Solved Exercises on Mental Subtraction Tricks in Grade 2

Master mental subtraction: counting back, breaking apart, compensation, number line jumps, and friendly numbers through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Back Method
Exercise 1
Solve mentally: 47 - 8
Definition:

Counting Back Method: Start with the larger number and count backward by the smaller number.

Counting Back Method:
  1. Start with the minuend (the number being subtracted from)
  2. Count backward one number at a time for the subtrahend (the number being subtracted)
  3. Keep track of each count until you reach zero
  4. The number you land on is the difference
Problem
47 - 8
Count back
46, 45, 44, 43, 42, 41, 40, 39
Answer
39
Step 1: Start with 47

We begin our count at the minuend: 47

Step 2: Count back 8 numbers

47 → 46 → 45 → 44 → 43 → 42 → 41 → 40 → 39

Step 3: Count each step

Step 1: 47-1=46, Step 2: 46-1=45, ..., Step 8: 40-1=39

47 - 8 = 39
Final answer:

47 - 8 = 39

Applied rules:

• Counting Back: Subtract by counting backward from the starting number

• Number Sense: Understanding that subtraction means moving left on the number line

• Sequential Counting: Each count represents subtracting 1

2 Breaking Apart Method
Exercise 2
Solve mentally: 63 - 17
Definition:

Breaking Apart Method: Break the subtrahend into tens and ones, then subtract in parts.

Problem
63 - 17
Break 17
10 + 7
Subtract in parts
63-10=53, 53-7=46
Step 1: Break the subtrahend (17) into tens and ones

17 = 10 + 7

Step 2: Subtract the tens first

63 - 10 = 53

Step 3: Subtract the remaining ones

53 - 7 = 46

Step 4: Combine the results

63 - 17 = 46

63 - 17 = 46
Final answer:

63 - 17 = 46

Applied rules:

• Decomposition: Breaking numbers into smaller, easier-to-handle parts

• Partial Subtraction: Subtracting in manageable chunks

• Place Value: Using knowledge of tens and ones to simplify calculations

3 Compensation Method
Exercise 3
Solve mentally: 56 - 19
Definition:

Compensation Method: Round one number to make the calculation easier, then adjust the answer.

Problem
56 - 19
Round 19 to 20
56 - 20
Adjust result
36 + 1 = 37
Step 1: Round the subtrahend to a friendly number

19 is close to 20, which is easier to subtract

Step 2: Perform the easier subtraction

56 - 20 = 36

Step 3: Adjust for the rounding

We subtracted 1 too many (20 instead of 19), so add 1 back: 36 + 1 = 37

Step 4: Verify the result

37 + 19 = 56, so our answer is correct

56 - 19 = 37
Final answer:

56 - 19 = 37

Applied rules:

• Rounding: Making numbers friendlier for mental calculation

• Compensation: Adjusting the result to account for rounding

• Verification: Checking that the answer makes sense

Rules and methods, laws,...
Counting Back: 47 - 8 = 47, 46, 45, 44, 43, 42, 41, 40, 39
Counting Back Method
Method 1
Counting Back
Start at the minuend and count backward
Method 2
Breaking Apart
Separate tens and ones for easier subtraction
Method 3
Compensation
Round numbers to make calculation easier
Key definitions:

Minuend: The number being subtracted from (in 47 - 8, 47 is the minuend)

Subtrahend: The number being subtracted (in 47 - 8, 8 is the subtrahend)

Difference: The result of subtraction (in 47 - 8 = 39, 39 is the difference)

Complete methodology:
  1. Analyze the numbers: Look at the minuend and subtrahend to determine which method works best
  2. Choose the method: Counting back for small subtrahends, breaking apart for larger ones, compensation for numbers near round numbers
  3. Apply the method: Follow the steps of the chosen technique
  4. Verify the result: Check your answer by adding the difference back to the subtrahend
Tip 1: Use counting back for subtractions where the subtrahend is less than 10.
Tip 2: For numbers ending in 9, try the compensation method (add 1 to make it round).
Tip 3: Practice with a number line to visualize the subtraction process.
Tip 4: Always check your answer by adding the difference back to the subtrahend.
Common errors: Forgetting to adjust when using compensation, miscounting when counting back, forgetting place value when breaking apart.
Key strategies: Recognize patterns, use known facts, break problems into smaller steps.
Mental subtraction strategies:

• Counting Back: Good for small numbers (subtracting 1-9)

• Breaking Apart: Separate tens and ones (e.g., 63 - 17 = 63 - 10 - 7)

• Compensation: Round one number and adjust (e.g., 56 - 19 = 56 - 20 + 1)

• Number Line Jumps: Visualize movement on a number line

• Friendly Numbers: Use doubles and near-doubles (e.g., 15 - 7 = 15 - 5 - 2)

Solution: Exercises 4 to 5
4 Number Line Jumps
Exercise 4
Solve mentally: 82 - 26
Definition:

Number Line Jumps: Visualize movement on a number line by jumping in tens and ones.

Problem
82 - 26
Jump by tens
82 → 72 → 62
Jump by ones
62 → 61 → 60 → 56
Step 1: Start at 82 on the number line

Visualize yourself at position 82

Step 2: Jump back by tens first (20 = 2 tens)

82 - 10 = 72, then 72 - 10 = 62

Step 3: Jump back by ones (6 = 6 ones)

62 - 1 = 61, 61 - 1 = 60, 60 - 1 = 59, 59 - 1 = 58, 58 - 1 = 57, 57 - 1 = 56

Step 4: Land at the final position

You end at position 56

82 - 26 = 56
Final answer:

82 - 26 = 56

Applied rules:

• Visualization: Using mental imagery to represent numbers on a line

• Grouping: Separating tens and ones for easier jumps

• Sequential Thinking: Moving step by step toward the answer

5 Friendly Numbers Method
Exercise 5
Solve mentally: 75 - 38
Definition:

Friendly Numbers Method: Use known facts and relationships to find the answer.

