Multiply 12345 by 6: Step-by-Step Integer Multiplication

Q: Why can't I just multiply each digit by 6 from left to right?

Because each digit represents a different place value! The '1' in 12345 means 10,000, not just 1. You must respect place values: $ 1×6 = 60,000 $ (not 6).

Q: Is there an easier way than breaking it into so many parts?

You could use standard multiplication (multiply column by column with carrying), but the distributive method helps you understand what's really happening in multiplication!

Q: Do I have to add the partial products in order?

No! Addition is commutative, so you can add them in any order. However, adding from largest to smallest (left to right) often feels more natural.

Q: What if I make an error in one of the smaller multiplications?

Double-check each step! Common errors: $ 40×6 = 240 $ (not 24), and $ 300×6 = 1800 $ (not 180). Count your zeros carefully!

Q: How can I verify my final answer is correct?

Use estimation! Round 12345 to 12000, then $ 12000×6 = 72000 $. Since 74070 is close to 72000, your answer makes sense!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We will use the distributive law

00:13 We will break down the number into its factors by tens, hundreds, etc.

00:32 We will multiply each factor separately, then add

01:06 We will solve each multiplication and then sum

01:42 We will solve one addition operation at a time

02:05 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

$12345\times6=$

2

Step-by-step solution

In order to simplify the resolution process, we begin by breaking down the number 12345 into a smaller addition exercise:

$(10000+2000+300+40+5)\times6=$

We multiply each term inside the parentheses by 6:

$(10000\times6)+(2000\times6)+(300\times6)+(40\times6)+(5\times6)=$

We then solve each of the exercises inside of the parentheses:

$60000+12000+1800+240+30=$

Lastly we solve the exercise from left to right:

$60000+12000=72000$

$72000+1800=73800$

$73800+240=74040$

$74040+30=74070$

3

Final Answer

74070

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Break down large numbers into place values for easier calculation
Technique: 12345 = 10000 + 2000 + 300 + 40 + 5, then multiply each by 6
Check: Add partial products: 60000 + 12000 + 1800 + 240 + 30 = 74070 ✓

Common Mistakes

Avoid these frequent errors

Multiplying digits individually without considering place value
Don't just multiply 1×6, 2×6, 3×6, 4×6, 5×6 to get 62345! This ignores place values and gives completely wrong results. Always break numbers into their actual place values (thousands, hundreds, tens, ones) before multiplying.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just multiply each digit by 6 from left to right?

+

Because each digit represents a different place value! The '1' in 12345 means 10,000, not just 1. You must respect place values: $1×6 = 60,000$ (not 6).

Is there an easier way than breaking it into so many parts?

+

You could use standard multiplication (multiply column by column with carrying), but the distributive method helps you understand what's really happening in multiplication!

Do I have to add the partial products in order?

+

No! Addition is commutative, so you can add them in any order. However, adding from largest to smallest (left to right) often feels more natural.

What if I make an error in one of the smaller multiplications?

+

Double-check each step! Common errors: $40×6 = 240$ (not 24), and $300×6 = 1800$ (not 180). Count your zeros carefully!

How can I verify my final answer is correct?

+

Use estimation! Round 12345 to 12000, then $12000×6 = 72000$ . Since 74070 is close to 72000, your answer makes sense!

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Multiply 12345 by 6: Step-by-Step Integer Multiplication

Distributive Property with Multi-Digit Multiplication

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