Solved Exercises on Addition Facts Within 100 in Grade 2

Master addition facts within 100: place value, regrouping, and mental math techniques through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding tens
Exercise 1
Complete the addition: 20 + 30 = ?
Definition:

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

Tens place: The second digit from the right in a number

Addition facts within 100: Addition problems where the sum is 100 or less

Place value method:
  1. Identify the tens: 20 has 2 tens, 30 has 3 tens
  2. Add the tens: 2 tens + 3 tens = 5 tens
  3. Convert to standard form: 5 tens = 50
  4. The answer is 50
Expression
20 + 30
Strategy
Add tens
Answer
50
Step 1: Identify the place values

20 = 2 tens and 0 ones

30 = 3 tens and 0 ones

Step 2: Add the tens

2 tens + 3 tens = 5 tens

Step 3: Write the answer

5 tens = 50

20 + 30 = 50
Final answer:

20 + 30 = 50

Applied rules:

• Place value: Add like place values (tens with tens, ones with ones)

• Regrouping: When adding tens, the result stays in the tens place

• Verification: Always check by counting or using another method

2 Adding tens and ones
Exercise 2
Complete the addition: 24 + 15 = ?
Definition:

Regrouping: Carrying over when the sum in a place value is 10 or more

Partial sums: Adding tens and ones separately

Expression
24 + 15
Strategy
Tens + Ones
Answer
39
Step 1: Break down by place value

24 = 20 + 4 (2 tens and 4 ones)

15 = 10 + 5 (1 ten and 5 ones)

Step 2: Add tens and ones separately

Tens: 20 + 10 = 30

Ones: 4 + 5 = 9

Step 3: Combine the partial sums

30 + 9 = 39

24 + 15 = 39
Final answer:

24 + 15 = 39

Applied rules:

• Place value addition: Add like place values separately

• Partial sums: Add tens and ones separately, then combine

• No regrouping needed: When ones sum is less than 10

3 Regrouping needed
Exercise 3
Complete the addition: 37 + 26 = ?
Definition:

Regrouping: When the sum in the ones place is 10 or more, carry over to the tens place

Expression
37 + 26
Strategy
Regrouping
Answer
63
Step 1: Add the ones

7 + 6 = 13

Since 13 ≥ 10, we regroup: 13 = 1 ten + 3 ones

Step 2: Add the tens

3 tens + 2 tens + 1 carried over ten = 6 tens

Step 3: Combine the results

6 tens + 3 ones = 63

Step 4: Confirm the answer

37 + 26 = 63

37 + 26 = 63
Final answer:

37 + 26 = 63

Applied rules:

• Regrouping rule: When ones sum ≥ 10, carry 1 to the tens place

• Place value: Keep track of tens and ones separately

• Carry over: Move the extra ten(s) to the next higher place value

Addition Facts Within 100 - Core Concepts
ab + cd ≤ 100
Addition Facts Within 100
Tens
20+30=50
Adding tens
Tens
40+50=90
Adding tens
No Regroup
23+14=37
Without regrouping
Regroup
38+25=63
With regrouping
Place Value
24 = 20 + 4
Tens and ones
Regrouping
13 = 1 ten + 3 ones
Breaking down
Partial Sums
24+15 = (20+10)+(4+5)
Separate addition
Carry Over
37+26: 7+6=13 → carry 1
Regrouping
Key definitions:

Addition: Combining two or more numbers to find their total

Sum: The result of adding numbers together

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

Tens place: The second digit from the right in a number

Ones place: The rightmost digit in a number

Regrouping: Carrying over when the sum in a place value is 10 or more

Partial sums: Adding tens and ones separately

Addition facts within 100: Addition problems where the sum is 100 or less

Addition strategies:
  1. Place value method: Add tens and ones separately
  2. Partial sums: Add each place value separately, then combine
  3. Regrouping: Carry over when ones sum is 10 or more
  4. Commutative property: Change order to make it easier
  5. Visualizing: Picture base-10 blocks or number lines
Tip 1: Always add the ones first, then the tens.
Tip 2: Use base-10 blocks or drawings to visualize regrouping.
Tip 3: Remember: if ones sum is 10 or more, you need to regroup.
Tip 4: Always verify by checking your work with another method.
Common errors: Forgetting to carry over when regrouping, mixing up tens and ones, starting addition from left to right instead of right to left.
Memorization tip: Remember that 10 ones equal 1 ten, and 10 tens equal 1 hundred.
Addition properties:

• Commutative Property: a + b = b + a (order doesn't matter)

• Identity Property: a + 0 = a (adding zero doesn't change the number)

• Associative Property: (a + b) + c = a + (b + c) (grouping doesn't matter)

Solution: Exercises 4 to 5
4 Mental math
Exercise 4
Complete the addition: 48 + 35 = ?
Definition:

Mental math: Solving math problems in your head without writing anything down

Expression
48 + 35
Strategy
Regrouping
Answer
83
Step 1: Add the ones

8 + 5 = 13

Since 13 ≥ 10, we regroup: 13 = 1 ten + 3 ones

Step 2: Add the tens

4 tens + 3 tens + 1 carried over ten = 8 tens

Step 3: Combine the results

8 tens + 3 ones = 83

48 + 35 = 83
Final answer:

48 + 35 = 83

Applied rules:

• Regrouping strategy: When ones sum ≥ 10, carry 1 to the tens place

• Place value: Keep track of tens and ones separately

• Mental calculation: Use known facts to solve efficiently

5 Word problem
Exercise 5
Emma has 56 stickers. Her friend gives her 29 more stickers. How many stickers does Emma have now?
Definition:

Word problem: A real-world situation that can be solved using math

Problem
56 + 29 = ?
Solution
Ones: 6+9=15 → carry 1
Answer
85 stickers
Step 1: Identify what we know

Emma starts with 56 stickers and gets 29 more

Step 2: Set up the equation

56 + 29 = ?

