Solved Exercises on Comparing Numbers (>, <, =) in Grade 1

Master number comparison: greater than, less than, and equal to symbols through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Comparing numbers with place value
Exercise 1
Compare these numbers using >, <, or =:
34 ___ 28, 45 ___ 49, 72 ___ 72
Definition:

Number comparison: Using symbols to show the relationship between two numbers

Number comparison method:
  1. Compare the tens digits first
  2. If tens are different, the number with more tens is greater
  3. If tens are the same, compare the ones digits
  4. Use the appropriate symbol: >, <, or =
>
Greater Than
<
Less Than
=
Equal To
Step 1: Compare 34 and 28

34: 3 tens, 4 ones; 28: 2 tens, 8 ones

Since 3 > 2, then 34 > 28

Step 2: Compare 45 and 49

45: 4 tens, 5 ones; 49: 4 tens, 9 ones

Same tens, but 5 < 9, so 45 < 49

Step 3: Compare 72 and 72

Both numbers are identical: 72 = 72

34 > 28
45 < 49
72 = 72
Final answer:

34 > 28, 45 < 49, 72 = 72

Applied rules:

• Place value priority: Compare tens first, then ones

• Symbol direction: Point toward the smaller number

• Equality: Same value means equal

2 Using the number line concept
Exercise 2
Compare these numbers using >, <, or =:
63 ___ 57, 81 ___ 85, 94 ___ 94
Definition:

Number line concept: On a number line, numbers increase from left to right

57
63
81
85
Step 1: Compare 63 and 57

63 comes after 57 on the number line, so 63 > 57

Step 2: Compare 81 and 85

81 comes before 85 on the number line, so 81 < 85

Step 3: Compare 94 and 94

Same number means 94 = 94

63 > 57
81 < 85
94 = 94
Final answer:

63 > 57, 81 < 85, 94 = 94

Applied rules:

• Number line principle: Greater numbers appear to the right

• Symbol memory: Think of the symbol as a hungry mouth facing the bigger number

• Equality: Identical numbers are equal

3 Comparing with zero in ones place
Exercise 3
Compare these numbers using >, <, or =:
40 ___ 39, 56 ___ 60, 70 ___ 70
Definition:

Zero as placeholder: Zero in the ones place doesn't mean the number is smaller overall

Numbers Tens Comparison Ones Comparison Result
40 vs 39 4 > 3 Not needed 40 > 39
56 vs 60 5 < 6 Not needed 56 < 60
70 vs 70 7 = 7 0 = 0 70 = 70
Step 1: Compare 40 and 39

40: 4 tens, 0 ones; 39: 3 tens, 9 ones

Since 4 > 3, then 40 > 39 (even though 0 < 9)

Step 2: Compare 56 and 60

56: 5 tens, 6 ones; 60: 6 tens, 0 ones

Since 5 < 6, then 56 < 60 (even though 6 > 0)

Step 3: Compare 70 and 70

Both numbers are identical: 70 = 70

40 > 39
56 < 60
70 = 70
Final answer:

40 > 39, 56 < 60, 70 = 70

Applied rules:

• Tens priority: Tens place is more significant than ones place

• Zero placeholder: Zero in ones place still represents a value

• Systematic comparison: Always compare tens first

Comparison Symbols and Rules
A > B, A < B, A = B
Comparison Relations
Greater Than
>
A is larger than B
Less Than
<
A is smaller than B
Equal To
=
A has same value as B
Key definitions:

Greater than (>): The number on the left is larger than the number on the right

Less than (<): The number on the left is smaller than the number on the right

Equal (=): Both numbers have the same value

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

Comparison methodology:
  1. Compare tens digits first: The number with more tens is greater
  2. If tens are equal: Compare the ones digits
  3. Select the symbol: Use >, <, or = based on the comparison
  4. Verify: Double-check the comparison makes sense
Tip 1: Remember: the "hungry mouth" always faces the bigger number.
Tip 2: Compare tens first, then ones if needed.
Tip 3: Use number lines to visualize comparisons.
Tip 4: Practice with concrete objects to build intuition.
Comparison priority: Tens place > Ones place in determining magnitude.
Memory aid: "Greater than" opens toward the larger number.
Comparison rules to remember:

