Solve the Multiplication: 5 × 17 × 2 Step-by-Step

Q: Why can I change the order of multiplication?

The commutative property says that $ a \times b = b \times a $. This works for multiplication (and addition) but not for subtraction or division!

Q: How do I know which numbers to multiply first?

Look for easy combinations! Numbers like 5×2=10, 4×25=100, or 8×125=1000 create round numbers that make the next step much simpler.

Q: What if there are more than three numbers to multiply?

The same rule applies! You can rearrange any number of factors in multiplication. Group them to make the easiest calculations possible.

Q: Does this work with fractions and decimals too?

Yes! The commutative property works with all types of numbers. For example: $ 0.5 \times 18 \times 2 = 0.5 \times 2 \times 18 = 1 \times 18 = 18 $

Q: What if I forget to rearrange and calculate left to right?

You'll still get the correct answer! Rearranging just makes calculations easier and faster. Both $ 5 \times 17 \times 2 $ and $ 5 \times 2 \times 17 $ equal 170.

Multiplication Operations with Commutative Property

$5\cdot17\cdot2=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Alright, let's solve this problem together.

00:08 First, we'll arrange the equation, so it's easier to work with.

00:12 Let's tackle each multiplication one at a time, then move on.

00:17 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5\cdot17\cdot2=\text{?}$

Step-by-step solution

According to the rules of the order of arithmetic operations, in an exercise where there is only one multiplication operation, the order of the numbers can be changed.

Hence we can rearrange the exercise to obtain a round number that will help us later in the solution:

$5\times2\times17=$

Now we solve the exercise from left to right:

$5\times2=10$

$10\times17=170$

Final Answer

170

Key Points to Remember

Essential concepts to master this topic

Commutative Property: In multiplication, you can rearrange factors in any order
Strategy: Group factors like $5 \times 2 = 10$ to create easier calculations
Verification: Check by calculating differently: $17 \times 10 = 170$ ✓

Common Mistakes

Avoid these frequent errors

Calculating from left to right without rearranging
Don't just multiply $5 \times 17 = 85$ first, then $85 \times 2 = 170$ - this makes calculations harder! While you get the right answer, you miss the chance to simplify. Always look for easier combinations like $5 \times 2 = 10$ first.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can I change the order of multiplication?

The commutative property says that $a \times b = b \times a$ . This works for multiplication (and addition) but not for subtraction or division!

How do I know which numbers to multiply first?

Look for easy combinations! Numbers like 5×2=10, 4×25=100, or 8×125=1000 create round numbers that make the next step much simpler.

What if there are more than three numbers to multiply?

The same rule applies! You can rearrange any number of factors in multiplication. Group them to make the easiest calculations possible.

Does this work with fractions and decimals too?

Yes! The commutative property works with all types of numbers. For example: $0.5 \times 18 \times 2 = 0.5 \times 2 \times 18 = 1 \times 18 = 18$

What if I forget to rearrange and calculate left to right?

You'll still get the correct answer! Rearranging just makes calculations easier and faster. Both $5 \times 17 \times 2$ and $5 \times 2 \times 17$ equal 170.

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