Solve for X in the Fraction Equation: 3x/4 = 16

Q: Why do I multiply both sides by 4 instead of just the left side?

You must maintain equality in equations! Whatever you do to one side, you must do to the other. Multiplying only one side by 4 would make different values on each side.

Q: How do I convert 64/3 to a mixed number?

Divide 64 by 3: 64 ÷ 3 = 21 remainder 1. So $ \frac{64}{3} = 21\frac{1}{3} $. The quotient becomes the whole number, the remainder becomes the new numerator.

Q: What if the fraction has a larger denominator like 8 or 12?

The same method works! Just multiply both sides by that denominator. For $ \frac{5x}{8} = 20 $, multiply both sides by 8 to get 5x = 160.

Q: Can I solve this by dividing both sides by 3/4 instead?

Yes! Dividing by $ \frac{3}{4} $ is the same as multiplying by $ \frac{4}{3} $. So 16 × 4/3 = 64/3. Both methods give the same answer!

Q: How do I check if 21⅓ is really correct?

Substitute back: $ \frac{3 \times 21\frac{1}{3}}{4} = \frac{3 \times \frac{64}{3}}{4} = \frac{64}{4} = 16 $ ✓. It works!

Linear Equations with Fractional Coefficients

$\frac{3x}{4}=16$

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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

00:07 Let's isolate the unknown X

00:09 Instead of division, we'll write multiplication by the reciprocal

00:17 We'll use long multiplication for calculation

00:32 We'll break down one fraction into a whole number and remainder

00:36 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

$\frac{3x}{4}=16$

Step-by-step solution

To solve the equation $\frac{3x}{4} = 16$ , we will eliminate the fraction by multiplying both sides by 4.

Step 1: Multiply both sides by 4:
$\left(\frac{3x}{4}\right) \times 4 = 16 \times 4$
Step 2: Simplify:
$3x = 64$
Step 3: Solve for $x$ by dividing both sides by 3:
$x = \frac{64}{3}$
Step 4: Simplify the fraction to a mixed number:
$x = 21\frac{1}{3}$

Therefore, the solution to the equation $\frac{3x}{4} = 16$ is $x = 21\frac{1}{3}$ .

Final Answer

$x=21\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by the denominator to eliminate fractions
Technique: Multiply $\frac{3x}{4} = 16$ by 4 gives 3x = 64
Check: Substitute $x = 21\frac{1}{3}$ back: $\frac{3(64/3)}{4} = 16$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting the denominator instead of multiplying
Don't add 4 to both sides or subtract 4 from the fraction = this doesn't eliminate the denominator! This leaves you stuck with fractions throughout. Always multiply both sides by the denominator to clear it completely.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I multiply both sides by 4 instead of just the left side?

You must maintain equality in equations! Whatever you do to one side, you must do to the other. Multiplying only one side by 4 would make different values on each side.

How do I convert 64/3 to a mixed number?

Divide 64 by 3: 64 ÷ 3 = 21 remainder 1. So $\frac{64}{3} = 21\frac{1}{3}$ . The quotient becomes the whole number, the remainder becomes the new numerator.

What if the fraction has a larger denominator like 8 or 12?

The same method works! Just multiply both sides by that denominator. For $\frac{5x}{8} = 20$ , multiply both sides by 8 to get 5x = 160.

Can I solve this by dividing both sides by 3/4 instead?

Yes! Dividing by $\frac{3}{4}$ is the same as multiplying by $\frac{4}{3}$ . So 16 × 4/3 = 64/3. Both methods give the same answer!

How do I check if 21⅓ is really correct?

Substitute back: $\frac{3 \times 21\frac{1}{3}}{4} = \frac{3 \times \frac{64}{3}}{4} = \frac{64}{4} = 16$ ✓. It works!

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