• Always compare tens place first

• If tens are equal, compare ones place

  • Greater than: > (opens toward larger number)
  • Less than: < (points toward smaller number)
  • Equal: = (same value)
    • Comparison Symbols Guide
    📊
    Greater Than (>)
    Opens toward the larger number
    5 > 3
    Less Than (<)
    Points toward the smaller number
    3 < 5
    Equal (=)
    Both sides have the same value
    4 = 4
    Place Value
    Compare tens first, then ones
    27 vs 31 → 2 < 3 → 27 < 31
    Solution: Exercises 4 to 5
    4 Mixed comparisons with different place values
    Exercise 4
    Compare these numbers using >, <, or =:
    87 ___ 78, 95 ___ 95, 63 ___ 69
    Definition:

    Mixed comparisons: Comparing numbers where place values affect the outcome differently

    Numbers Tens Ones Comparison
    87 vs 78 8 > 7 7 > 8 87 > 78
    95 vs 95 9 = 9 5 = 5 95 = 95
    63 vs 69 6 = 6 3 < 9 63 < 69
    Step 1: Compare 87 and 78

    87: 8 tens, 7 ones; 78: 7 tens, 8 ones

    Tens: 8 > 7, so 87 > 78 (ones don't matter)

    Step 2: Compare 95 and 95

    Both numbers are identical: 95 = 95

    Step 3: Compare 63 and 69

    63: 6 tens, 3 ones; 69: 6 tens, 9 ones

    Tens equal, ones: 3 < 9, so 63 < 69

    87 > 78
    95 = 95
    63 < 69
    Final answer:

    87 > 78, 95 = 95, 63 < 69

    Applied rules:

    • Priority rule: Tens place always determines the result when different

    • Equality rule: Both numbers must be identical

    • Ones rule: Only compare ones when tens are equal

    5 Ordering numbers
    Exercise 5
    Put these numbers in order from least to greatest:
    47, 39, 52, 35, 47
    Definition:

    Ordering numbers: Arranging numbers from smallest to largest (or vice versa) using comparison skills

    Number Tens Ones Position
    35 3 5 1st
    39 3 9 2nd
    47 4 7 3rd
    47 4 7 4th
    52 5 2 5th
    Step 1: Group by tens

    Numbers with 3 tens: 35, 39

    Numbers with 4 tens: 47, 47

    Numbers with 5 tens: 52

    Step 2: Order within each group

    3 tens group: 35 < 39

    4 tens group: 47 = 47

    Step 3: Combine groups

    From least to greatest: 35, 39, 47, 47, 52

    35, 39, 47, 47, 52
    Final answer:

    35, 39, 47, 47, 52

    Applied rules:

    • Grouping method: Organize by tens place first

    • Within-group ordering: Compare ones when tens are equal

    • Sequential arrangement: Place in ascending order

    Comprehensive Summary: Comparing Numbers (>, <, =)
    A > B, A < B, A = B
    Comparison Relations
    Key definitions:

    Greater than (>): The number on the left has a higher value than the number on the right

    Less than (<): The number on the left has a lower value than the number on the right

    Equal (=): Both numbers represent the same quantity

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

    Comparison: Determining the relationship between two or more numbers

    Complete comparison methodology:
    1. Identify place values: Determine tens and ones for each number
    2. Compare tens first: The number with more tens is greater
    3. Compare ones if needed: If tens are equal, compare ones digits
    4. Select the symbol: Use >, <, or = appropriately
    5. Verify the result: Double-check the comparison makes sense
    Tip 1: Think of the symbol as a hungry mouth that always wants to eat the bigger number.
    Tip 2: Always compare the tens place first - it's more significant than ones.
    Tip 3: Use number lines to visualize where numbers fall in relation to each other.
    Tip 4: Practice with real objects to build concrete understanding of "more" and "less".
    Comparison hierarchy: Tens place > Ones place in determining magnitude.
    Symbol memory: The wide end always faces the larger number.
    Essential comparison rules:

