Solved Exercises on Relationship Between Addition and Subtraction in Grade 1

Master the relationship between addition and subtraction: inverse operations, fact families, and problem solving through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Inverse Operations
Exercise 1
Show that 5 + 3 = 8 and 8 - 3 = 5 are related
Definition:

Inverse Operations: Addition and subtraction are opposite operations

Related Facts: Facts that use the same numbers in different ways

Fact Family: A set of related addition and subtraction facts

Inverse Relationship Method:
  1. Start with an addition fact (5 + 3 = 8)
  2. Use the same numbers to make a subtraction fact
  3. Notice that addition and subtraction undo each other
  4. Write the complete fact family
Addition
+
More
=
Total
Start
-
Take Away
=
Left
Step 1: Start with an addition fact

5 + 3 = 8

Step 2: Use the same numbers for subtraction

8 - 3 = 5

Step 3: Notice the relationship

Addition puts numbers together, subtraction takes them apart

Step 4: Verify the relationship

5 + 3 = 8 and 8 - 3 = 5 ✓

5 + 3 = 8
8 - 3 = 5
Final answer:

These facts are related because they use the same numbers and are inverse operations

Applied rules:

• Inverse operations: Addition and subtraction undo each other

• Same numbers: Related facts use the same three numbers

• Fact family: Four related facts using the same numbers

2 Fact Families
Exercise 2
Show the fact family for 4, 6, and 10
Definition:

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

Three Numbers: Two addends and one sum that form four related facts

4 + 6 = 10
→
6 + 4 = 10
10 - 4 = 6
→
10 - 6 = 4
Step 1: Identify the three numbers

We have 4, 6, and 10

Step 2: Write the addition facts

4 + 6 = 10 and 6 + 4 = 10

Step 3: Write the subtraction facts

10 - 4 = 6 and 10 - 6 = 4

Step 4: Verify the relationships

All facts use the same three numbers and are related

4 + 6 = 10
6 + 4 = 10
10 - 4 = 6
10 - 6 = 4
Final answer:

The fact family for 4, 6, and 10 includes 4 related facts

Applied rules:

• Fact family: Contains 2 addition and 2 subtraction facts

• Commutative property: Order doesn't matter in addition

• Inverse relationship: Addition and subtraction are opposite operations

3 Using Addition to Check Subtraction
Exercise 3
Solve 9 - 4 = ? and check your answer using addition
Definition:

Verification: Using the inverse operation to check your answer

Check Method: Adding the result to the subtracted number to get the original

Step 1: Solve the subtraction

9 - 4 = 5

Step 2: Check using addition

If 9 - 4 = 5, then 5 + 4 should equal 9

Step 3: Perform the check

5 + 4 = 9 ✓

Step 4: Confirm the answer

Since 5 + 4 = 9, our subtraction was correct

9 - 4 = 5
Check: 5 + 4 = 9 ✓
Final answer:

9 - 4 = 5, verified by checking with addition

Applied rules:

• Verification: Use inverse operation to check answers

• Relationship: Subtraction and addition are connected

• Confidence: Checking helps ensure accuracy

Rules and methods, laws,...
\(5 + 3 = 8\)
Inverse Operations
Inverse
Operations
Addition and subtraction undo each other
Fact
Family
Four related facts using same numbers
Verification
Method
Add result to subtracted number
Key definitions:

Inverse Operations: Operations that undo each other (addition and subtraction)

Fact Family: A set of related addition and subtraction facts using the same numbers

Verification: Using the inverse operation to check an answer

Complete methodology:
  1. Identify numbers: Recognize the numbers involved in the operation
  2. Apply operation: Perform addition or subtraction
  3. Recognize relationship: Understand how the operations are connected
  4. Verify answer: Use the inverse operation to check
  5. Record facts: Write the complete fact family
Tip 1: Remember: addition and subtraction are opposite operations.
Tip 2: Always check your subtraction by adding back.
Tip 3: Practice fact families to see the relationship clearly.
Tip 4: Think of addition as "putting together" and subtraction as "taking apart."
Common errors: Forgetting to check answers, mixing up operations.
Key concepts: Understanding that operations are connected and can verify each other.
Rules to remember:

• Inverse relationship: Addition and subtraction are opposite operations

• Verification: Always check subtraction by adding back

• Fact families: Four related facts using the same three numbers

• Connection: Understanding this relationship helps solve problems

Fact Family Examples
3+5=8
5+3=8
8-3=5
8-5=3
2+7=9
7+2=9
9-2=7
9-7=2
4+6=10
6+4=10
10-4=6
10-6=4
Solution: Exercises 4 to 5
4 Word Problems with Relationships
Exercise 4
Sarah has 7 apples. She gets 3 more apples. Then she gives away 3 apples. How many apples does Sarah have now? Show the relationship.
Definition:

Word Problem: A math question written in story form

Real-world Application: Connecting math to everyday situations

Step 1: Identify the operations

First: 7 + 3 (gets more)

Then: 10 - 3 (gives away)

