Solve -450÷(50/-3)-(-3x-14): Complex Order of Operations

Q: Why does dividing by a negative fraction give a positive result?

When you divide by $ \frac{50}{-3} $, you're really multiplying by its reciprocal $ \frac{-3}{50} $. Since negative times negative equals positive, $ -450 \times \frac{-3}{50} = +27 $!

Q: How do I know when to use the reciprocal?

Whenever you see division by a fraction, flip that fraction and change division to multiplication. Think: "dividing by half is the same as multiplying by 2".

Q: What's the difference between ÷ and : in math?

They mean exactly the same thing! The colon (:) is just another way to write division, commonly used in some countries. Both $ -450 ÷ \frac{50}{-3} $ and $ -450 : \frac{50}{-3} $ are identical.

Q: Why do I get confused with all these negative signs?

Take it one step at a time! First handle the division, then work with parentheses. Remember: two negatives make a positive, and distributing a negative flips all signs inside.

Q: How can I check if 41 + 3x is really correct?

Step 1: Pick any value for x (like x = 0)Step 2: Calculate both the original expression and your answerStep 3: If they match, you're right!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:14 Negative times negative always equals positive

00:21 Negative times positive always equals negative

00:29 Let's factor 450 into factors 9 and 50

00:38 Negative times negative always equals positive

00:49 Let's simplify what we can

00:54 Let's solve 9 times 3

01:00 Let's group the factors

01:03 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

$-450:\frac{50}{-3}-((-3x)+(-14))=\text{?}$

2

Step-by-step solution

To solve the given expression, we'll simplify it step-by-step:

Step 1: Simplify the fraction
$\frac{50}{-3}$ simplifies to $-\frac{50}{3}$ .
Step 2: Perform the division
The expression $-450:\frac{50}{-3}$ can be rewritten as $-450 \times -\frac{3}{50}$ since division by a fraction is equivalent to multiplication by its reciprocal.
Calculate the multiplication
$-450 \times -\frac{3}{50} = 450 \times \frac{3}{50} = 450 \times 0.06 = 27$ .
Step 3: Simplify the expression within parentheses
The expression $(-3x) + (-14)$ simplifies to $-3x - 14$ .
Step 4: Combine all parts
The complete expression $(-450:\frac{50}{-3}) - ((-3x) + (-14))$ simplifies to $27 - (-3x - 14)$ .
Simplify further
This becomes $27 + 3x + 14 = 41 + 3x$ .

Therefore, the solution to the problem is $41 + 3x$ .

3

Final Answer

$41+3x$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Division by a fraction equals multiplication by its reciprocal
Technique: $-450 \div \frac{50}{-3} = -450 \times \frac{-3}{50} = 27$
Check: Substitute x value back into original expression to verify final answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign correctly
Don't just remove parentheses without changing signs = $27 - (-3x - 14)$ becomes $27 - 3x - 14$ (wrong)! This ignores the negative in front of parentheses. Always distribute the negative: $27 - (-3x - 14) = 27 + 3x + 14$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why does dividing by a negative fraction give a positive result?

+

When you divide by $\frac{50}{-3}$ , you're really multiplying by its reciprocal $\frac{-3}{50}$ . Since negative times negative equals positive, $-450 \times \frac{-3}{50} = +27$ !

How do I know when to use the reciprocal?

+

Whenever you see division by a fraction, flip that fraction and change division to multiplication. Think: "dividing by half is the same as multiplying by 2".

What's the difference between ÷ and : in math?

+

They mean exactly the same thing! The colon (:) is just another way to write division, commonly used in some countries. Both $-450 ÷ \frac{50}{-3}$ and $-450 : \frac{50}{-3}$ are identical.

Why do I get confused with all these negative signs?

+

Take it one step at a time! First handle the division, then work with parentheses. Remember: two negatives make a positive, and distributing a negative flips all signs inside.

How can I check if 41 + 3x is really correct?

+

Step 1: Pick any value for x (like x = 0)
Step 2: Calculate both the original expression and your answer
Step 3: If they match, you're right!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties 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

Solve -450÷(50/-3)-(-3x-14): Complex Order of Operations

Order of Operations with Negative Fractions

❤️ Continue Your Math Journey!