    • Tens priority: Compare tens digits first in two-digit numbers

    • Ones tiebreaker: Only compare ones digits when tens are equal

    • Greater than: Symbol (>) opens toward the larger number

    • Less than: Symbol (<) points toward the smaller number

    • Equality: Use (=) when both numbers have identical value

    Comparison Strategy Guide
    📊
    Place Value First
    Always compare tens before ones
    47 vs 52 → 4 < 5 → 47 < 52
    Greater Than
    Wide opening faces the larger number
    7 > 5
    Less Than
    Pointing toward the smaller number
    3 < 8
    Equal To
    Same value on both sides
    6 = 6
    Key takeaways:

    • Understanding place value is crucial for accurate comparisons

    • The comparison process is systematic: tens first, then ones

    • Symbols have specific meanings that must be understood precisely

    • Practice with various number combinations builds confidence

    Questions & Answers

    Question: Why does 40 come after 39? I thought 4 is smaller than 3!

    Answer: Great question! You're comparing just the digits, but we need to compare the whole numbers:

    • 40 means: 4 tens and 0 ones (40 total)
    • 39 means: 3 tens and 9 ones (39 total)
    • Comparison: 40 is greater than 39 because 4 tens (40) is more than 3 tens (30)

    Think of it like having 4 bags of 10 candies vs 3 bags of 10 candies plus 9 loose candies. The 4 bags have more!

    Remember: Tens place is more important than ones place in determining the size of a number!

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

    Answer: Here are several memory aids that work well:

    • Hungry mouth: The symbol looks like a mouth that always wants to eat the bigger number
    • Pointing finger: The narrow part points to the smaller number
    • Letter L: Less than symbol (<) looks like the letter L
    • Practice with pictures: Draw dots or objects to represent numbers

    Example: 5 > 3 because the "mouth" opens toward 5 (the bigger number).

    Tip: Have your child physically make the symbols with their arms to reinforce the concept!

    Question: When comparing 23 and 32, why is 32 bigger? Doesn't 2 come first in the alphabet?

    Answer: That's a clever thought! But numbers work differently than letters:

    • 23 means: 2 tens and 3 ones (20 + 3 = 23)
    • 32 means: 3 tens and 2 ones (30 + 2 = 32)
    • Comparison: 3 tens (30) is more than 2 tens (20), so 32 > 23

    Think of it like having 3 bags of 10 candies vs 2 bags of 10 candies. The 3 bags definitely have more!

    The first digit (leftmost) tells us how many tens we have, which is more important than the ones!

    Example: 23 = 20 + 3 = 23, 32 = 30 + 2 = 32, and 32 is greater than 23!

    Question: How can I help my child understand that comparing numbers is important in real life?

    Answer: Connect number comparison to everyday situations:

    • Shopping: Comparing prices ("This costs $5, that costs $3, so $3 is less expensive")
    • Ages: "I am 30 years old, you are 6 years old. I am older than you"
    • Toys: Comparing quantities ("You have 8 toys, I have 5 toys. You have more")
    • Time: "Recess is in 10 minutes, lunch is in 20 minutes. Recess comes first"

    Practice during daily activities: comparing heights, weights, amounts of food, number of pages in books, etc.

    Tip: Make it a game - "Find something in the room that has more than 5 items!"

    Question: What's the connection between comparing numbers and future math concepts?

    Answer: Number comparison is foundational for many advanced concepts:

    • Ordering: Arranging numbers from least to greatest
    • Estimation: Understanding which numbers are closer to a target
    • Operations: Understanding that addition makes numbers larger, subtraction makes them smaller
    • Algebra: Solving inequalities (x > 5, y < 10)
    • Data analysis: Interpreting graphs and charts

    Students who master number comparison develop stronger number sense, which supports all future mathematical learning.

    Example: Understanding that 45 > 38 helps with problems like "What number is 7 more than 38?"

    This skill creates a strong foundation for mathematical reasoning!