Simplify the Expression: 3.4-3.4a+2.6b-7.5a with Like Terms

Q: Why can't I combine the 'a' terms with the 'b' terms?

Like terms must have exactly the same variable part. Since 'a' and 'b' are different variables, $ -3.4a $ and $ 2.6b $ cannot be combined - they're as different as apples and oranges!

Q: What do I do with the constant term 3.4?

The constant term 3.4 has no variable, so it stands alone. It cannot be combined with terms that have variables like $ -3.4a $ or $ 2.6b $.

Q: How do I add negative decimal coefficients?

Treat it like regular addition with signs: $ -3.4 + (-7.5) = -3.4 - 7.5 = -10.9 $. The negative signs stay with the coefficients!

Q: Can I rearrange the terms in my final answer?

Yes! $ 3.4 - 10.9a + 2.6b $ is the same as $ -10.9a + 2.6b + 3.4 $. The order doesn't matter in addition and subtraction.

Q: What if I have more than two like terms to combine?

Add all the coefficients together! For example, if you had $ 2a - 5a + 3a $, you'd calculate $ (2 - 5 + 3)a = 0a = 0 $.

Combining Like Terms with Decimal Coefficients

$3.4-3.4a+2.6b-7.5a=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:03 Mark the appropriate variables

00:08 Use the commutative law and arrange the appropriate variables together

00:28 Collect like terms

00:42 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

$3.4-3.4a+2.6b-7.5a=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Identify the terms involving the same variables.
Combine like terms, particularly those involving $a$ .
Simplify the expression based on the calculations.

Now, let's work through each step:
Step 1: The given expression is $3.4 - 3.4a + 2.6b - 7.5a$ .
Step 2: Identify the like terms:
- The terms with $a$ are $-3.4a$ and $-7.5a$ .
Step 3: Combine these like terms:
- Calculate $-3.4a - 7.5a = (-3.4 - 7.5)a = -10.9a$ .
Step 4: Substitute back into the expression:
- The simplified expression is $3.4 - 10.9a + 2.6b$ .

Therefore, the solution to the problem is $3.4 - 10.9a + 2.6b$ .

Final Answer

^{$3.4-10.9a+2.6b$}

Key Points to Remember

Essential concepts to master this topic

Like Terms: Same variables with same powers can be combined
Technique: Add coefficients: $-3.4a - 7.5a = -10.9a$
Check: Count terms before and after: 4 terms become 3 terms ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients of different variables
Don't combine -3.4a + 2.6b = -0.8ab! Variables must be identical to combine. The 'a' terms and 'b' terms are completely separate. Always group identical variable terms only.

Practice Quiz

Test your knowledge with interactive questions

$3x+4x+7+2=\text{?}$

FAQ

Everything you need to know about this question

Why can't I combine the 'a' terms with the 'b' terms?

Like terms must have exactly the same variable part. Since 'a' and 'b' are different variables, $-3.4a$ and $2.6b$ cannot be combined - they're as different as apples and oranges!

What do I do with the constant term 3.4?

The constant term 3.4 has no variable, so it stands alone. It cannot be combined with terms that have variables like $-3.4a$ or $2.6b$ .

How do I add negative decimal coefficients?

Treat it like regular addition with signs: $-3.4 + (-7.5) = -3.4 - 7.5 = -10.9$ . The negative signs stay with the coefficients!

Can I rearrange the terms in my final answer?

Yes! $3.4 - 10.9a + 2.6b$ is the same as $-10.9a + 2.6b + 3.4$ . The order doesn't matter in addition and subtraction.

What if I have more than two like terms to combine?

Add all the coefficients together! For example, if you had $2a - 5a + 3a$ , you'd calculate $(2 - 5 + 3)a = 0a = 0$ .

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