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

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

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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