Subtraction Facts with Answers - Grade 2 Mathematics - Exercises with solutions

Master subtraction facts with complete answers: basic subtraction, number bonds, counting back, fact families, and subtraction strategies through these 10 detailed exercises with verified solutions.

Solutions: Exercises 1 to 10
1 Basic subtraction
Exercise 1
What is 8 - 3?
Difficulty: Beginner Time: ~2 minutes Skills: Basic Subtraction
Definition:

Subtraction: Taking away one number from another to find the difference

Note: Subtraction finds how many are left when we take away a certain amount.

Step-by-step subtraction method:
  1. Start with the first number (minuend)
  2. Take away the second number (subtrahend)
  3. Count how many are left (difference)
Original Problem
8 - 3
Solution
5
Step 1: Start with 8

We have 8 objects: ⭐⭐⭐⭐⭐⭐⭐⭐

Step 2: Take away 3

Remove 3 objects: ⭐⭐⭐⭐⭐ (⭐⭐⭐)

Step 3: Count what's left

5 objects remain: ⭐⭐⭐⭐⭐

8 - 3 = 5
Final answer:

8 - 3 = 5

Applied rules:

• Subtraction: Take away the subtrahend from the minuend

• Counting: Count how many remain after taking away

• Practice Tip: Use fingers or objects to visualize the subtraction

Related Examples:
  • 6 - 2 = 4 - Practice with smaller numbers
  • 9 - 4 = 5 - Practice with different combinations
  • 7 - 1 = 6 - Practice with single subtraction
Quick Tips:
  • Subtraction is the opposite of addition
  • You can check by adding: 5 + 3 = 8 ✓
  • Always start with the bigger number when subtracting
Frequently Asked Questions:

Q: What if I subtract a bigger number from a smaller one?
A: At this level, we only subtract smaller numbers from bigger numbers.

Q: How do I know which number is bigger?
A: The first number (minuend) should be bigger than the second number (subtrahend).

2 Number bonds
Exercise 2
What is 7 - 4?
Difficulty: Beginner Time: ~2 minutes Skills: Number Bonds, Part-Whole Relationships
Definition:

Number bond: Shows how numbers are related in addition and subtraction

Note: Number bonds help us understand that 7 can be broken into 4 and 3.

Step-by-step number bond method:
  1. Think about what number goes with 4 to make 7
  2. Use the relationship: 4 + ? = 7
  3. Since 4 + 3 = 7, then 7 - 4 = 3
Original Problem
7 - 4
Number Bond
4 + 3 = 7
Solution
3
Step 1: Think about the whole

We want to break apart 7

Step 2: One part is 4

So 7 = 4 + ?

Step 3: Find the missing part

4 + 3 = 7, so 7 - 4 = 3

7 - 4 = 3
Final answer:

7 - 4 = 3

Applied rules:

• Number bond: 7 can be split into 4 and 3

• Relationship: Addition and subtraction are inverse operations

• Practice Tip: Know number bonds to 10 to help with subtraction

Related Examples:
  • 6 = 4 + 2, so 6 - 4 = 2
  • 8 = 5 + 3, so 8 - 5 = 3
  • 9 = 6 + 3, so 9 - 6 = 3
Quick Tips:
  • Number bonds help you see subtraction as "what's missing?"
  • Know your number bonds to 10: 1+9, 2+8, 3+7, 4+6, 5+5
  • Use addition to check: 3 + 4 = 7 ✓
Frequently Asked Questions:

Q: What are number bonds?
A: Number bonds show how a number can be split into parts. For example, 7 can be 4 and 3.

Q: How do number bonds help with subtraction?
A: They help you think "what number added to 4 gives me 7?" which leads to 7 - 4 = 3.

3 Counting back strategy
Exercise 3
What is 9 - 2?
Difficulty: Beginner Time: ~2 minutes Skills: Counting Back Strategy
Definition:

Counting back: Starting from the first number and counting backwards by the second number

Note: This is a mental math strategy for subtraction.

