Subtraction with 20 - Solved Exercises

Master subtraction with 20: basic facts, place value concepts, and related strategies through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Subtraction with 20
Exercise 1
Solve: 20 - 5 = ?, 20 - 8 = ?, 20 - 12 = ?, 20 - 15 = ?
Definition:

Subtraction with 20: Taking away from 20, which extends place value understanding beyond 10.

Solution methods:
  1. Counting back: Start at 20, count backward by the number being subtracted
  2. Using two ten frames: Fill 20 spaces and remove the specified number
  3. Think addition: What number added to the subtrahend equals 20?
  4. Break into parts: Use 10 as a bridge (20 - 5 = 10 + 5 = 15)
Problem Set
20-5, 20-8, 20-12, 20-15
Answers
15, 12, 8, 5
Step 1: 20 - 5

Count back: 20→19→18→17→16→15 (5 steps) = 15

Step 2: 20 - 8

Think addition: What + 8 = 20? Answer: 12, so 20 - 8 = 12

Step 3: 20 - 12

Break into parts: 20 - 10 = 10, then 10 - 2 = 8

Step 4: 20 - 15

Use known fact: 15 + 5 = 20, so 20 - 15 = 5

20 - 5 = 15, 20 - 8 = 12, 20 - 12 = 8, 20 - 15 = 5
Final answers:

20 - 5 = 15, 20 - 8 = 12, 20 - 12 = 8, 20 - 15 = 5

Applied rules:

• Subtraction with 20: Extends place value understanding beyond 10

• Verification: Add answer to subtrahend to check (15 + 5 = 20)

• Patterns: Notice that 20 - n and n + ? = 20 are related

2 Place Value Concept
Exercise 2
Solve: 23 - 20 = ?, 27 - 20 = ?, 25 - 20 = ?, 29 - 20 = ?
Definition:

Place value subtraction: Subtracting 20 from numbers in the twenties, focusing on the tens place.

Problem Set
23-20, 27-20, 25-20, 29-20
Answers
3, 7, 5, 9
Step 1: 23 - 20

23 has 2 tens and 3 ones. Remove 2 tens: 23 - 20 = 3

Step 2: 27 - 20

27 has 2 tens and 7 ones. Remove 2 tens: 27 - 20 = 7

Step 3: 25 - 20

25 has 2 tens and 5 ones. Remove 2 tens: 25 - 20 = 5

Step 4: 29 - 20

29 has 2 tens and 9 ones. Remove 2 tens: 29 - 20 = 9

23 - 20 = 3, 27 - 20 = 7, 25 - 20 = 5, 29 - 20 = 9
Final answers:

23 - 20 = 3, 27 - 20 = 7, 25 - 20 = 5, 29 - 20 = 9

Applied rules:

• Place value: Removing 20 leaves only the ones digit

• Pattern: The answer is always the ones digit of the original number

• Verification: Add 20 back to check (3 + 20 = 23)

3 Fact Family Connection
Exercise 3
Complete the fact families: 20 - 13 = ?, 13 + ? = 20, ? + 13 = 20, ? - 13 = 7
Definition:

Fact family: Related addition and subtraction facts using the same three numbers.

Fact Family
7, 13, 20
Complete Set
20-13=7, 13+7=20, 7+13=20, 20-7=13
Step 1: 20 - 13 = 7

What's left when 13 is taken from 20? Answer: 7

Step 2: 13 + 7 = 20

What number added to 13 makes 20? Answer: 7

Step 3: 7 + 13 = 20

Commutative property: 13 + 7 = 7 + 13 = 20

Step 4: 20 - 7 = 13

What's left when 7 is taken from 20? Answer: 13

20 - 13 = 7, 13 + 7 = 20, 7 + 13 = 20, 20 - 7 = 13
Final answers:

20 - 13 = 7, 13 + 7 = 20, 7 + 13 = 20, 20 - 7 = 13

Applied rules:

