Simplify the Algebraic Expression: Solve 49 + 2a - (54a + 9a ÷ (5a × 3))

Q: Why does 9a ÷ 15a become just 3/5?

When dividing terms with the same variable, the variables cancel out! Think of it as $ \frac{9a}{15a} = \frac{9}{15} \times \frac{a}{a} = \frac{9}{15} \times 1 = \frac{3}{5} $.

Q: What if a equals zero in this problem?

If a = 0, then $ 9a ÷ (5a × 3) $ becomes $ 0 ÷ 0 $, which is undefined. That's why we assume a ≠ 0 for this expression to make sense.

Q: How do I convert 49 - 3/5 to a mixed number?

First convert 49 to fifths: $ 49 = \frac{245}{5} $. Then subtract: $ \frac{245}{5} - \frac{3}{5} = \frac{242}{5} = 48\frac{2}{5} $.

Q: Why is the final answer negative with the a term?

We have 2a - 54a = -52a. Since we're subtracting a larger coefficient (54) from a smaller one (2), the result is negative.

Q: Can I solve this without following order of operations?

No! Order of operations is a fundamental rule in mathematics. Ignoring it will give you completely wrong answers. Always do operations inside parentheses first, then multiplication and division, then addition and subtraction.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Negative times positive is always negative

00:14 Write division as a fraction

00:22 Collect terms

00:26 Simplify what's possible

00:37 Factor 9 into 3 and 3

00:40 Simplify what's possible

00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$49+2a-(54a+9a:(5a\cdot3))=\text{?}$

2

Step-by-step solution

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

Step 1: Simplify the expression within the division $9a:(5a\cdot3)$ .
Step 2: Simplify the expression by performing the arithmetic operations.

Let's solve the problem step by step:
**Step 1**: Simplify $9a:(5a\cdot3)$ .
First, compute the product in the denominator: $5a \cdot 3 = 15a$ .
Now, perform the division: $9a \div 15a = \frac{9a}{15a} = \frac{9}{15} = \frac{3}{5}$ , assuming $a \neq 0$ .

**Step 2**: Substitute back into the original expression:
The expression becomes $49 + 2a - (54a + \frac{3}{5})$ .
Now distribute the negative sign: $49 + 2a - 54a - \frac{3}{5}$ Combine like terms: $(49 - \frac{3}{5}) + (2a - 54a)$ Simplify: $48\frac{2}{5} - 52a$

Therefore, the solution to the problem is $48\frac{2}{5}-52a$ .

3

Final Answer

$48\frac{2}{5}-52a$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always follow PEMDAS/BODMAS when simplifying algebraic expressions
Technique: Simplify $9a \div 15a = \frac{9}{15} = \frac{3}{5}$ by canceling variables
Check: Substitute a value: when a=1, expression equals $48\frac{2}{5} - 52$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations in algebraic expressions
Don't solve 54a + 9a ÷ (5a × 3) as (54a + 9a) ÷ (5a × 3) = wrong answer! This changes the meaning completely. Always handle division and multiplication before addition, following PEMDAS strictly.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why does 9a ÷ 15a become just 3/5?

+

When dividing terms with the same variable, the variables cancel out! Think of it as $\frac{9a}{15a} = \frac{9}{15} \times \frac{a}{a} = \frac{9}{15} \times 1 = \frac{3}{5}$ .

What if a equals zero in this problem?

+

If a = 0, then $9a ÷ (5a × 3)$ becomes $0 ÷ 0$ , which is undefined. That's why we assume a ≠ 0 for this expression to make sense.

How do I convert 49 - 3/5 to a mixed number?

+

First convert 49 to fifths: $49 = \frac{245}{5}$ . Then subtract: $\frac{245}{5} - \frac{3}{5} = \frac{242}{5} = 48\frac{2}{5}$ .

Why is the final answer negative with the a term?

+

We have 2a - 54a = -52a. Since we're subtracting a larger coefficient (54) from a smaller one (2), the result is negative.

Can I solve this without following order of operations?

+

No! Order of operations is a fundamental rule in mathematics. Ignoring it will give you completely wrong answers. Always do operations inside parentheses first, then multiplication and division, then addition and subtraction.

How can I check if my final answer is correct?

+

Pick a simple value for a (like a = 1) and substitute it into both the original expression and your answer. If they give the same result, you're correct!

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Simplify the Algebraic Expression: Solve 49 + 2a - (54a + 9a ÷ (5a × 3))

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