Solve the Fraction Equation: Finding X in 1/8x = 3/4

Q: Why do I multiply by 8 instead of dividing by 1/8?

Both methods work, but multiplying by 8 is much simpler! Dividing by $ \frac{1}{8} $ means multiplying by its reciprocal (8), so you're doing the same thing anyway.

Q: What if the coefficient was a different fraction like 2/3?

Same principle! If you had $ \frac{2}{3}x = 5 $, multiply both sides by 3 to get $ 2x = 15 $, then divide by 2 to get $ x = \frac{15}{2} $.

Q: How do I check my answer when it's not a whole number?

Substitute your answer back into the original equation. Convert to decimals if needed: $ \frac{1}{8} \times 6 = 0.125 \times 6 = 0.75 = \frac{3}{4} $ ✓

Q: What's the difference between 1/8x and x/8?

$ \frac{1}{8}x $ means "one-eighth times x" while $ \frac{x}{8} $ means "x divided by 8". They're the same value but written differently!

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{1}{8}x=\frac{3}{4}$

❤️ 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 Solve

00:07 Chapter Title

00:10 Let's arrange the equation so that one side has only the unknown X

00:21 Let's simplify what we can

00:30 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

Solve for X:

$\frac{1}{8}x=\frac{3}{4}$

Step-by-step solution

We use the formula:

$\frac{a}{b}x=\frac{c}{d}$

$x=\frac{bc}{ad}$

We multiply the numerator by X and write the exercise as follows:

$\frac{x}{8}=\frac{3}{4}$

We multiply both sides by 8 to eliminate the fraction's denominator:

$8\times\frac{x}{8}=\frac{3}{4}\times8$

On the left side, it seems that the 8 is reduced and the right section is multiplied:

$x=\frac{24}{4}=6$

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by the denominator to isolate x
Technique: Multiply both sides by 8: $x = \frac{3}{4} \times 8 = 6$
Check: Substitute back: $\frac{1}{8}(6) = \frac{6}{8} = \frac{3}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the coefficient instead of multiplying
Don't divide both sides by 1/8 thinking it's like regular division = confusing fractions! Dividing by a fraction means multiplying by its reciprocal, which is harder. Always multiply both sides by the denominator to clear the fraction.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I multiply by 8 instead of dividing by 1/8?

Both methods work, but multiplying by 8 is much simpler! Dividing by $\frac{1}{8}$ means multiplying by its reciprocal (8), so you're doing the same thing anyway.

What if the coefficient was a different fraction like 2/3?

Same principle! If you had $\frac{2}{3}x = 5$ , multiply both sides by 3 to get $2x = 15$ , then divide by 2 to get $x = \frac{15}{2}$ .

How do I check my answer when it's not a whole number?

Substitute your answer back into the original equation. Convert to decimals if needed: $\frac{1}{8} \times 6 = 0.125 \times 6 = 0.75 = \frac{3}{4}$ ✓

Can I cross-multiply to solve this?

Not directly! Cross-multiplication works for equations like $\frac{x}{8} = \frac{3}{4}$ , but your original equation has the form $\frac{1}{8}x = \frac{3}{4}$ . Use the multiplication method instead.

What's the difference between 1/8x and x/8?

$\frac{1}{8}x$ means "one-eighth times x" while $\frac{x}{8}$ means "x divided by 8". They're the same value but written differently!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) 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