Solve the Equation: -y/5 = -25 | Linear Equation Practice

Q: How do I handle the double negative signs?

Remember that negative times negative equals positive! When you have $ -25 \times (-5) $, the two negative signs cancel out to give you positive 125.

Q: Can I solve this by multiplying both sides by 5?

Yes! You can multiply both sides by 5 to get $ -y = -125 $, then multiply both sides by -1 to get $ y = 125 $. This gives the same answer!

Q: What if I get confused by all the negative signs?

Take it one step at a time! Write down each step clearly and double-check your signs. Remember: Negative ÷ Negative = PositiveAlways verify by substituting your answer back

Q: How do I check if y = 125 is correct?

Substitute back into the original equation: $ \frac{-125}{5} = -25 $. Since $ -25 = -25 $ is true, your answer is correct! ✓

Linear Equations with Negative Fractions

$\frac{-y}{5}=-25$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown Y

00:07 We'll divide by the unknown coefficient to isolate Y

00:19 We'll write division as multiplication by the reciprocal

00:27 We'll use long multiplication for calculation

00:33 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

$\frac{-y}{5}=-25$

Step-by-step solution

We begin by multiplying the simple fraction by y:

$\frac{-1}{5}\times y=-25$

We then reduce both terms by $-\frac{1}{5}$

$y=\frac{-25}{-\frac{1}{5}}$

Finally we multiply the fraction by negative 5:

$y=-25\times(-5)=125$

Final Answer

$y=125$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by the denominator to eliminate fractions
Technique: When dividing by a negative, $\frac{-25}{-\frac{1}{5}} = -25 \times (-5) = 125$
Check: Substitute back: $\frac{-125}{5} = -25$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to handle negative signs correctly
Don't multiply -25 by 5 to get -125! This ignores the double negative when dividing by -1/5. The negatives cancel out: -25 ÷ (-1/5) = -25 × (-5) = 125. Always track negative signs carefully through each step.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do we multiply by -5 instead of dividing by -1/5?

Dividing by a fraction is the same as multiplying by its reciprocal! When you divide by $-\frac{1}{5}$ , you multiply by $-5$ . This makes the calculation much easier.

How do I handle the double negative signs?

Remember that negative times negative equals positive! When you have $-25 \times (-5)$ , the two negative signs cancel out to give you positive 125.

Can I solve this by multiplying both sides by 5?

Yes! You can multiply both sides by 5 to get $-y = -125$ , then multiply both sides by -1 to get $y = 125$ . This gives the same answer!

What if I get confused by all the negative signs?

Take it one step at a time! Write down each step clearly and double-check your signs. Remember:

Negative ÷ Negative = Positive
Always verify by substituting your answer back

How do I check if y = 125 is correct?

Substitute back into the original equation: $\frac{-125}{5} = -25$ . Since $-25 = -25$ is true, your answer is correct! ✓

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