Step-by-step counting back method:
  1. Start at the first number (9)
  2. Count backwards by the second number (2)
  3. Land on the answer (7)
Original Problem
9 - 2
Counting Back
9 → 8 → 7
Solution
7
Step 1: Start at 9

Begin counting: 9

Step 2: Count back 2

9 → 8 → 7 (count 2 steps back)

Step 3: Land on the answer

We land on 7

9 - 2 = 7
Final answer:

9 - 2 = 7

Applied rules:

• Counting back: Move backwards on the number line

• Strategy: This helps with mental math

• Practice Tip: Use fingers or number line to visualize counting back

Related Examples:
  • 8 - 3: Start at 8, count back 3 → 8, 7, 6, 5 → Answer: 5
  • 6 - 1: Start at 6, count back 1 → 6, 5 → Answer: 5
  • 10 - 4: Start at 10, count back 4 → 10, 9, 8, 7, 6 → Answer: 6
Quick Tips:
  • Count back slowly and carefully
  • This strategy works best for small numbers being subtracted
  • Use your fingers to help keep track of counting back
Frequently Asked Questions:

Q: When should I use counting back?
A: Use it for small subtrahends (like subtracting 1, 2, or 3).

Q: What if I count back too far?
A: Start over and count more carefully, or use objects to help.

Solutions: Exercises 4 to 5
4 Fact families
Exercise 4
If 5 + 3 = 8, what is 8 - 3?
Definition:

Fact family: A group of related addition and subtraction facts using the same numbers

Note: The numbers 5, 3, and 8 form a fact family: 5+3=8, 3+5=8, 8-3=5, 8-5=3.

Step-by-step fact family method:
  1. Recognize that 5, 3, and 8 are in the same fact family
  2. If 5 + 3 = 8, then 8 - 3 = 5 (the other addend)
  3. Verify: 5 + 3 = 8 and 8 - 3 = 5
Given Fact
5 + 3 = 8
Related Subtraction
8 - 3 = ?
Solution
5
Step 1: Recognize the fact family

Numbers 5, 3, and 8 are related

Step 2: Use the relationship

If 5 + 3 = 8, then 8 - 3 = 5

Step 3: Verify the answer

5 + 3 = 8 ✓ and 8 - 3 = 5 ✓

8 - 3 = 5
Final answer:

8 - 3 = 5

Applied rules:

• Fact family: Addition and subtraction facts using same numbers

• Inverse operations: Addition and subtraction undo each other

• Practice Tip: Know fact families to build fluency

Related Examples:
  • If 4 + 2 = 6, then 6 - 2 = 4
  • If 7 + 1 = 8, then 8 - 1 = 7
  • If 6 + 3 = 9, then 9 - 3 = 6
Quick Tips:
  • Fact families show the connection between addition and subtraction
  • Knowing one fact helps you know three others
  • Use fact families to check your work
Frequently Asked Questions:

Q: What is a fact family?
A: A group of related addition and subtraction facts using the same three numbers.

Q: How do fact families help with subtraction?
A: If you know an addition fact, you automatically know the related subtraction facts.

5 Missing numbers
Exercise 5
What number makes this sentence true: 6 - ? = 2?
Definition:

Missing number: Finding the unknown value in a subtraction equation

Note: We need to find what number subtracted from 6 gives 2.

Step-by-step missing number method:
  1. Think: "What number taken from 6 leaves 2?"
  2. Use addition: 2 + ? = 6
  3. Since 2 + 4 = 6, then 6 - 4 = 2
Original Problem
6 - ? = 2
Inverse Operation
2 + ? = 6
Solution
4
Step 1: Understand the problem

We need to find what number subtracted from 6 equals 2

Step 2: Use inverse operation

Instead of subtracting, we add: 2 + ? = 6

Step 3: Solve the addition

2 + 4 = 6, so the missing number is 4

Step 4: Verify

6 - 4 = 2 ✓

6 - 4 = 2
Final answer:

The missing number is 4

Applied rules:

• Inverse operations: Addition and subtraction undo each other

• Missing number: Use the inverse operation to find it

• Verification: Always check your answer

• Practice Tip: Turn subtraction problems with missing numbers into addition problems

Related Examples:
  • 8 - ? = 5 → 5 + ? = 8 → ? = 3
  • ? - 3 = 4 → 3 + 4 = ? → ? = 7
  • 9 - ? = 1 → 1 + ? = 9 → ? = 8
Quick Tips:
  • Turn subtraction with missing numbers into addition problems
  • Always check your answer by substituting back
  • Use number lines or objects to visualize the problem
Frequently Asked Questions:

Q: How do I solve problems with missing numbers?
A: Use the inverse operation. If subtracting, add the known numbers to find the missing one.

