Solve 48,534 - 27,302 Using Number Line Jump Strategy

Q: Why do we break 27,302 into smaller parts?

Breaking 27,302 into 20,000 + 7,000 + 300 + 2 makes each subtraction jump easier to visualize and calculate. It's like taking small, manageable steps instead of one giant leap!

Q: Do I have to subtract in this exact order?

No! You can subtract the parts in any order you want. Some students prefer largest to smallest (20,000 first), others prefer place value order. The final answer will be the same!

Q: What if I make a mistake in one of the steps?

That's okay! The beauty of this method is you can check each step individually. If one jump seems wrong, just recalculate that specific subtraction without starting over.

Q: Can I use this method for addition too?

Absolutely! For addition, you'd jump forward on the number line instead of backward. Break the number into parts and make forward jumps: $ +20,000, +7,000, +300, +2 $

Multi-Digit Subtraction with Decomposition Strategy

$48,534-27,302=$

Solve the exercise using the number line jumps below:

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$48,534-27,302=$

Solve the exercise using the number line jumps below:

Step-by-step solution

To solve the subtraction problem $48,534 - 27,302$ using a number line, follow these steps:

Start at the larger number, $48,534$ .
The provided number line shows breakdowns of the subtraction as follows:

First jump: Subtract 20,000.
Second jump: Subtract 7,000.
Third jump: Subtract 300.
Fourth jump: Subtract 2.

Applying these steps, let's calculate:

Step 1: $48,534 - 20,000 = 28,534$

Step 2: $28,534 - 7,000 = 21,534$

Step 3: $21,534 - 300 = 21,234$

Step 4: $21,234 - 2 = 21,232$

Therefore, the final result after making all the deductions on the number line is $21,232$ , which matches choice 3 from the provided answer options.

Final Answer

$21,232$

Key Points to Remember

Essential concepts to master this topic

Strategy: Break down the subtrahend into place values for easier jumps
Technique: Jump backwards by 20,000 + 7,000 + 300 + 2 = 27,302
Check: Verify $21,232 + 27,302 = 48,534$ ✓

Common Mistakes

Avoid these frequent errors

Adding jump values instead of subtracting sequentially
Don't jump forward or add the decomposed values = wrong direction on number line! This leads to answers that are way too large. Always subtract each jump value step-by-step from your current position.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct answer:

$693+705=\text{ ?}$

FAQ

Everything you need to know about this question

Why do we break 27,302 into smaller parts?

Breaking 27,302 into 20,000 + 7,000 + 300 + 2 makes each subtraction jump easier to visualize and calculate. It's like taking small, manageable steps instead of one giant leap!

Do I have to subtract in this exact order?

No! You can subtract the parts in any order you want. Some students prefer largest to smallest (20,000 first), others prefer place value order. The final answer will be the same!

What if I make a mistake in one of the steps?

That's okay! The beauty of this method is you can check each step individually. If one jump seems wrong, just recalculate that specific subtraction without starting over.

How is this different from regular subtraction?

Regular column subtraction works from right to left with regrouping. The number line method lets you work with whole place values and see the subtraction visually as backward jumps.

Can I use this method for addition too?

Absolutely! For addition, you'd jump forward on the number line instead of backward. Break the number into parts and make forward jumps: $+20,000, +7,000, +300, +2$

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