Problem
75 - 38
Think: 75 - 40
75 - 40 = 35
Add back the 2
35 + 2 = 37
Step 1: Recognize that 38 is close to 40

40 is a friendly number that's easy to subtract from 75

Step 2: Subtract the friendly number (40)

75 - 40 = 35

Step 3: Adjust for the difference

We subtracted 2 more than we needed (since 40 - 38 = 2), so add 2 back

Step 4: Calculate the final answer

35 + 2 = 37

Step 5: Verify the result

37 + 38 = 75, confirming our answer is correct

75 - 38 = 37
Final answer:

75 - 38 = 37

Applied rules:

• Number Relationships: Recognizing that 38 is 2 less than 40

• Compensation: Adjusting the calculation to work with friendlier numbers

• Addition/Subtraction Connection: Using addition to verify subtraction

Mental Subtraction Strategies and Techniques
Counting Back: 47 - 8 = 47, 46, 45, 44, 43, 42, 41, 40, 39 = 39
Counting Back Strategy
Key definitions:

Subtraction: The operation of taking one number away from another

Mental Math: Performing calculations in your head without paper or calculator

Friendly Numbers: Numbers that are easy to work with mentally (like multiples of 10)

Complete methodology:
  1. Look at the numbers: Examine the minuend and subtrahend to choose the best strategy
  2. Select the method: Counting back for small subtrahends, breaking apart for larger ones, compensation for numbers near round numbers
  3. Execute the method: Follow the specific steps for your chosen technique
  4. Verify the result: Check your answer by adding the difference back to the subtrahend
Tip 1: For subtracting 9, subtract 10 and add 1 back (e.g., 45 - 9 = 45 - 10 + 1 = 36)
Tip 2: Use doubles facts to help with subtraction (if 8 + 8 = 16, then 16 - 8 = 8)
Tip 3: When subtracting across tens (like 52 - 8), break it into parts (52 - 2 - 6)
Tip 4: Practice with visual aids like number lines or counters before going mental
Common errors: Forgetting to adjust when using compensation, miscounting when counting back, forgetting place value when breaking apart.
Success habits: Regular practice, checking answers, visualizing the process, recognizing patterns.
Mental subtraction strategies:

• Counting Back: Good for small numbers (subtracting 1-9)

• Breaking Apart: Separate tens and ones (e.g., 63 - 17 = 63 - 10 - 7)

• Compensation: Round one number and adjust (e.g., 56 - 19 = 56 - 20 + 1)

• Number Line Jumps: Visualize movement on a number line

• Friendly Numbers: Use doubles and near-doubles (e.g., 15 - 7 = 15 - 5 - 2)

• Addition Facts: Use known addition facts to solve subtraction (if 8 + 7 = 15, then 15 - 7 = 8)

Mental Subtraction Workflow

🔢
Step-by-Step Process
1
Look at the numbers
2
Choose a method
3
Calculate mentally
4
Check answer
Number Line Visualization
Mental subtraction involves visualizing movement along a number line, starting from the minuend and moving backward by the value of the subtrahend.
Practice Daily for Mental Math Mastery!

Questions & Answers

Question: I don't understand when to use counting back versus breaking apart. Can you explain the difference?

Answer: Great question! The choice depends on the size of the number you're subtracting:

  • Counting Back: Best when subtracting small numbers (usually 1-9). It's quick and straightforward. Example: 47 - 8 = 46, 45, 44, 43, 42, 41, 40, 39 = 39
  • Breaking Apart: Better when subtracting larger numbers (double digits). It's easier to handle tens and ones separately. Example: 63 - 17 = 63 - 10 - 7 = 53 - 7 = 46

Think of it this way: if the number you're subtracting is small, counting back is like taking a few steps backward. If it's bigger, breaking it apart is like taking a big step (the tens) and then smaller steps (the ones).

Try both methods with the same problem to see which feels easier for you!

Question: My child struggles with mental math. How can I help them practice these subtraction tricks at home?

Answer: Here are effective ways to practice mental subtraction at home:

  • Use everyday situations: While shopping, ask "If we had 56 apples and ate 19, how many are left?"
  • Number line walks: Draw a number line on paper or floor tape, have your child physically move backward to visualize subtraction
  • Playing cards: Draw two cards and practice subtracting the smaller from the larger
  • Story problems: Create fun stories like "Tommy had 82 marbles, he lost 26, how many does he have now?"

Start with smaller numbers and gradually increase difficulty. Make it a game - perhaps a race to see who can solve it faster!

Encourage your child to explain their thinking. This helps reinforce the concepts and reveals any misunderstandings.

Question: Why do we need different methods? Can't I just subtract normally?

Answer: Different methods make subtraction easier in different situations! Think of it like having different tools:

  • Some problems are easier with counting back (like 47 - 3)
  • Others are easier when you break them apart (like 52 - 18)
  • Some are easier with compensation (like 63 - 19, which becomes 63 - 20 + 1)

Having multiple methods gives you flexibility. You can choose the one that makes the most sense for each problem. It's like having a toolbox - sometimes you need a hammer, sometimes a screwdriver!

As you practice, you'll develop number sense and automatically choose the best method for each problem.