Q: What if the missing number is the first one?
A: For ? - 3 = 4, add the two known numbers: 3 + 4 = 7, so ? = 7.

Solutions: Exercises 6 to 10
6 Subtraction strategies
Exercise 6
What is 10 - 7?
Definition:

Subtraction strategies: Different ways to solve subtraction problems efficiently

Note: Strategies include counting back, using number bonds, or thinking about how many more to reach the first number.

Step-by-step strategy method:
  1. Think about the relationship: 7 + ? = 10
  2. Use number bonds: 7 and 3 make 10
  3. Therefore: 10 - 7 = 3
Original Problem
10 - 7
Number Bond
7 + 3 = 10
Solution
3
Step 1: Think about what goes with 7 to make 10

7 + ? = 10

Step 2: Use number bond knowledge

7 and 3 are partners that make 10

Step 3: Apply to subtraction

If 7 + 3 = 10, then 10 - 7 = 3

10 - 7 = 3
Final answer:

10 - 7 = 3

Applied rules:

• Number bond strategy: Use known partnerships

• Relationship: Addition and subtraction are connected

• Practice Tip: Master number bonds to 10 for quick subtraction

Related Examples:
  • 10 - 6: 6 + 4 = 10, so 10 - 6 = 4
  • 10 - 9: 9 + 1 = 10, so 10 - 9 = 1
  • 10 - 4: 4 + 6 = 10, so 10 - 4 = 6
Quick Tips:
  • Know your number bonds to 10 fluently
  • Think "how many more" to reach the first number
  • Use counting back for smaller differences
Frequently Asked Questions:

Q: What are good subtraction strategies?
A: Use number bonds, count back, or think about addition facts.

Q: Should I always use the same strategy?
A: Use the strategy that feels easiest for each problem.

7 Word problem
Exercise 7
Sarah had 8 apples. She gave 3 to her friend. How many apples does Sarah have now?
Definition:

Word problem: A mathematical problem presented in a story format

Note: We need to identify the operation needed to solve the problem.

Step-by-step word problem method:
  1. Read the problem carefully
  2. Identify the starting amount (8 apples)
  3. Identify what is taken away (3 apples)
  4. Set up the subtraction: 8 - 3 = ?
  5. Solve: 8 - 3 = 5
Starting Amount
8 apples
Amount Given Away
3 apples
Remaining Amount
5 apples
Step 1: Identify what we know

Sarah started with 8 apples

Step 2: Identify what happened

She gave away 3 apples

Step 3: Set up the subtraction

8 - 3 = ?

Step 4: Solve

8 - 3 = 5

Step 5: Answer the question

Sarah has 5 apples now

Sarah has 5 apples now
Final answer:

Sarah has 5 apples now

Applied rules:

• Problem solving: Identify key information

• Operation identification: Giving away means subtraction

• Contextual answer: Include units in your answer

• Practice Tip: Draw pictures to represent word problems

Related Examples:
  • Tom had 7 pencils, lost 2 → 7 - 2 = 5 pencils left
  • Maria had 9 stickers, used 4 → 9 - 4 = 5 stickers left
  • There were 6 birds, 2 flew away → 6 - 2 = 4 birds left
Quick Tips:
  • Look for keywords like "gave", "took", "used", "left" for subtraction
  • Draw a picture to represent the problem
  • Always answer with a complete sentence
Frequently Asked Questions:

Q: How do I know when to subtract in word problems?
A: Look for words like "gave", "lost", "used", "took", "away", or "left".

Q: What if I'm not sure which operation to use?
A: Think about whether the amount is getting bigger (add) or smaller (subtract).

8 Fact fluency
Exercise 8
What is 15 - 8?
Definition:

Fact fluency: Quick and accurate recall of subtraction facts

Note: Fluency comes from practice and understanding number relationships.

Step-by-step fluency method:
  1. Recognize this as a subtraction fact within 20
  2. Use a strategy: count back from 15 by 8
  3. Or think: 8 + ? = 15
  4. Since 8 + 7 = 15, then 15 - 8 = 7
Original Problem
15 - 8
Number Bond
8 + 7 = 15
Solution
7
Step 1: Recognize the problem type

This is a subtraction fact within 20

Step 2: Use number bond knowledge

Think: what number added to 8 makes 15?