• Fact families: Addition and subtraction are inverse operations

• Relationship: If a + b = c, then c - a = b and c - b = a

• Verification: All four facts in the family are related

📚 SUBTRACTION WITH 20 - COMPLETE SUMMARY

Definitions:

  • Subtraction with 20: Taking away from 20 or subtracting 20 from larger numbers
  • Place Value: Understanding that numbers have tens and ones places
  • Fact Family: A group of related addition and subtraction facts using the same numbers
  • Bridge to 10: Using 10 as a reference point to make subtraction easier
  • Decomposition: Breaking numbers into parts to make subtraction easier

Core Rules & Principles:

  • Subtracting from 20: The answer is always what's needed to make 20
  • Subtracting 20: The answer is always the ones digit of the original number
  • Verification: Always check by adding the answer back to the subtracted amount
  • Fact Families: Addition and subtraction are inverse operations

Step-by-Step Methods:

  1. For 20 - n: Count back n steps from 20, or think "What + n = 20?"
  2. For n - 20: Focus on the ones place of the original number
  3. For fact families: Identify the three numbers and create four related facts
  4. Verify: Always add the difference to the subtracted number to check

Examples (Simple to Advanced):

  • Basic: 20 - 5 = 15
  • Place Value: 24 - 20 = 4
  • Fact Family: 20 - 13 = 7, 13 + 7 = 20, 7 + 13 = 20, 20 - 7 = 13
  • Application: "I have 20 stickers and give away 8. How many left?" → 20 - 8 = 12

Tips & Tricks:

  • Use Two Ten Frames: Visualize 20 as two sets of 10
  • Think Addition: For 20 - 14, ask "What + 14 = 20?"
  • Pattern Recognition: When subtracting 20, the ones digit stays the same
  • Break into Parts: Use 20 - 15 as (20 - 10) - 5 = 10 - 5 = 5

Common Pitfalls:

  • Confusing 20 - n with n - 20
  • Forgetting that subtracting 20 changes only the tens place
  • Not recognizing the relationship between addition and subtraction
  • Making calculation errors with larger numbers

Key Notes for Memorization:

  • Practice the pairs that make 20: 1+19, 2+18, 3+17, 4+16, 5+15, 6+14, 7+13, 8+12, 9+11, 10+10
  • When subtracting 20, focus only on the ones digit
  • Addition and subtraction are opposites: one undoes the other
  • Use the 10 strategy: break subtraction into two steps (20 - 17 = 20 - 10 - 7 = 3)
Subtraction with 20 Concepts
20 - n = (20 - n), n - 20 = ones digit
Subtraction Patterns
Subtracting from 20
20 - 13 = 7 because 13 + 7 = 20
Complement to 20
Subtracting 20
25 - 20 = 5 (ones digit)
Place value concept
Fact Families
13+7=20, 7+13=20, 20-13=7, 20-7=13
Related facts
Key Rule: Subtraction with 20 builds place value understanding.
Verification: Always add the answer back to check.
Solution Strategies:
  1. Use two ten frames: Visualize the numbers
  2. Think addition: What number added equals 20?
  3. Focus on place value: When subtracting 20, ones digit stays
  4. Check with fact families: Verify with related facts
Tip 1: Know the pairs that make 20 automatically.
Tip 2: When subtracting 20, just look at the ones digit.
Tip 3: Draw dots in two ten frames to visualize the problem.
Tip 4: Always verify by adding your answer back.
Practice and Applications
20 - 14 = 6, so 6 + 14 = 20
Inverse Relationship
Practice Concepts:

