Solve: Finding the Product of 10×103×10 Using Multiplication Properties

Q: Why should I change the order of multiplication?

The commutative property lets you multiply in any order! Grouping the two 10s together gives you $ 10\times10=100 $, which is much easier to work with than $ 10\times103 $.

Q: How do I multiply 100 by 103 quickly?

Think of it as 100 × (100 + 3). This gives you $ 100\times100 + 100\times3 = 10,000 + 300 = 10,300 $. Or simply add two zeros to 103!

Q: What if the numbers were in a different order?

It doesn't matter! Whether it's $ 10\times103\times10 $ or $ 103\times10\times10 $, the commutative property means you can always rearrange to make calculation easier.

Q: Can I use this strategy with other numbers?

Absolutely! Always look for patterns like multiples of 10, 100, or numbers that are easy to multiply together. Group these first to simplify your work.

Q: How do I know my answer is reasonable?

Estimate first! $ 10\times100\times10 = 10,000 $, so your answer should be slightly more than 10,000. Since $ 10,300 > 10,000 $, it makes sense!

Multiplication Properties with Commutative Strategy

Solve the following exercise:

$10\times103\times10=\text{ ?}$

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Step-by-step video solution

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00:00 Solve

00:03 Let's arrange the exercise so it will be convenient for us to solve

00:09 Let's solve each multiplication separately

00:14 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Solve the following exercise:

$10\times103\times10=\text{ ?}$

Step-by-step solution

Since the exercise involves only multiplication, we can use the commutative property in order to simplify the calculation:

$10\times10\times103=$

Now let's solve the exercise from left to right:

$10\times10=100$

$100\times103=10,300$

Final Answer

$10,300$

Key Points to Remember

Essential concepts to master this topic

Commutative Property: Change order to group easier calculations together
Strategy: Calculate $10\times10=100$ first, then multiply by 103
Check: Verify $100\times103=10,300$ by counting zeros ✓

Common Mistakes

Avoid these frequent errors

Calculating left to right without regrouping
Don't compute $10\times103=1,030$ then $1,030\times10=10,300$ ! This makes the calculation harder and more error-prone. Always look for opportunities to group factors of 10 together first using the commutative property.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why should I change the order of multiplication?

The commutative property lets you multiply in any order! Grouping the two 10s together gives you $10\times10=100$ , which is much easier to work with than $10\times103$ .

How do I multiply 100 by 103 quickly?

Think of it as 100 × (100 + 3). This gives you $100\times100 + 100\times3 = 10,000 + 300 = 10,300$ . Or simply add two zeros to 103!

What if the numbers were in a different order?

It doesn't matter! Whether it's $10\times103\times10$ or $103\times10\times10$ , the commutative property means you can always rearrange to make calculation easier.

Can I use this strategy with other numbers?

Absolutely! Always look for patterns like multiples of 10, 100, or numbers that are easy to multiply together. Group these first to simplify your work.

How do I know my answer is reasonable?

Estimate first! $10\times100\times10 = 10,000$ , so your answer should be slightly more than 10,000. Since $10,300 > 10,000$ , it makes sense!

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