Step 3: Solve

8 + 7 = 15, so 15 - 8 = 7

Step 4: Verify

7 + 8 = 15 ✓

15 - 8 = 7
Final answer:

15 - 8 = 7

Applied rules:

• Fact fluency: Aim for quick recall of basic facts

• Strategies: Use number bonds, counting back, or other methods

• Verification: Check using the inverse operation

• Practice Tip: Regular practice builds fluency over time

Related Examples:
  • 12 - 5 = 7 (because 5 + 7 = 12)
  • 14 - 6 = 8 (because 6 + 8 = 14)
  • 13 - 9 = 4 (because 9 + 4 = 13)
Quick Tips:
  • Practice regularly to build fluency
  • Use flashcards or games for practice
  • Focus on facts that are challenging for you
Frequently Asked Questions:

Q: What is fact fluency?
A: It's the ability to recall math facts quickly and accurately without having to calculate.

Q: How can I improve my fact fluency?
A: Practice regularly, use strategies, and play math games to make it fun.

9 Subtraction patterns
Exercise 9
What pattern do you notice in these problems: 10 - 1 = 9, 10 - 2 = 8, 10 - 3 = 7?
Definition:

Subtraction pattern: A consistent relationship between numbers in subtraction problems

Note: Recognizing patterns helps with mental math and fact fluency.

Step-by-step pattern recognition method:
  1. Look at the minuends (first numbers): all are 10
  2. Look at the subtrahends (second numbers): 1, 2, 3 (increasing by 1)
  3. Look at the differences (answers): 9, 8, 7 (decreasing by 1)
  4. Notice the pattern: as the number subtracted increases by 1, the answer decreases by 1
Pattern Sequence
10-1=9, 10-2=8, 10-3=7
Pattern Rule
Subtract more, get less
Next in Pattern
10-4=6
Step 1: Analyze the minuends

All problems start with 10

Step 2: Analyze the subtrahends

They increase: 1, 2, 3 (each is 1 more than the previous)

Step 3: Analyze the differences

They decrease: 9, 8, 7 (each is 1 less than the previous)

Step 4: Identify the pattern

When we subtract 1 more, we get 1 less as the answer

As the number subtracted increases by 1, the answer decreases by 1
Final answer:

When we subtract 1 more, we get 1 less as the answer. So 10 - 4 = 6, 10 - 5 = 5, etc.

Applied rules:

• Pattern recognition: Look for consistent relationships

• Number sense: Understand how numbers relate to each other

• Generalization: Apply the pattern to predict next answers

• Practice Tip: Look for patterns to make connections between facts

Related Examples:
  • 9 - 1 = 8, 9 - 2 = 7, 9 - 3 = 6 (decreasing by 1 each time)
  • 8 - 1 = 7, 8 - 2 = 6, 8 - 3 = 5 (same pattern)
  • 12 - 2 = 10, 12 - 3 = 9, 12 - 4 = 8 (pattern continues)
Quick Tips:
  • Patterns help you remember multiple facts at once
  • Understanding patterns builds number sense
  • Look for patterns when practicing sets of facts
Frequently Asked Questions:

Q: Why are patterns important in math?
A: Patterns help us predict and understand relationships between numbers.

Q: How do I find patterns in subtraction?
A: Look at how the numbers change in each part of the equation.

10 Mixed practice
Exercise 10
Solve: 13 - 6 + 2
Definition:

Mixed operations: Problems involving more than one operation (subtraction and addition)

Note: When addition and subtraction are in the same problem, we solve from left to right.

