Simplify the Expression: 7.3·4a + 2.3 + 8a

Q: Why can't I add 2.3 to 37.2a to get 39.5a?

Because constants and variables are different types! Think of it like trying to add 3 apples + 5 oranges - you can't combine them into 8 "apporanges." Keep them separate: $ 37.2a + 2.3 $

Q: Do I multiply 7.3 × 4 first or 4 × a first?

Always multiply the numbers first! Calculate $ 7.3 \times 4 = 29.2 $, then you have $ 29.2a $. This follows the order of operations correctly.

Q: How do I know which terms are like terms?

Like terms have the same variable part! In this problem, $ 29.2a $ and $ 8a $ are like terms because both have 'a'. The constant $ 2.3 $ stands alone.

Q: Is 37.2a + 2.3 really the final answer?

Yes! This is fully simplified because you cannot combine the variable term $ 37.2a $ with the constant $ 2.3 $. They must stay separate.

Algebraic Simplification with Decimal Coefficients

$7.3\cdot4a+2.3+8a=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's start by simplifying the expression.

00:12 Remember, we always do multiplication and division before we add or subtract.

00:24 Next, let's mark the important variables.

00:29 Using the commutative law, arrange similar variables together.

00:38 Now combine the like terms.

00:48 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7.3\cdot4a+2.3+8a=\text{?}$

Step-by-step solution

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

$7.3×4a + 2.3 + 8a =$

$29.2a + 2.3 + 8a =$

$37.2a + 2.3$

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

Final Answer

$37.2a+2.3$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply coefficients first, then combine like terms separately
Technique: Calculate 7.3 × 4a = 29.2a, then add 29.2a + 8a = 37.2a
Check: Verify constants and variables are grouped correctly: 37.2a + 2.3 ✓

Common Mistakes

Avoid these frequent errors

Adding constants to variable terms
Don't try to combine 2.3 + 37.2a = 39.5a! Constants and variables are different types and cannot be added together. Always keep them separate: the answer is 37.2a + 2.3, not a single term.

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 2.3 to 37.2a to get 39.5a?

Because constants and variables are different types! Think of it like trying to add 3 apples + 5 oranges - you can't combine them into 8 "apporanges." Keep them separate: $37.2a + 2.3$

Do I multiply 7.3 × 4 first or 4 × a first?

Always multiply the numbers first! Calculate $7.3 \times 4 = 29.2$ , then you have $29.2a$ . This follows the order of operations correctly.

How do I know which terms are like terms?

Like terms have the same variable part! In this problem, $29.2a$ and $8a$ are like terms because both have 'a'. The constant $2.3$ stands alone.

Is 37.2a + 2.3 really the final answer?

Yes! This is fully simplified because you cannot combine the variable term $37.2a$ with the constant $2.3$ . They must stay separate.

What if I need to find the value of 'a'?

You can't find a specific value for 'a' from this expression alone - it's simplification, not solving! To find 'a', you'd need an equation like $37.2a + 2.3 = 0$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Expressions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime