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

Add fifty units to the number 31.

What is the resulting number?

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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