Simplify the Expression: 0.2x + 8.6x + 0.65x

Combining Like Terms with Decimal Coefficients

Solve the following:

0.2x+8.6x+0.65x= 0.2x+8.6x+0.65x=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's solve the problem step by step.
00:12 First, we'll tackle the leftmost operation.
00:17 Next, let's split the number into a whole part and a remainder.
00:32 Now, we'll use long addition to find the remainder.
00:57 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following:

0.2x+8.6x+0.65x= 0.2x+8.6x+0.65x=

2

Step-by-step solution

According to the order of operations, we must solve the exercise from left to right:

0.2x+8.6x=8.8x 0.2x+8.6x=8.8x

We'll also break down 8.8 into a smaller addition exercise that will be easier for us to calculate:

8x+0.8x+0.65x= 8x+0.8x+0.65x=

Now we'll use the commutative property since the exercise only involves addition.

Let's focus on the leftmost addition exercise, remembering that:

0.8=0.80 0.8=0.80

Next, we'll calculate the exercise below:

0.80x+0.65x=1.45x 0.80x+0.65x=1.45x

Finally, we are left with the following:

8x+1.45x=9.45x 8x+1.45x=9.45x

3

Final Answer

9.45x 9.45x

Key Points to Remember

Essential concepts to master this topic
  • Combining Rule: Add coefficients of like terms while keeping variable unchanged
  • Technique: Align decimals vertically: 0.20 + 8.60 + 0.65 = 9.45
  • Check: Factor out x: x(0.2 + 8.6 + 0.65) = 9.45x โœ“

Common Mistakes

Avoid these frequent errors
  • Adding decimal coefficients incorrectly
    Don't rush decimal addition like 0.2 + 8.6 + 0.65 = 17.1! Misaligned decimal places create wrong sums. Always line up decimal points vertically: 0.20 + 8.60 + 0.65 = 9.45.

Practice Quiz

Test your knowledge with interactive questions

\( \text{0.6+0}.5= \)

+=

FAQ

Everything you need to know about this question

Why do I only add the numbers and not the x's?

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The variable x stays the same because you're combining like terms. Think of it like: 2 apples + 3 apples = 5 apples. You add the quantities but keep the same type of object!

Should I convert decimals to fractions first?

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No need! Working with decimals directly is often easier and faster. Just be careful to line up decimal points when adding: 0.20+8.60+0.65 0.20 + 8.60 + 0.65

What if the decimals have different numbers of places?

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Add trailing zeros to make them the same length. For example, treat 0.2 as 0.20 and 8.6 as 8.60. This prevents alignment errors when adding.

How can I check my decimal addition?

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Use estimation first: 0.2 + 8.6 + 0.65 is close to 0 + 9 + 1 = 10. Since 9.45 is close to 10, our answer makes sense!

What if I get a different answer than the choices?

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Double-check your decimal alignment and addition. Common errors include misplacing decimal points or forgetting to carry over when adding columns.

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