Solve the Expression: 2x × 4.65 × 6.3 Decimal Multiplication

Decimal Multiplication with Variable Coefficients

Solve the following problem:

2x×4.65×6.3= 2x\times4.65\times6.3=

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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 We'll follow the order of operations, moving from left to right.
00:19 Now, we'll use the distributive property. We'll split the expression into a whole number and remainder.
00:25 Remember, multiply each factor separately.
00:41 Here's our first multiplication step.
00:54 We'll use long multiplication to complete this step.
01:00 Be sure to keep an eye on the decimal point.
01:18 Great job! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

2x×4.65×6.3= 2x\times4.65\times6.3=

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 by itself, for example in this case: 2×x 2\times x
Therefore, we can apply the distributive property in order to separate the variable, and come back to it later.
Solve the exercise from left to right.

Solve the left exercise by breaking down the decimal number into an addition problem of a whole number and a decimal number as follows:

2×(4+0.65)= 2\times(4+0.65)=

Multiply 2 by each term inside of parentheses:

(2×4)+(2×0.65)= (2\times4)+(2\times0.65)=

Solve each of the expressions inside of the parentheses as follows:

8+1.3=9.3 8+1.3=9.3

We obtain the following exercise:

9.3×6.3= 9.3\times6.3=

Solve the exercise vertically in order to simplify the solution process.

It's important to be careful with the proper placement of the exercise, using the decimal point as an anchor.
Then we can proceed to multiply in order, first the ones digit of the first number by the ones digit of the second number. Then the tens digit of the first number by the ones digit of the second number, and so on.

9.3×6.3=58.59 9.3\\\times6.3\\=58.59

Don't forget to add the variable at the end resulting in the following answer:

58.59x 58.59x

3

Final Answer

58.59x 58.59x

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply decimal numbers first, then attach the variable
  • Technique: Calculate 2 × 4.65 × 6.3 = 58.59, then add x
  • Check: Count decimal places: 4.65 (2 places) × 6.3 (1 place) = 3 places ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to include the variable in final answer
    Don't calculate 2 × 4.65 × 6.3 = 58.59 and stop there! This gives just a number instead of the algebraic expression. Always remember that 2x means 2 times x, so your final answer must include the variable: 58.59x.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why can I multiply the numbers and keep the variable separate?

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Because multiplication is commutative! The expression 2x × 4.65 × 6.3 means 2 × x × 4.65 × 6.3. You can rearrange to get (2 × 4.65 × 6.3) × x, which gives you 58.59x.

How do I multiply 2 × 4.65 × 6.3 step by step?

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First multiply 2 × 4.65 = 9.3. Then multiply 9.3 × 6.3 = 58.59. When multiplying decimals, count the total decimal places: 4.65 has 2 places, 6.3 has 1 place, so your answer needs 3 decimal places.

What if I get confused about where to put the decimal point?

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Use the decimal place rule: Add up all decimal places in the numbers you're multiplying. In this problem, 4.65 (2 places) + 6.3 (1 place) = 3 total places, so 58.59 has 3 decimal places.

Can I solve this problem in a different order?

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Absolutely! You could calculate 4.65 × 6.3 = 29.295 first, then multiply by 2 to get 58.59. The associative property means the order doesn't matter as long as you multiply all the numbers.

How do I check if 58.59x is the right answer?

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Verify your decimal multiplication:

  • 2 × 4.65 = 9.30
  • 9.30 × 6.3 = 58.59
  • Don't forget the variable: 58.59x

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