Solve the Multiplication Problem: Calculate 3×560

Multiplication with Three-Digit Numbers

3×560= 3\times560=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's use the distributive law
00:06 Let's break down 560 into 500 plus 60
00:18 Let's multiply each factor separately and sum
00:33 Let's solve each multiplication and then sum
00:47 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3×560= 3\times560=

2

Step-by-step solution

To make solving easier, we break down 560 into more comfortable numbers, preferably round ones.

We obtain:

3×(500+60)= 3\times(500+60)=

We multiply 3 by each of the terms in parentheses:

(3×500)+(3×60)= (3\times500)+(3\times60)=

We solve the exercises in parentheses and obtain:

1,500+180=1,680 1,500+180=1,680

3

Final Answer

1680

Key Points to Remember

Essential concepts to master this topic
  • Distributive Property: Break down large numbers into hundreds and tens
  • Technique: Calculate 3×500=1500 and 3×60=180 separately
  • Check: Add partial products: 1500+180=1680 matches original calculation ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add partial products correctly
    Don't calculate 3×500=1500 and 3×60=180 but then add them wrong = incorrect final answer! Students often make arithmetic errors when combining the partial products. Always double-check your addition: 1500+180=1680.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(30-21)= \)

FAQ

Everything you need to know about this question

Why do we break 560 into 500+60 instead of other combinations?

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We choose place value chunks like 500+60 because they're easier to multiply mentally. You could use 550+10, but round hundreds and tens are simpler to calculate quickly!

Can I just multiply 3×560 directly without breaking it down?

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Yes, but breaking it down using the distributive property makes it much easier and reduces mistakes. It's especially helpful for mental math and understanding the process step-by-step.

What if I get different partial products when I break down the number differently?

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The final answer should always be the same! For example, 3×(400+160) 3×(400+160) gives 1200+480=1680, same as our method. This shows the distributive property works with any breakdown.

How do I know which method is faster?

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Practice both! Mental breakdown is great for building number sense, while standard algorithm (stacking) works well for larger numbers. Choose what feels most comfortable for you.

What should I do if I make an error in my partial products?

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Always double-check each step! Verify 3×500=1500 and 3×60=180 separately, then confirm 1500+180=1680. If your final answer doesn't match the choices, review each calculation.

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