
67
Number 2
59
Comparison
67 > 59
Step 1: Compare tens digits

6 tens vs 5 tens → 6 > 5

Tens: 6
Ones: 7
Tens: 5
Ones: 9
Step 2: Since 6 > 5, we don't need to compare ones

67 has more tens than 59, so 67 > 59

Step 3: Visual representation

67: 6 tens and 7 ones vs 59: 5 tens and 9 ones

67 > 59
Final answer:

67 is greater than 59 because 6 tens is more than 5 tens

Applied rules:

• Highest place value rule: Compare the highest place value first

• Early termination: If higher place values differ, lower ones don't matter

• Visual comparison: Blocks help visualize quantity differences

Rules and methods, laws,...
23 = 2 tens + 3 ones
Place Value Representation
Rule 1
Compare tens first
Start with highest place value
Rule 2
If tens equal, compare ones
Move to next place value
Rule 3
Use >, <, or =
Symbol comparison
Key definitions:

Place value: Position of a digit determines its value

Tens place: Left digit in 2-digit number (value × 10)

Ones place: Right digit in 2-digit number (value × 1)

Complete methodology:
  1. Identify place values: Separate tens and ones
  2. Compare tens digits: Higher tens = larger number
  3. If tens equal: Compare ones digits
  4. Write comparison: Use appropriate symbol
Tip 1: Remember: 1 ten = 10 ones, so tens are more valuable.
Tip 2: Draw blocks to visualize: 10 blocks = 1 ten block.
Tip 3: Always compare from left to right (highest to lowest).
Tip 4: If tens are different, ones don't matter.
Common errors: Comparing ones first, forgetting place value, mixing up symbols.
Memory aid: "Tens come first, then ones - just like reading left to right!"
Rules to know by heart:

• Place value rule: Tens digit is worth 10 times the ones digit

• Comparison order: Compare from highest place value to lowest

• Symbol meanings: > (greater than), < (less than), = (equal to)

• Early stopping: If higher place values differ, stop comparing

Solution: Exercises 4 to 5
4 Equal numbers comparison
Exercise 4
Compare 34 and 34 using place value
Are they equal?
Definition:

Equal numbers: Same digits in same place values

Number 1
34
Number 2
34
Comparison
34 = 34
Step 1: Compare tens digits

Both numbers have 3 tens: 34 has 3 tens, 34 has 3 tens

Tens: 3
Ones: 4
Tens: 3
Ones: 4
Step 2: Compare ones digits

Both numbers have 4 ones: 4 = 4

Step 3: Since all digits match, numbers are equal

34 = 34 because both have 3 tens and 4 ones

34 = 34
Final answer:

34 equals 34 because they have the same tens and ones digits

Applied rules:

• Equality rule: Numbers are equal if all corresponding digits match

• Complete comparison: Check all place values

• Symbol usage: Use = when numbers are identical

5 Complex comparison
Exercise 5
Compare 71 and 85 using place value
Which number is smaller?
Definition:

Smaller number: Number with lesser value in highest differing place

Number 1
71
Number 2
85
Comparison
71 < 85
Step 1: Compare tens digits

7 tens vs 8 tens → 7 < 8

Tens: 7
Ones: 1
Tens: 8
Ones: 5
Step 2: Since 7 < 8, we conclude 71 < 85

No need to compare ones because tens already determine the relationship

Step 3: Verify with visual representation

71: 7 tens and 1 one vs 85: 8 tens and 5 ones

71 < 85
Final answer:

71 is smaller than 85 because 7 tens is less than 8 tens

Applied rules:

• Priority rule: Higher place values take precedence

• Efficiency rule: Stop comparing once difference is found

• Visual confirmation: Use blocks to verify comparisons

Place Value Comparison Fundamentals
23 = 2×10 + 3×1
Place Value Formula
Key definitions:

Place value: The value of a digit based on its position in a number

Comparison: Determining if one number is greater than, less than, or equal to another

Symbol meanings: > (greater than), < (less than), = (equal to)

Complete methodology:
  1. Separate digits: Identify tens and ones in each number
  2. Compare tens: Look at the tens place first
  3. Compare ones (if needed): Only if tens are equal
  4. Write result: Use appropriate comparison symbol
Tip 1: Always start from the left (highest place value).
Tip 2: If tens are different, ones don't matter for comparison.
Tip 3: Use base-10 blocks to visualize the quantities.
Tip 4: Remember: 10 ones = 1 ten, so tens are more valuable.
Common errors: Comparing ones first, misreading place values, confusing symbols.
Memory aids: "Big fish eats big number" (>) and "smaller number gets the small end".
Essential rules:

• Place value hierarchy: Tens > Ones (left to right)

• Comparison sequence: Highest place value first

• Equality condition: All corresponding digits must match

• Efficiency principle: Stop when first difference is found

Questions & Answers

Question: Why do we compare the tens first and not the ones? It seems backwards.

Answer: Great question! We compare tens first because they represent bigger amounts. Think of it this way:

  • 1 ten = 10 ones, so tens are worth much more than ones
  • If you have 3 tens (30) and I have 2 tens (20), I don't even need to know how many ones I have - my 30 will always be bigger than your 20+
  • It's like comparing bags of candy: if I have 3 full bags and you have 2 full bags, my total will be bigger regardless of how many loose candies are in our bags

We always go from biggest to smallest: tens, then ones, then tenths (in later grades). This ensures we make the right comparison!

Question: My child is confused about the > and < symbols. How can I help them remember which is which?

Answer: There are several helpful memory tricks for the comparison symbols:

  • Alligator method: The "alligator mouth" opens toward the bigger number (the alligator wants to eat the bigger meal!)
  • Arrow method: The symbol points to the smaller number (think of it as an arrow pointing to the little guy)
  • Hand method: Make the symbol with your hands - the wide part is the bigger side

For example: 23 < 32 means "23 is less than 32" - the narrow end points to 23, the smaller number.

Practice with physical objects (blocks, toys) to reinforce the concept before moving to abstract symbols.

Question: What happens when the tens are the same in both numbers? Do I still compare them?

Answer: Excellent observation! When tens are the same, that means both numbers have the same amount of tens, so we move to the next place value - the ones place!

Think of it like this: if you and your friend both have 4 bags of marbles (same tens), but you have 7 marbles in your bags and your friend has 3 marbles, you have more total marbles.

Example: Compare 47 and 43

  • Both have 4 tens (same amount of "big groups")
  • So we compare the ones: 7 ones vs 3 ones
  • Since 7 > 3, then 47 > 43

The rule is: if the highest place values are equal, move to the next place value until you find a difference!