Solve the Equation: (-?/4)×38÷(-9)=-5

Q: Why do we multiply by -9 first instead of dividing?

We're working backwards to isolate the unknown! Since the original equation divides by -9, we multiply both sides by -9 to 'undo' that division step.

Q: How do I handle the negative signs correctly?

Follow the sign rules carefully: negative × negative = positive, but positive × negative = negative. In our problem: $ (-5) \times (-9) = +45 $, then $ 45 \times (-4) = -180 $.

Q: How do I simplify fractions like 180/38?

Find the greatest common factor (GCF) of both numbers. Here, 180 = 2×90 and 38 = 2×19, so GCF is 2. Divide both numerator and denominator by 2: $ \frac{180}{38} = \frac{90}{19} $.

Q: Can I check my answer somehow?

Yes! Substitute $ ? = -\frac{90}{19} $ back into the original equation. Calculate $ \frac{-90/19}{-4} \times 38 ÷ (-9) $ and verify it equals -5.

Algebraic Equations with Mixed Operations

$\frac{\text{?}}{-4}\cdot38:-9=-5$

❤️ 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

00:00 Find the unknown

00:04 Move the product to the numerator

00:13 We want to isolate the unknown

00:37 Negative times negative always equals positive

00:42 Positive times negative always equals negative

01:00 Calculate the products

01:05 Isolate the unknown

01:17 Factor 180 into 2 and 90

01:20 Factor 38 into 2 and 19

01:24 Reduce what's possible

01:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{\text{?}}{-4}\cdot38:-9=-5$

Step-by-step solution

Let's add 38 to the multiplication exercise in the fraction in the following way:

$\frac{?\times38}{-4}:-9=-5$

Let's multiply by minus 9:

$\frac{?\times38}{-4}=-5\times-9$

Let's multiply by minus 4:

$?\times38=-5\times-9\times-4$

Let's solve the right side first.

Note that we are first multiplying between two negative numbers, so the result must be a positive number:

$-5\times-9=+45$

Now we are multiplying a positive number by a negative number, so the result must be a negative number:

$45\times-4=-180$

Now we got the exercise:

$38?=-180$

Let's divide by 38:

$?=-\frac{180}{38}$

Let's break down 180 and 38 into multiplication exercises:

$?=-\frac{2\times90}{2\times19}$

Let's reduce between the 2 in the numerator and denominator:

$?=-\frac{90}{19}$

Final Answer

$-\frac{90}{19}$

Key Points to Remember

Essential concepts to master this topic

Order: Isolate the unknown by working backwards through operations
Technique: Multiply first: $-5 \times (-9) = +45$
Check: Substitute $-\frac{90}{19}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting sign rules when multiplying negatives
Don't multiply -5 × (-9) and get -45! Two negatives make a positive, so the result should be +45. Always remember: negative × negative = positive, positive × negative = negative.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

Why do we multiply by -9 first instead of dividing?

We're working backwards to isolate the unknown! Since the original equation divides by -9, we multiply both sides by -9 to 'undo' that division step.

How do I handle the negative signs correctly?

Follow the sign rules carefully: negative × negative = positive, but positive × negative = negative. In our problem: $(-5) \times (-9) = +45$ , then $45 \times (-4) = -180$ .

Why is the answer a fraction instead of a whole number?

Not all equations have whole number solutions! When we divide -180 by 38, we get $-\frac{180}{38}$ which simplifies to $-\frac{90}{19}$ after reducing by 2.

How do I simplify fractions like 180/38?

Find the greatest common factor (GCF) of both numbers. Here, 180 = 2×90 and 38 = 2×19, so GCF is 2. Divide both numerator and denominator by 2: $\frac{180}{38} = \frac{90}{19}$ .

Can I check my answer somehow?

Yes! Substitute $? = -\frac{90}{19}$ back into the original equation. Calculate $\frac{-90/19}{-4} \times 38 ÷ (-9)$ and verify it equals -5.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) 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 the Equation: (-?/4)×38÷(-9)=-5

Algebraic Equations with Mixed Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we multiply by -9 first instead of dividing?

How do I handle the negative signs correctly?

Why is the answer a fraction instead of a whole number?

How do I simplify fractions like 180/38?

Can I check my answer somehow?

🌟 Unlock Your Math Potential

More Questions

Multiplication and Division of Signed Mumbers

Calculate Test Score: 5 Points Right, -2 Points Wrong in 20-Question Exam

Sequential Division Problem: Tracking Position After Dividing by 3, 1/8, and 4

Calculate Test Points: 5 for Correct, -2 for Wrong, -4 for Unattempted Answers

Solve the Multiplication Equation: Finding the Factor in -12·8=-24

All Operations in Signed Numbers

Solve: -6·6÷-3÷? = 24 | Sequential Division Challenge

Solve the Equation: Finding the Missing Sign in (-5)·(?3)=15

Solve for Missing Divisor in -9×-7÷?=-3: Step-by-Step Solution

Solve the Multiplication Equation: 10 × ? = -100