Solve: 15.6 × 5.2x × 0.3 - Decimal and Variable Multiplication

Decimal Multiplication with Variables

Solve the following problem:

15.6×5.2x×0.3= 15.6\times5.2x\times0.3=

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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 use long multiplication to solve the multiplication
00:20 Pay attention to the decimal point
00:37 This is the first multiplication
00:53 Again, let's use long multiplication to solve the multiplication
01:03 0 multiplied by any number always equals 0
01:09 Pay attention to the decimal point
01:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

15.6×5.2x×0.3= 15.6\times5.2x\times0.3=

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: 5.2×x 5.2\times x
Therefore, we can apply the distributive property in order to separate the variable, and come back to it later.
Proceed to solve the exercise from left to right.

Solve the left exercise vertically in order to avoid confusion as shown below:

     15.6×    5.2= 81.12 ~~~~~15.6 \\\times~~~~5.2 \\=~81.12

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

We should obtain the following:

81.21×0.3= 81.21\times0.3=

Remember that:

0.3=0.30 0.3=\text{0}.30

Calculate:

24.336 24.336

Let's not forget to add the variable at the end resulting in the following answer:

24.336x 24.336 x

3

Final Answer

24.336x 24.336x

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply decimals first, then attach the variable at end
  • Technique: Calculate 15.6 × 5.2 = 81.12, then multiply by 0.3
  • Check: Count decimal places: 15.6(1) + 5.2(1) + 0.3(1) = 3 places in 24.336x ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to include the variable in final answer
    Don't calculate 15.6 × 5.2 × 0.3 = 24.336 and stop there! This gives just a number instead of the algebraic expression. Always remember that 5.2x means 5.2 times x, so your final answer must include the variable: 24.336x.

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 separately from the variable?

+

Because multiplication is commutative! The expression 15.6 × 5.2x × 0.3 can be rearranged as (15.6 × 5.2 × 0.3) × x. You multiply all the numbers together first, then attach the variable.

How do I keep track of decimal places when multiplying three decimals?

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Count the decimal places in each number: 15.6 has 1 place, 5.2 has 1 place, and 0.3 has 1 place. Your answer should have 3 total decimal places: 24.336.

What if I get confused with the decimal point placement?

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Work step by step! First calculate 15.6×5.2=81.12 15.6 \times 5.2 = 81.12 , then multiply 81.12×0.3=24.336 81.12 \times 0.3 = 24.336 . Breaking it into two steps reduces errors.

Can I use a calculator for decimal multiplication?

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Yes! Calculators are great for checking your work. But make sure you understand the process and don't forget to include the variable x in your final answer.

What does 5.2x actually mean?

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The expression 5.2x means 5.2 times x. There's an invisible multiplication sign between the number and variable. So 5.2x is the same as writing 5.2×x 5.2 \times x .

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