Solve 75-38 Using Number Line Jumps: Step-by-Step Subtraction

Number Line Subtraction with Decomposition Strategy

Solve the subtraction exercise using jumps on the number line below:

7538= 75-38=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the subtraction exercise using jumps on the number line below:

7538= 75-38=

2

Step-by-step solution

To solve this subtraction problem using jumps on a number line, we will break down the steps as follows:

  • Step 1: Start at 75 75 on the number line.
  • Step 2: Subtract the 30 30 part of 38 38 by moving 30 spaces back from 75 75 . This gets us to 45 45 because 7530=45 75 - 30 = 45 .
  • Step 3: Subtract the remaining 8 8 by moving 8 spaces back from 45 45 . This lands us on 37 37 because 458=37 45 - 8 = 37 .

Each movement on the number line helps visualize the subtraction in stages. By splitting the subtraction of 38 38 into 30+8 30 + 8 , the student appreciates each component's effect on the original number.

Therefore, the solution to the subtraction problem 7538 75 - 38 is 37 37 .

3

Final Answer

37 37

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Break down subtraction into tens and ones place values
  • Technique: Split 38 into 30 + 8, subtract each part separately
  • Check: Verify by addition: 37 + 38 should equal 75 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting digits without considering place value
    Don't just subtract 5-8 and 7-3 separately = wrong answer like 45! This ignores place value and borrowing rules. Always break down by place value: subtract 30 first, then subtract 8.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

Why do I split 38 into 30 + 8 instead of other combinations?

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Breaking numbers into tens and ones matches our place value system! It makes the jumps easier to visualize and count on the number line.

What if I want to subtract 38 all at once?

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That's much harder to visualize and count! Decomposition (breaking it into smaller parts) makes subtraction clearer and reduces counting errors.

Can I subtract the 8 first, then the 30?

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Yes! The order doesn't matter in subtraction jumps. You'll get the same answer: 758=67 75 - 8 = 67 , then 6730=37 67 - 30 = 37 .

How do I know which direction to jump on the number line?

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For subtraction, always jump backwards (left) on the number line. For addition, jump forwards (right). Remember: subtract = go back!

What if I make a counting mistake while jumping?

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Always double-check by adding your answer back: 37+38 37 + 38 . If you get 75, your subtraction is correct!

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