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:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve a problem together!

00:13 Chapter Title.

00:16 First, let's arrange the equation to have the unknown X on one side.

00:27 Now, let's simplify as much as we can.

00:36 And there you have it! That's the solution to our 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

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

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!

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