Solve for X in the Equation: 5x = 3/8

Q: Why do I divide by 5 instead of multiply?

You need to isolate x by getting rid of the 5 that's multiplying it. The opposite of multiplication is division, so you divide both sides by 5.

Q: How do I divide a fraction by a whole number?

Dividing by a whole number is the same as multiplying by its reciprocal. So $ \frac{3}{8} ÷ 5 = \frac{3}{8} \times \frac{1}{5} = \frac{3}{40} $.

Q: How do I know if my fraction answer is simplified?

Check if the numerator and denominator have any common factors. Since 3 and 40 share no common factors other than 1, $ \frac{3}{40} $ is already in simplest form.

Q: What if I get confused about which operation to use?

Remember: you want to undo what's being done to x. Since x is being multiplied by 5, you need to divide by 5 to cancel it out.

Linear Equations with Fractional Constants

Solve for X:

$5x=\frac{3}{8}$

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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 X

00:10 If we have an unknown with coefficient A equal to fraction (C divided by B)

00:15 To isolate the unknown X, we divide by coefficient A

00:18 We will use this formula in our exercise

00:22 We'll arrange the equation so that one side will have only the unknown X

00:28 We'll calculate the denominator

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

Solve for X:

$5x=\frac{3}{8}$

Step-by-step solution

$ax=\frac{c}{b}$

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

Final Answer

$\frac{3}{40}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Divide both sides by the coefficient of x
Technique: Divide $\frac{3}{8}$ by 5 to get $\frac{3}{8} \times \frac{1}{5} = \frac{3}{40}$
Check: Substitute back: $5 \times \frac{3}{40} = \frac{15}{40} = \frac{3}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying both sides by 5 instead of dividing
Don't multiply both sides by 5 to get $25x = \frac{15}{8}$ ! This makes the equation more complex and leads to wrong answers. Always divide both sides by the coefficient to isolate x.

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 divide by 5 instead of multiply?

You need to isolate x by getting rid of the 5 that's multiplying it. The opposite of multiplication is division, so you divide both sides by 5.

How do I divide a fraction by a whole number?

Dividing by a whole number is the same as multiplying by its reciprocal. So $\frac{3}{8} ÷ 5 = \frac{3}{8} \times \frac{1}{5} = \frac{3}{40}$ .

Can I convert the fraction to a decimal first?

You could, but it's usually easier to keep it as a fraction. Converting $\frac{3}{8}$ to 0.375 and then dividing by 5 gives 0.075, but $\frac{3}{40}$ is the exact answer.

How do I know if my fraction answer is simplified?

Check if the numerator and denominator have any common factors. Since 3 and 40 share no common factors other than 1, $\frac{3}{40}$ is already in simplest form.

What if I get confused about which operation to use?

Remember: you want to undo what's being done to x. Since x is being multiplied by 5, you need to divide by 5 to cancel it out.

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