Number Bonds: Understanding how numbers combine to make 20

Place Value: Recognizing tens and ones positions

Fact Families: Connecting addition and subtraction

Practice Activities:
  1. Fill two ten frames: Show subtraction visually
  2. Write fact families: Practice related facts
  3. Solve word problems: Apply concepts in context
  4. Play number bond games: Make learning fun
Common Mistake: Confusing 20 - n with n - 20.
Memory Aid: "What goes with 13 to make 20?" for 20 - 13.
Practice Strategy: Start with manipulatives, then move to abstract.
Verification: Always add difference to subtracted amount to check.
Subtraction Properties: Order matters, zero property (n-0=n), n-n=0.
Place Value Skills: Foundation for larger number operations.
Essential Subtraction with 20 Facts:

• Subtraction with 20 builds foundational place value understanding

• The pairs that make 20 should be memorized: (1,19), (2,18), (3,17), (4,16), (5,15), (6,14), (7,13), (8,12), (9,11), (10,10)

• When subtracting 20 from twenty-something numbers, the answer is the ones digit

• Always verify your answer by adding the difference back to the subtracted amount

Extended Learning Concepts
20 - n and n + ? = 20 are related
Inverse Operations
Extended concepts:

Decomposition: Breaking numbers into parts to make subtraction easier

Compensation: Adjusting numbers to make subtraction simpler

Regrouping: Preparing for subtraction with borrowing

Advanced methodology:
  1. Connect to 30: Extend patterns to subtraction within 30
  2. Use number lines: Visualize jumps of 20
  3. Group strategies: Organize numbers for easier computation
  4. Verify with multiple methods: Cross-check answers
Tip 1: Once you know 20 - 7 = 13, you know 27 - 20 = 7.
Tip 2: Use your knowledge of 20 to solve bigger problems.
Tip 3: Practice with two ten frames to visualize the relationships.
Tip 4: Connect subtraction with 20 to addition facts.
Common errors: Confusing direction of subtraction, place value misunderstandings.
Success strategies: Visual aids, fact families, consistent practice.
Advanced principles for subtraction with 20:

• Understanding subtraction with 20 is foundational for multi-digit operations

• Patterns with 20 extend to larger numbers (100s, 1000s)

• The relationship between addition and subtraction is fundamental to algebra

• Verification through inverse operations builds mathematical reasoning

• Place value understanding from 20 subtraction supports number sense

Questions & Answers

Question: My child understands 20 - 5 = 15, but struggles with 25 - 20 = 5. Why is this happening and how can I help?

Answer: This is a common challenge! Your child likely understands taking away from 20 but hasn't yet grasped place value. Here's how to help:

  • Use base-10 blocks: Show 25 as 2 tens and 5 ones, then remove 2 tens.
  • Emphasize that 25 means "2 tens and 5 ones".
  • Practice with number lines: start at 25, jump back 20 to land on 5.
  • Connect to real-world examples: "I have 25 candies, give away 20, how many left?"

The key is helping them see that subtracting 20 affects only the tens place, leaving the ones digit unchanged.

Consistent visual representation will build the necessary understanding of place value.

Question: What are the most effective visual tools for teaching subtraction with 20 to first graders?

Answer: Visual tools are essential for concrete understanding:

  • Two ten frames: Fill with counters and remove some to show subtraction.
  • Base-10 blocks: Represent tens and ones concretely.
  • Number lines: Show jumps of 20 for place value concepts.
  • Finger counting: Use all 20 fingers for basic facts.

Example: For 20 - 7, fill two ten frames with 20 counters, remove 7, and count the remaining 13.

Transition from concrete to pictorial to abstract representations gradually.

Question: How can I help students who mix up addition and subtraction facts with 20?

Answer: This confusion is common and can be addressed through structured practice:

  • Emphasize the relationship: 13 + 7 = 20 and 20 - 7 = 13 are connected.
  • Use fact family triangles to show the relationship visually.
  • Practice both operations together to reinforce differences.
  • Ask: "Are we putting together or taking apart?" to clarify operation.

Create anchor charts showing the relationship between addition and subtraction with 20.

Regular practice with fact families helps students see the inverse relationship between operations.