Step-by-step mixed operations method:
  1. Solve operations from left to right
  2. First: 13 - 6 = 7
  3. Then: 7 + 2 = 9
Original Problem
13 - 6 + 2
First Operation
13 - 6 = 7
Second Operation
7 + 2 = 9
Final Answer
9
Step 1: Solve the first operation (left to right)

13 - 6 = 7

Step 2: Solve the second operation

Now we have 7 + 2 = 9

Step 3: Final answer

13 - 6 + 2 = 9

13 - 6 + 2 = 9
Final answer:

9

Applied rules:

• Order of operations: For addition and subtraction, go left to right

• Sequential solving: Solve one operation at a time

• Verification: Check each step as you go

• Practice Tip: Work through mixed problems step by step

Related Examples:
  • 15 - 7 + 3: First 15 - 7 = 8, then 8 + 3 = 11
  • 12 + 4 - 5: First 12 + 4 = 16, then 16 - 5 = 11
  • 10 - 3 + 6: First 10 - 3 = 7, then 7 + 6 = 13
Quick Tips:
  • For mixed addition and subtraction, work left to right
  • Solve one operation at a time
  • Keep track of your intermediate results
Frequently Asked Questions:

Q: Which operation do I do first in mixed problems?
A: For addition and subtraction, always work from left to right.

Q: What if there are parentheses?
A: Do operations in parentheses first, then left to right for the rest.

Detailed Summary: Subtraction Facts with Answers
Key Concepts and Definitions:

Subtraction: The mathematical operation of taking away one number (subtrahend) from another number (minuend) to find the difference. It represents "taking away" or "finding how many are left."

Minuend: The first number in a subtraction problem; the number from which another number is subtracted (e.g., in 8 - 3 = 5, 8 is the minuend).

Subtrahend: The second number in a subtraction problem; the number that is subtracted from the minuend (e.g., in 8 - 3 = 5, 3 is the subtrahend).

Difference: The answer to a subtraction problem; the result of subtracting one number from another (e.g., in 8 - 3 = 5, 5 is the difference).

Fact Family: A group of related addition and subtraction facts that use the same three numbers (e.g., 5 + 3 = 8, 3 + 5 = 8, 8 - 3 = 5, 8 - 5 = 3).

Core Rules and Principles:
  1. Inverse Relationship: Addition and subtraction are inverse operations; they undo each other.
  2. Order Matters: Unlike addition, subtraction is not commutative (8 - 3 ≠ 3 - 8).
  3. Positive Results: When subtracting a smaller number from a larger number, the result is positive.
  4. Zero Property: Any number minus itself equals zero (a - a = 0).
  5. Identity Property: Any number minus zero equals itself (a - 0 = a).
Effective Strategies:
  • Counting Back: Start with the minuend and count backward by the subtrahend
  • Number Bonds: Think about what number added to the subtrahend equals the minuend
  • Fact Families: Use known addition facts to solve subtraction problems
  • Using Doubles: Leverage known doubles facts (e.g., knowing 5+5=10 helps with 10-5=5)
Common Mistakes to Avoid:
  • Subtracting in the wrong order (confusing minuend and subtrahend)
  • Not checking answers by adding the difference to the subtrahend
  • Forgetting that subtraction is not commutative
  • Getting confused with missing number problems
Memory Techniques:
  • Practice number bonds to 10 and 20 regularly
  • Use visual aids like number lines, counters, or drawings
  • Create stories or rhymes to remember challenging facts
  • Play math games that reinforce subtraction facts
Checking Your Work:
  • Add the difference to the subtrahend to verify it equals the minuend
  • Use a different strategy to solve the same problem
  • Estimate to see if your answer makes sense
  • Look for patterns in your answers
Progressive Examples:
  • Simple: 5 - 2 = 3 (counting back from 5)
  • Medium: 9 - 4 = 5 (using number bond: 4 + 5 = 9)
  • Advanced: 15 - 8 = 7 (using fact family: 8 + 7 = 15)
  • Complex: 13 - 6 + 2 = 9 (left-to-right operations)

Key Takeaways for Memorization

  • Subtraction is the inverse of addition - use addition facts to solve subtraction
  • Number bonds to 10 are foundational: 1+9, 2+8, 3+7, 4+6, 5+5
  • Always verify your subtraction by adding the answer to the number you subtracted
  • Practice regularly to build automaticity with subtraction facts
  • Understand that order matters in subtraction (unlike addition)
Key Laws, Methods, Rules, and Definitions
Minuend - Subtrahend = Difference
Subtraction Structure
Key definitions:

Subtraction: Taking away one number from another to find the difference

Minuend: The first number in subtraction (the number we start with)

Subtrahend: The second number in subtraction (the number we take away)

