Simplify the Expression: 39.3÷4a + 5a + 8.2 + 13z

Q: Why can't I combine 5a with 9.825/a?

These are unlike terms! The first has a in the numerator, the second has a in the denominator. You can only combine terms with identical variable parts.

Q: What does the colon (:) mean in 39.3:4a?

The colon means division, just like ÷. So 39.3:4a is the same as 39.3 ÷ 4a or $ \frac{39.3}{4a} $.

Q: Should I convert 9.825 to a fraction?

You can if needed, but the decimal form is perfectly acceptable. If you do convert, $ 9.825 = \frac{393}{40} $.

Q: What if I calculated 39.3 ÷ 4 wrong?

Double-check: $ 39.3 ÷ 4 = 9.825 $. You can verify by multiplying: 9.825 × 4 = 39.3 ✓

Algebraic Simplification with Division and Terms

$39.3:4a+5a+8.2+13z=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's simplify the expression, step by step.

00:14 Remember, always tackle multiplication and division first, before you do addition and subtraction. It's like following the rules of a game!

00:41 Next, let's calculate the quotient. Nice and easy!

00:54 And there you have it. This is the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$39.3:4a+5a+8.2+13z=\text{?}$

Step-by-step solution

To solve the problem, we will simplify the expression $39.3 : 4a + 5a + 8.2 + 13z$ . Let's break down the steps:

Step 1: Simplify the division $39.3 : 4a$ .
To solve $39.3 : 4a$ , we treat this as $\frac{39.3}{4a}$ .
Calculating the division: $\frac{39.3}{4} = 9.825$ . Therefore, $\frac{39.3}{4a} = \frac{9.825}{a}$ .
Step 2: Rearrange the terms.
We now have $\frac{9.825}{a} + 5a + 8.2 + 13z$ . No like terms for direct combination exist as these are distinct variables and constants.
Step 3: Write the expression.
The terms should be written in a neat, arranged form as $13z + 8.2 + \frac{9.825}{a} + 5a$ .

Therefore, the simplified expression is $\ 13z + 8.2 + \frac{9.825}{a} + 5a$ .

Final Answer

_{^{$13z+8.2+\frac{9.825}{a}+5a$}}

Key Points to Remember

Essential concepts to master this topic

Division Rule: Convert 39.3 ÷ 4a to fraction $\frac{39.3}{4a} = \frac{9.825}{a}$
Technique: Calculate division first: 39.3 ÷ 4 = 9.825
Check: Verify no like terms can be combined: variables a and z are different ✓

Common Mistakes

Avoid these frequent errors

Trying to combine unlike terms
Don't combine 5a with $\frac{9.825}{a}$ or with 13z = incorrect grouping! These have different variables or variable powers and cannot be added. Always identify like terms first (same variable, same power) before combining.

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 5a with 9.825/a?

These are unlike terms! The first has a in the numerator, the second has a in the denominator. You can only combine terms with identical variable parts.

What does the colon (:) mean in 39.3:4a?

The colon means division, just like ÷. So 39.3:4a is the same as 39.3 ÷ 4a or $\frac{39.3}{4a}$ .

Should I convert 9.825 to a fraction?

You can if needed, but the decimal form is perfectly acceptable. If you do convert, $9.825 = \frac{393}{40}$ .

How do I arrange the final answer?

Group constants together and arrange terms in a logical order. The correct answer places 13z + 8.2 first, then the fraction and variable terms.

What if I calculated 39.3 ÷ 4 wrong?

Double-check: $39.3 ÷ 4 = 9.825$ . You can verify by multiplying: 9.825 × 4 = 39.3 ✓

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