Solved Exercises on Odd and Even Numbers 1 to 100 in Grade 1

Master odd and even numbers 1 to 100: identification, patterns, and number sequences through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Identifying odd and even in 1-100 range
Exercise 1
Circle the even numbers and underline the odd numbers in this list: 45, 68, 73, 82, 91, 96
Definition:

Even numbers: Numbers that can be divided by 2 without a remainder. Odd numbers: Numbers that cannot be divided by 2 without a remainder.

Identification method:
  1. Look at the last digit of each number
  2. If the last digit is 0, 2, 4, 6, or 8, the number is even
  3. If the last digit is 1, 3, 5, 7, or 9, the number is odd
  4. This rule works for all numbers from 1 to 100
Original List
45, 68, 73, 82, 91, 96
Last Digits
5, 8, 3, 2, 1, 6
Classification
O, E, O, E, O, E
Step 1: Examine each number individually

Look at the last digit of each number: 45 (last digit 5), 68 (last digit 8), etc.

Step 2: Apply the last digit rule

45: ends in 5 (odd), 68: ends in 8 (even), 73: ends in 3 (odd), 82: ends in 2 (even), 91: ends in 1 (odd), 96: ends in 6 (even)

Step 3: Classify each number

Even numbers: 68, 82, 96 (end in 2, 6, 8)
Odd numbers: 45, 73, 91 (end in 1, 3, 5)

Even: 68, 82, 96
Odd: 45, 73, 91
Final answer:

Even numbers: 68, 82, 96
Odd numbers: 45, 73, 91

Applied rules:

• Even numbers: Divisible by 2 with no remainder

• Odd numbers: Not divisible by 2 (remainder of 1)

• Last digit rule: Works for all numbers 1-100

2 Counting odd and even numbers in a range
Exercise 2
How many even numbers are there from 1 to 20? How many odd numbers?
Definition:

Counting in ranges: Systematically identifying and counting odd/even numbers within a specific number range

Range
1 to 20
Even Numbers
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Count
10 even, 10 odd
Step 1: List all numbers from 1 to 20

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Step 2: Separate into odd and even

Even: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Odd: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Step 3: Count each group

There are 10 even numbers and 10 odd numbers in the range 1-20

10 even numbers, 10 odd numbers
Final answer:

There are 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) and 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) from 1 to 20.

Applied rules:

• Alternating pattern: Odd and even numbers alternate in sequence

• Equal distribution: In any range of 2n consecutive numbers, there are n even and n odd numbers

• Systematic counting: Organize numbers to avoid missing any

3 Finding patterns in odd and even sequences
Exercise 3
Complete this sequence of odd numbers: 11, 13, 15, 17, ___, ___, ___
Definition:

Odd number sequence: A pattern where each number is 2 more than the previous odd number

Given Pattern
11, 13, 15, 17, ___, ___, ___
Rule
Add 2
Completed
11, 13, 15, 17, 19, 21, 23
Step 1: Identify the pattern

Looking at 11, 13, 15, 17 - each number is 2 more than the previous

Step 2: Confirm these are odd numbers

All shown numbers (11, 13, 15, 17) end in 1, 3, 5, 7 (odd digits)

Step 3: Apply the pattern to find missing numbers

17 + 2 = 19, 19 + 2 = 21, 21 + 2 = 23

Step 4: Verify the results

19, 21, and 23 are all odd numbers (end in 1, 3, 9)

11, 13, 15, 17, 19, 21, 23
Final answer:

The missing numbers are 19, 21, and 23. The complete pattern is: 11, 13, 15, 17, 19, 21, 23

Applied rules:

• Pattern recognition: Identify the consistent operation between consecutive numbers

• Odd number pattern: Odd numbers increase by 2 (1, 3, 5, 7, 9, 11...)

• Consistency: Apply the same operation to find missing values

Visual Infographic: Odd and Even Numbers 1 to 100

Odd and Even Numbers 1 to 100

Patterns and Sequences

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
→
3
→
5
→
7
→
9
→
11
2
→
4
→
6
→
8
→
10
→
12
24
Even (ends in 4)
37
Odd (ends in 7)
58
Even (ends in 8)
63
Odd (ends in 3)
Even Numbers Pattern
In 1-100: 2, 4, 6, 8, 10, 12, 14... Always end in 0, 2, 4, 6, 8.
Odd Numbers Pattern
In 1-100: 1, 3, 5, 7, 9, 11, 13... Always end in 1, 3, 5, 7, 9.
Equal Distribution
From 1 to 100: 50 even numbers and 50 odd numbers.
Alternating Pattern
Odd, even, odd, even... continues throughout 1 to 100.
Rules and methods, laws,...
\(n \div 2 = \text{whole number (even)}\)
Even Number Test
Even
\(n \div 2 = \text{no remainder}\)
Divisible by 2
Odd
\(n \div 2 = \text{remainder 1}\)
Not divisible by 2
Pattern
\(2, 4, 6... / 1, 3, 5...\)
Alternating sequence
Even numbers: Divisible by 2 with no remainder. End in 0, 2, 4, 6, 8.
Odd numbers: Not divisible by 2 (remainder of 1). End in 1, 3, 5, 7, 9.
Key Concepts: Odd and Even Numbers 1 to 100
\(n \mod 2\)
Remainder Check
Key definitions:

Even number: A number that can be divided by 2 with no remainder

Odd number: A number that cannot be divided by 2 without a remainder

Last digit rule: For numbers 1-100, only the last digit determines odd/even

Complete methodology:
  1. Identify the number: Look at the number you want to classify
  2. Check the last digit: Focus only on the units place
  3. Apply the rule: Even digits (0,2,4,6,8) = even, odd digits (1,3,5,7,9) = odd
  4. Verify with division: Divide by 2 and check for remainder
Tip 1: For numbers 1-100, only the last digit matters for odd/even.
Tip 2: Remember the pattern: odd, even, odd, even... repeats.
Tip 3: From 1 to 100, there are exactly 50 even and 50 odd numbers.
Tip 4: Practice with larger numbers to see the pattern holds.
Common errors: Forgetting that only the last digit matters for larger numbers.
Practice tips: Work with number ranges to understand patterns.
Key rules to remember:

• Even numbers: Divisible by 2 (remainder 0)

• Odd numbers: Not divisible by 2 (remainder 1)

• Last digit rule: Works for all numbers 1-100

• Equal distribution: 50 even and 50 odd numbers in 1-100 range

Questions & Answers

Question: Why are there exactly 50 even numbers and 50 odd numbers from 1 to 100?

Answer: This happens because of the alternating pattern! Look at the sequence: 1 (odd), 2 (even), 3 (odd), 4 (even)... This pattern continues throughout. Since there are 100 numbers total, and they alternate evenly, exactly half (50) are even and half (50) are odd.

Think of it like pairs: (1,2), (3,4), (5,6)... up to (99,100). Each pair has one odd and one even number, so with 50 pairs, we have 50 odds and 50 evens.

Question: My child sometimes gets confused with larger numbers. How can I help them understand that only the last digit matters?

Answer: This is a common challenge! Help your child understand by explaining that the tens and hundreds digits don't affect odd/even status. Use examples:

  • 45 vs 85: Both end in 5, so both are odd
  • 24 vs 74: Both end in 4, so both are even
  • 12 vs 112: Both end in 2, so both are even

Emphasize that only the last digit (the "ones place") determines if a number is odd or even, regardless of how large the number is.

Question: What about numbers bigger than 100? Do the same rules apply?

Answer: Yes! The same rules apply to ALL numbers, not just those from 1 to 100. The last digit rule works for any number:

  • Numbers ending in 0, 2, 4, 6, 8 are always even
  • Numbers ending in 1, 3, 5, 7, 9 are always odd
  • This works for 1000, 10,000, or even bigger numbers!

For example: 124 is even (ends in 4), 357 is odd (ends in 7), 1002 is even (ends in 2).

Detailed Summary: Odd and Even Numbers 1 to 100

Definitions

Even Numbers: Numbers that can be divided by 2 with no remainder. In the range 1-100, these numbers end in 0, 2, 4, 6, or 8.

Odd Numbers: Numbers that cannot be divided by 2 without a remainder. In the range 1-100, these numbers end in 1, 3, 5, 7, or 9.

Last Digit Rule: For any number, only the final digit determines if it's odd or even.

Alternating Pattern: In counting order, odd and even numbers alternate consistently.

Core Rules and Laws
  • Even Rule: n ÷ 2 = whole number (no remainder), where n is even
  • Odd Rule: n ÷ 2 = whole number with remainder 1, where n is odd
  • Last Digit Rule: Only the units digit determines odd/even status (works for all numbers)
  • Equal Distribution Rule: In any range of 2n consecutive integers, there are n even and n odd numbers
Step-by-Step Methods
  1. Identify the Number: Look at the number you want to classify
  2. Focus on Last Digit: Only consider the units (rightmost) digit
  3. Apply Last Digit Rule: Even digits (0,2,4,6,8) = even number; odd digits (1,3,5,7,9) = odd number
  4. Verify with Division: Divide by 2 to confirm remainder (0 for even, 1 for odd)
  5. Count in Ranges: Use alternating pattern to count odd/even numbers in a range
Examples (Simple → Advanced)
Simple Example
Number 6: Ends in 6 (even digit) → Even
Number 7: Ends in 7 (odd digit) → Odd
Intermediate Example
Number 45: Ends in 5 (odd digit) → Odd
Number 68: Ends in 8 (even digit) → Even
Advanced Example
Number 93: Ends in 3 (odd digit) → Odd
Number 100: Ends in 0 (even digit) → Even
Tips, Tricks, and Common Pitfalls
  • Tip 1: Remember: only the last digit matters for odd/even classification
  • Tip 2: The pattern alternates: odd, even, odd, even, throughout 1-100
  • Tip 3: From 1 to 100, there are exactly 50 even and 50 odd numbers
  • Pitfall 1: Thinking that larger numbers follow different rules (they don't!)
  • Pitfall 2: Forgetting that 0 is considered an even digit
  • Pitfall 3: Misclassifying numbers when focusing on tens/hundreds instead of units
Key Notes for Memorization
  • Even digits: 0, 2, 4, 6, 8 - any number ending in these is even
  • Odd digits: 1, 3, 5, 7, 9 - any number ending in these is odd
  • From 1 to 100: 50 even numbers and 50 odd numbers
  • The alternating pattern (odd, even, odd, even...) continues throughout
  • Remember: 0 is even (0 ÷ 2 = 0 remainder 0)
  • This rule works for ALL numbers, not just 1-100