Difference: The answer to a subtraction problem

Complete methodology:
  1. Identify the problem: Recognize what is being asked
  2. Choose a strategy: Counting back, number bonds, or fact families
  3. Apply the method: Follow the steps of your chosen strategy
  4. Verify the result: Check by adding the difference to the subtrahend
Tip 1: Use number bonds to 10 to help with subtraction facts quickly.
Tip 2: Count back for small numbers being subtracted (like subtracting 1, 2, or 3).
Tip 3: Addition and subtraction are inverse operations; use one to check the other.
Tip 4: Look for patterns in subtraction facts to help with memorization.
Common errors: Subtracting in wrong order, forgetting to borrow, miscounting.
Fluency building: Practice number bonds, use flashcards, play math games.
Rules to remember:

• Subtraction means to take away or find the difference

• You cannot subtract a larger number from a smaller one at this level

• Addition and subtraction are inverse operations

• For mixed operations, work from left to right

• Always check your work by adding the difference to the subtrahend

Rules and Methods for Subtraction Facts
a - b = c means b + c = a
Inverse Relationship
Strategy 1
Counting Back
Start with the first number and count backward
Strategy 2
Number Bonds
Think about what number goes with the subtrahend to make the minuend
Strategy 3
Fact Families
Use related addition facts to solve subtraction

Key Takeaways

  • Subtraction finds how many are left when we take away
  • Know your number bonds to 10 fluently
  • Addition and subtraction are inverse operations
  • Use multiple strategies to solve subtraction problems
  • Regular practice builds fact fluency

Questions & Answers

Question: I don't understand why 8 - 3 = 5 but 3 - 8 doesn't work. Can you explain the difference?

Answer: Great question! The difference is about the order of numbers in subtraction:

  • In 8 - 3, we start with 8 and take away 3. This works because we have enough to take away.
  • In 3 - 8, we start with 3 and want to take away 8. This doesn't work because we only have 3 things, but we want to take away 8 things.

Think of it like having cookies: If you have 8 cookies and eat 3, you have 5 left. But if you have 3 cookies and try to give away 8, you can't do it!

This is why in subtraction, the first number (minuend) needs to be bigger than or equal to the second number (subtrahend).

Question: My child struggles with subtraction facts like 9 - 4. What strategies can help them memorize these facts?

Answer: Here are effective strategies for learning subtraction facts:

  • Number Bonds: Help your child learn that 9 = 4 + 5, so 9 - 4 = 5
  • Counting Back: For 9 - 4, start at 9 and count back 4: 9, 8, 7, 6, 5
  • Fact Families: If they know 4 + 5 = 9, they know 9 - 4 = 5 and 9 - 5 = 4
  • Visual Aids: Use fingers, counters, or drawings to physically remove items

Practice regularly with games, flashcards, or apps. Focus on a few facts at a time rather than overwhelming them with all facts at once.

Remember, memorization comes after understanding, so make sure they understand what subtraction means first.

Question: How can I check if my subtraction answer is right?

Answer: There are several ways to check your subtraction:

  • Addition Check: Add your answer to the number you subtracted. For example, if 8 - 3 = 5, check: 5 + 3 = 8 ✓
  • Counting Up: From your answer, count up to the original number. For 8 - 3 = 5: 5 + 3 = 8 ✓
  • Visual Check: Draw pictures or use objects to represent the problem
  • Estimation: Make sure your answer makes sense. 8 - 3 should be less than 8.

The addition check is the most reliable method because addition and subtraction are inverse operations.

It's always good to check your work, especially when learning new math concepts!

Math Glossary

Subtraction
The operation of taking away one number from another to find the difference. Symbol: -
Minuend
The first number in a subtraction problem; the number from which another number is subtracted.
Subtrahend
The second number in a subtraction problem; the number that is subtracted from the minuend.
Difference
The answer to a subtraction problem; how much is left after subtraction.
Fact Family
A group of related addition and subtraction facts using the same three numbers, showing the relationship between operations.

Elementary Math Educational Team

Certified Elementary Teachers & Curriculum Specialists

Our team of experienced elementary math teachers and curriculum developers creates research-based, student-friendly subtraction resources. All content is aligned with Common Core State Standards for Mathematics and reviewed by mathematics education experts to ensure accuracy and pedagogical effectiveness for Grade 2 learners.