Solve 11x × 5 × 6: Multi-Factor Multiplication with Variables

Variable Multiplication with Multiple Factors

Solve the following problem:

11x×5×6= 11x\times5\times6=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together.
00:10 First, we'll use the commutative property to rearrange the numbers.
00:17 Now, let's do long multiplication step by step.
00:21 Remember, zero times any number equals zero.
00:32 And that's how we find the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

11x×5×6= 11x\times5\times6=

2

Step-by-step solution

Upon observing the exercise note that we have two "regular" numbers and one number with a variable.
Given that this is a multiplication exercise, multiplying a number with a variable by a number without a variable doesn't present a problem.

In fact, it's important to remember that a variable attached to a number represents multiplication itself, for example in this case: 11×x 11\times x
Therefore, we can apply the distributive property to separate the variable, and come back to it later.
Proceed to solve the exercise from right to left since it's simpler this way.

5×6=30 5\times6=30

We obtain the following:

11x×30= 11x\times30=

We'll put aside the x and add it at the end of the exercise.

By solving the exercise in an organized way we simplify the solution process.

It's important to maintain the correct order when solving the problem, meaning first multiply the ones of the first number by the ones of the second number,
then the tens of the first number by the ones of the second number, and so on.

30×11=330 30\\\times11\\=330

Don't forget to add the variable at the end. The answer is as follows:

330x 330x

3

Final Answer

330x 330x

Key Points to Remember

Essential concepts to master this topic
  • Rule: Variables stay attached while numbers multiply together separately
  • Technique: Calculate 5 × 6 = 30, then multiply 11x × 30 = 330x
  • Check: Verify coefficient: 11 × 5 × 6 = 330, so answer is 330x ✓

Common Mistakes

Avoid these frequent errors
  • Adding coefficients instead of multiplying
    Don't add 11 + 5 + 6 = 22x! This treats multiplication signs as addition signs and gives completely wrong results. Always multiply all numerical coefficients: 11 × 5 × 6 = 330x.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why doesn't the variable x change during multiplication?

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The variable x represents an unknown number, and we're only multiplying the coefficient (the number in front of x). Think of 11x as "11 groups of x" - when you multiply by 5 and 6, you get "330 groups of x" or 330x.

Do I have to multiply from left to right?

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No! Multiplication is commutative, meaning you can multiply in any order. You could do 5 × 6 = 30 first, then 11 × 30 = 330, or multiply all three: 11 × 5 × 6 = 330.

What if there are multiple variables like 3x × 4y?

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Multiply the numbers together and keep all variables: 3x × 4y = 12xy 12xy . Each different variable stays separate in your final answer.

How do I know when to multiply versus add with variables?

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Look at the operation symbol! If you see × (times) or numbers/variables written next to each other like 11x, then multiply. If you see + or -, then add or subtract like terms.

Can I check my answer without knowing what x equals?

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Yes! Pick any number for x and substitute it into both the original problem and your answer. For example: if x = 2, then 11(2)×5×6=660 11(2) \times 5 \times 6 = 660 and 330(2)=660 330(2) = 660

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