Simplify the Expression: 7.8 + 3.5a - 80b - 7.8b + 3.9a

Q: Why can't I add the 'a' terms to the 'b' terms?

Variables represent different unknown values. Adding 3.5a + (-80b) would be like adding 3.5 apples + (-80) bananas - they're completely different things! Only combine terms with identical variables.

Q: How do I handle negative signs when combining like terms?

Treat negative signs as part of the coefficient. For -80b - 7.8b, think of it as $ (-80) + (-7.8) = -87.8 $, so the result is $ -87.8b $.

Q: Do I need to write the terms in a specific order?

Not required, but it's good practice to write constant terms first, then variables in alphabetical order: 7.8 + 7.4a - 87.8b looks neat and organized.

Q: How can I check if I combined the decimals correctly?

Double-check your decimal arithmetic! For the a-terms: $ 3.5 + 3.9 = 7.4 $. For b-terms: $ -80 + (-7.8) = -87.8 $. Use a calculator if needed!

Combining Like Terms with Decimal Coefficients

^{$7.8+3.5a-80b-7.8b+3.9a=\text{?}$}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's simplify this expression together.

00:12 First, identify and mark the right variables.

00:16 Now, use the commutative law to rearrange them neatly.

00:39 Group the same kinds of terms, also known as like terms.

00:52 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

^{$7.8+3.5a-80b-7.8b+3.9a=\text{?}$}

Step-by-step solution

To solve this problem, we need to simplify the given expression:

1. Identify and group similar terms:

Constant term: $7.8$
Terms with $a$ : $3.5a + 3.9a$
Terms with $b$ : $-80b - 7.8b$

2. Simplify each group:

Combine terms with $a$ :
$3.5a + 3.9a = (3.5 + 3.9)a = 7.4a$
Combine terms with $b$ :
$-80b - 7.8b = (-80 - 7.8)b = -87.8b$

3. The constant term remains $7.8$ .

4. Therefore, the simplified expression is:
$7.8 + 7.4a - 87.8b$

Thus, the correct answer is $\boxed{7.8 + 7.4a - 87.8b}$

Final Answer

^{$7.8+7.4a-87.8b$}

Key Points to Remember

Essential concepts to master this topic

Rule: Group terms with same variables: constants, a-terms, b-terms
Technique: Add coefficients: 3.5a + 3.9a = (3.5 + 3.9)a = 7.4a
Check: Verify each group separately: 3.5 + 3.9 = 7.4 and -80 + (-7.8) = -87.8 ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients from different variables together
Don't combine 3.5a with -80b to get -76.5ab = wrong variable mixing! Different variables cannot be combined. Always keep terms with different variables separate and only add coefficients of identical variable terms.

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 add the 'a' terms to the 'b' terms?

Variables represent different unknown values. Adding 3.5a + (-80b) would be like adding 3.5 apples + (-80) bananas - they're completely different things! Only combine terms with identical variables.

How do I handle negative signs when combining like terms?

Treat negative signs as part of the coefficient. For -80b - 7.8b, think of it as $(-80) + (-7.8) = -87.8$ , so the result is $-87.8b$ .

What if there's only one term with a variable?

If there's only one term (like if we had just 7.8), it stays exactly the same! You can only combine terms when you have two or more terms with the same variable.

Do I need to write the terms in a specific order?

Not required, but it's good practice to write constant terms first, then variables in alphabetical order: 7.8 + 7.4a - 87.8b looks neat and organized.

How can I check if I combined the decimals correctly?

Double-check your decimal arithmetic! For the a-terms: $3.5 + 3.9 = 7.4$ . For b-terms: $-80 + (-7.8) = -87.8$ . Use a calculator if needed!

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