Solve the Multiplication: Calculate 5×7×13×6

Q: Why can I change the order of multiplication?

The commutative property of multiplication says that changing the order doesn't change the result. So $ 5×7×13×6 $ equals $ 7×13×5×6 $ or any other arrangement!

Q: How do I know which numbers to group together?

Look for pairs that make nice, round numbers or are easier to calculate. In this problem, 7×13=91 and 5×6=30 are both manageable numbers to multiply together.

Q: What if I get a different answer doing it left to right?

If you get a different answer, you made a calculation error. The final result should always be the same regardless of order. Double-check your arithmetic step by step.

Q: Is 91×30 really easier than the original problem?

Yes! Multiplying 91×30 means 91×3×10 = 273×10 = 2730. Using the zero at the end makes it much simpler than dealing with four separate numbers.

Q: Can I group more than two numbers at once?

Absolutely! You could do $ (5×7×13)×6 $ or $ 5×(7×13×6) $. Choose whatever grouping makes the calculation easiest for you.

Multiplication Properties with Strategic Grouping

$5\cdot7\cdot13\cdot6=\text{?}$

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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 arrange the equation so it will be easier for us to solve

00:11 Let's solve each multiplication separately and then continue

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5\cdot7\cdot13\cdot6=\text{?}$

Step-by-step solution

According to the rules of the order of operations, since the exercise only involves multiplication, you can swap the order of the numbers.

We rearrange the numbers to create pairs of multiplication exercises, which will then give us a simpler equation:

$7\times13\times5\times6=(7\times13)\times(5\times6)$

We solve the exercises in parentheses:

$91\times30=2730$

Final Answer

2730

Key Points to Remember

Essential concepts to master this topic

Commutative Property: Numbers can be multiplied in any order
Strategic Grouping: Pair numbers like (7×13) and (5×6) for easier calculation
Verification: Check by multiplying all numbers left to right: 5×7×13×6 = 2730 ✓

Common Mistakes

Avoid these frequent errors

Multiplying numbers strictly left to right without grouping
Don't compute 5×7=35, then 35×13=455, then 455×6=2730! This creates large, difficult numbers that increase calculation errors. Always rearrange and group numbers to create easier pairs like (7×13)×(5×6) = 91×30.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can I change the order of multiplication?

The commutative property of multiplication says that changing the order doesn't change the result. So $5×7×13×6$ equals $7×13×5×6$ or any other arrangement!

How do I know which numbers to group together?

Look for pairs that make nice, round numbers or are easier to calculate. In this problem, 7×13=91 and 5×6=30 are both manageable numbers to multiply together.

What if I get a different answer doing it left to right?

If you get a different answer, you made a calculation error. The final result should always be the same regardless of order. Double-check your arithmetic step by step.

Is 91×30 really easier than the original problem?

Yes! Multiplying 91×30 means 91×3×10 = 273×10 = 2730. Using the zero at the end makes it much simpler than dealing with four separate numbers.

Can I group more than two numbers at once?

Absolutely! You could do $(5×7×13)×6$ or $5×(7×13×6)$ . Choose whatever grouping makes the calculation easiest for you.

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