Solve 3400 - 680 Using Number Line Jump Strategy

Q: Why break 680 into 400 + 200 + 80 instead of just subtracting 680 directly?

Breaking it down makes the mental math much easier! Working with round hundreds and tens helps you visualize the jumps clearly and reduces calculation errors.

Q: Can I use different jump sizes like 600 + 80?

Absolutely! You can break 680 into any combination that adds up correctly. Choose sizes that feel comfortable for your mental math skills.

Q: How do I know I'm at the right final position?

Check by adding your jumps back: $ 2720 + 680 = 3400 $. If you get back to where you started, you're correct!

Multi-Step Subtraction with Strategic Jump Decomposition

Solve the exercise using the number line jumps below:

$3400-680=$

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Step-by-step written solution

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Understand the problem

Solve the exercise using the number line jumps below:

$3400-680=$

Step-by-step solution

To solve the subtraction $3400 - 680$ using a number line approach:

First, we start at the number $3400$ .
We then subtract $400$ by making a backward jump on the number line, taking us to $3000$ .
Next, we subtract another $200$ , taking us further back to $2800$ .
Finally, we subtract $80$ , landing us at the final answer of $2720$ .

Therefore, the result of the subtraction $3400 - 680$ is $\textbf{2720}$ .

Final Answer

$2720$

Key Points to Remember

Essential concepts to master this topic

Strategy: Break down 680 into manageable parts like 400 + 200 + 80
Technique: Start at 3400, jump back 400 to reach 3000
Check: Add jumps back: 2720 + 80 + 200 + 400 = 3400 ✓

Common Mistakes

Avoid these frequent errors

Subtracting each jump value from the original number separately
Don't subtract each jump (400, 200, 80) from 3400 separately = three different wrong answers! This ignores the sequential nature of jumps on a number line. Always move step-by-step along the line, using each result as the starting point for the next jump.

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 break 680 into 400 + 200 + 80 instead of just subtracting 680 directly?

Breaking it down makes the mental math much easier! Working with round hundreds and tens helps you visualize the jumps clearly and reduces calculation errors.

Can I use different jump sizes like 600 + 80?

Absolutely! You can break 680 into any combination that adds up correctly. Choose sizes that feel comfortable for your mental math skills.

What if I make a jump in the wrong direction?

If you accidentally jump forward instead of backward, you'll get a number larger than 3400. Remember: subtraction means moving left (backward) on the number line!

How do I know I'm at the right final position?

Check by adding your jumps back: $2720 + 680 = 3400$ . If you get back to where you started, you're correct!

Is this method faster than regular subtraction?

It depends on your comfort level! Number line jumps help you visualize the problem and avoid borrowing mistakes, making it great for building understanding.

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