Step 2: Solve the first operation

7 + 3 = 10

Step 3: Solve the second operation

10 - 3 = 7

Step 4: Notice the relationship

Adding 3 and then subtracting 3 brings us back to 7

7 + 3 = 10
10 - 3 = 7
Final answer:

Sarah has 7 apples now (same as she started with)

Applied rules:

• Story understanding: Find the important numbers and operations

• Operation identification: "Gets more" means addition, "gives away" means subtraction

• Relationship demonstration: Addition and subtraction undo each other

5 Mixed Problems
Exercise 5
Solve: 12 - 5 = ? and verify using addition. Also show the complete fact family.
Definition:

Mixed Problems: Different operations to practice the relationship

Complete Family: Showing all four related facts

Step 1: Solve the subtraction

12 - 5 = 7

Step 2: Verify using addition

Check: 7 + 5 = 12 ✓

Step 3: Write the complete fact family

7 + 5 = 12

5 + 7 = 12

12 - 7 = 5

12 - 5 = 7

Step 4: Notice the pattern

All facts use the same three numbers (7, 5, 12)

12 - 5 = 7
Fact Family: 7+5=12, 5+7=12, 12-7=5, 12-5=7
Final answer:

12 - 5 = 7, verified by addition, with complete fact family shown

Applied rules:

• Verification: Always check subtraction with addition

• Fact families: Show all four related facts

• Consistent numbers: All facts in family use same three numbers

Relationship Between Addition and Subtraction - Complete Guide
\(5 + 3 = 8\)
Inverse Operations
Key definitions:

Inverse Operations: Operations that undo each other (addition and subtraction)

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

Verification: Using the inverse operation to check an answer

Complete methodology:
  1. Number Recognition: Identify the numbers involved in the operation
  2. Operation Selection: Choose addition or subtraction based on the problem
  3. Sequential Execution: Perform the operation step by step
  4. Relationship Recognition: Understand how addition and subtraction are connected
  5. Result Verification: Check the answer using the inverse operation
  6. Fact Recording: Write the complete fact family
Tip 1: Think of addition as "building up" and subtraction as "breaking down."
Tip 2: Practice with fact families to see the relationship clearly.
Tip 3: Always check your subtraction by adding back to verify.
Tip 4: Use visual aids like number lines to see the inverse relationship.
Visual benefits: Concrete objects and visual aids make the relationship clear.
Memory aids: Understanding relationships helps remember both operations.
Essential formulas:

• Inverse relationship: If a + b = c, then c - b = a

• Fact family: Contains 2 addition and 2 subtraction facts

• Verification: Result + Subtracted = Original number

• Commutative property: a + b = b + a

Addition and Subtraction Relationship Workflow

📊
Step-by-Step Process
1
Identify
2
Operate
3
Relate
4
Verify
5
Record
Inverse Operations

5 + 3 = 8

8 - 3 = 5

3 + 5 = 8

8 - 5 = 3

Practice Makes Perfect!

Questions & Answers

Question: Why do addition and subtraction undo each other? They seem like different operations.

Answer: Great question! Addition and subtraction are like opposite actions. Here's why they undo each other:

  • Addition: Puts things together, makes numbers bigger
  • Subtraction: Takes things away, makes numbers smaller
  • Opposite directions: One moves forward, one moves backward
  • Balance: They cancel each other out

Think of it like walking: adding is walking forward, subtracting is walking backward!

Example: If you walk forward 3 steps (add 3), then walk backward 3 steps (subtract 3), you end up where you started!

Question: My child sometimes forgets to check their subtraction with addition. How can I help them remember?

Answer: Here are effective strategies to help your child remember to check:

  • Verbal routine: "After subtracting, always add back to check"
  • Visual reminder: Write "Check with addition" on worksheets
  • Physical action: Have them circle the result and add the subtracted number
  • Verification phrase: "Does this make sense?"

Try this activity: After solving 8 - 3 = 5, have your child write 5 + 3 = 8 to verify.

Practice checking regularly until it becomes a natural habit!

Question: Sometimes I mix up addition and subtraction. How can I remember which is which?

Answer: It's normal to mix them up! Here are memory tricks:

  • Addition: "+" means "put together" or "get more"
  • Subtraction: "-" means "take away" or "get less"
  • Visual memory: Plus sign has more lines (more), minus sign has fewer lines (less)
  • Keyword recognition: "more," "total," "altogether" = addition
  • Keyword recognition: "take away," "left," "remain" = subtraction

Think of it like this: Addition builds up, subtraction breaks down.

Example: "I have 5 cookies and get 2 more" → addition (5 + 2)

Question: What are some fun ways to practice the relationship between addition and subtraction?

Answer: Fun practice makes learning stick! Here are engaging activities:

  • Fact family houses: Draw houses with 3 numbers on the roof and 4 facts inside
  • Number line walks: Walk forward for addition, backward for subtraction
  • Balance scales: Show how both sides must balance
  • Story problems: Create stories that involve both operations

Engaging activities:

  • Play "Fact Family Bingo" with number cards
  • Create addition/subtraction flip cards
  • Use dominoes to show related facts
  • Build with blocks to visualize the relationship

The key is making the connection feel natural and intuitive!