Step 3: Add the ones

6 + 9 = 15, so we write 5 and carry 1 ten

Step 4: Add the tens

5 tens + 2 tens + 1 carried ten = 8 tens

Step 5: Combine the results

8 tens + 5 ones = 85

56 + 29 = 85
Final answer:

Emma has 85 stickers now

Applied rules:

• Word problem solving: Identify known information and what you need to find

• Regrouping: When ones sum ≥ 10, carry 1 to the tens place

• Real-world connection: Math helps us solve everyday problems

Addition Facts Within 100 - Complete Summary
ab + cd ≤ 100
Addition Facts Within 100
Key definitions:

Addition: The operation of combining two or more numbers to find their total

Sum: The answer when you add numbers together

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

Tens place: The second digit from the right in a number

Ones place: The rightmost digit in a number

Regrouping: Carrying over when the sum in a place value is 10 or more

Partial sums: Adding tens and ones separately

Addition facts within 100: Addition problems where the sum is 100 or less

Complete methodology:
  1. Analyze the expression: Look at the place values of each number
  2. Choose the method: Place value addition, partial sums, or mental math
  3. Apply the method: Follow the steps of the chosen technique
  4. Check for regrouping: If ones sum ≥ 10, carry over to tens place
  5. Verify the result: By using another method or estimation
Tip 1: Master addition within 10 first - it's the foundation for larger numbers.

Tip 2: Use the "making 10" strategy to help with mental math.

Tip 3: Practice with visual aids like base-10 blocks or number lines.

Tip 4: Always check your work by estimating (round numbers and add).

Common errors: Forgetting to carry over when regrouping, mixing up tens and ones, starting addition from left to right instead of right to left.

Memory tip: Remember that 10 ones equal 1 ten, and 10 tens equal 1 hundred.

Addition strategies within 100:

Adding tens: 20 + 30 = 50 (think 2 tens + 3 tens = 5 tens)

Without regrouping: 23 + 14 = 37 (add tens: 20+10=30, add ones: 3+4=7, combine: 30+7=37)

With regrouping: 38 + 25 = 63 (add ones: 8+5=13→carry 1, add tens: 3+2+1=6, result: 63)

Mental math: Break numbers into tens and ones to make addition easier

Visualization: Addition Within 100
Addition Patterns
Consider the following addition patterns:
20+30=50, 40+50=90, 24+15=39, 37+26=63

Analysis: These patterns show important relationships in addition within 100:

  • Adding tens: Focus on the tens digits and add zeros
  • Adding without regrouping: Add tens and ones separately
  • Adding with regrouping: When ones sum ≥ 10, carry over
  • These patterns help solve problems more efficiently

Questions & Answers

Question: Why do we need to learn addition within 100? Isn't that too big for me?

Answer: Addition within 100 is an important milestone in math! Here's why it's valuable:

  • Real-world applications: Shopping, counting money, measuring
  • Foundation: It prepares you for even bigger numbers
  • Place value understanding: Helps you understand tens and ones
  • Mental math: Builds skills for solving problems quickly

Don't worry - it builds on what you already know! You'll master it step by step.

Question: My child gets confused when regrouping. How can I help them understand carrying over?

Answer: Regrouping can be tricky! Try these approaches:

  • Use manipulatives: Base-10 blocks or bundles of straws to show 10 ones becoming 1 ten
  • Visual representation: Draw circles for ones, lines for tens
  • Concrete language: Say "10 ones become 1 ten" instead of just "carry the 1"
  • Practice with small numbers: Start with problems that definitely need regrouping

The key is helping them understand WHY we regroup, not just HOW!

Question: I sometimes forget if I need to carry a number or not. How can I remember?

Answer: Here's a simple rule to remember:

Check the ones place:

  • If ones add up to 9 or less: NO regrouping needed
  • If ones add up to 10 or more: YES, regroup is needed!

Examples:

  • 23 + 14: 3 + 4 = 7 (less than 10) → no regrouping
  • 37 + 26: 7 + 6 = 13 (more than 10) → regroup needed

Always check the ones first - that's the key!

Question: How can I check if my addition within 100 is correct?

Answer: Here are reliable methods to check addition within 100:

Method 1 - Estimation:

  • Round numbers to the nearest ten and add
  • Example: For 48 + 35, round to 50 + 40 = 90
  • Your actual answer should be close to this estimate

Method 2 - Subtraction:

  • Take your answer and subtract one of the original numbers
  • Should equal the other number
  • Example: 48 + 35 = 83, then 83 - 48 = 35 ✓

Method 3 - Add in reverse order:

  • Change the order of the numbers and add again
  • Should get the same answer

These methods help build confidence and catch errors!

Question: What's the fastest way to get better at addition within 100?

Answer: Here are the most effective strategies for mastering addition within 100:

  1. Master place value: Understand tens and ones thoroughly
  2. Practice basic facts: Strengthen addition within 10 first
  3. Start with no regrouping: Build confidence with easier problems
  4. Progress to regrouping: Once comfortable, tackle carrying over
  5. Use visual aids: Base-10 blocks, number lines, or drawings
  6. Practice daily: Even 10-15 minutes makes a big difference

Remember: quality practice is more important than quantity!