Solve the Fraction Equation: 4/9x = 18 to Find X

Q: What's the difference between coefficient and reciprocal?

The coefficient is the number multiplying x (here it's $ \frac{4}{9} $). The reciprocal flips the fraction: $ \frac{4}{9} $ becomes $ \frac{9}{4} $. We multiply by the reciprocal to cancel out the coefficient!

Q: Why can't I just move the fraction to the other side?

You can, but you'd be dividing by $ \frac{4}{9} $, which means multiplying by its reciprocal anyway! It's clearer to multiply both sides by $ \frac{9}{4} $ directly.

Q: How do I multiply 18 by 9/4 without a calculator?

Think of it as $ \frac{18 \times 9}{4} = \frac{162}{4} $. Since 162 ÷ 4 = 40.5, you can also calculate $ 18 \times 2.25 = 40.5 $ (because $ \frac{9}{4} = 2.25 $).

Q: What if my answer doesn't look right?

Always check by substituting back! If $ \frac{4}{9} \times 40.5 $ equals 18, then x = 40.5 is correct. Don't trust your intuition—trust the math!

Q: Can x be bigger than the number on the right side?

Absolutely! When the coefficient is a proper fraction (less than 1), like $ \frac{4}{9} $, the solution will be larger than the constant term. This makes perfect sense mathematically.

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{4}{9}x=18$

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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 We'll multiply by the reciprocal fraction to eliminate the fraction

00:16 We'll reduce what we can

00:23 We'll factor 18 into factors 9 and 2

00:30 We'll factor 4 into factors 2 and 2

00:37 We'll reduce what we can

00:48 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:

$\frac{4}{9}x=18$

Step-by-step solution

This linear equation problem can be solved by isolating the variable $x$ . Here's how we proceed:

Step 1: Multiply both sides of the equation by the reciprocal of the coefficient of $x$ . In this case, the coefficient is $\frac{4}{9}$ , so its reciprocal is $\frac{9}{4}$ .

$\frac{9}{4} \times \frac{4}{9} x = 18 \times \frac{9}{4}$

This simplifies to:

$x = \frac{9}{4} \times 18$

Step 2: Perform the multiplication on the right side of the equation.

$x = \frac{9 \times 18}{4}$

Simplify the expression:

$x = \frac{162}{4}$

$x = 40.5$

Therefore, the value of $x$ that satisfies the equation is $40.5$ .

Final Answer

$40.5$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by reciprocal of fractional coefficient
Technique: Reciprocal of $\frac{4}{9}$ is $\frac{9}{4}$ , so $x = 18 \times \frac{9}{4}$
Check: Substitute x = 40.5: $\frac{4}{9} \times 40.5 = 18$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the fraction instead of multiplying by its reciprocal
Don't divide both sides by $\frac{4}{9}$ = getting $x = 18 ÷ \frac{4}{9}$ wrong! Division by fractions is confusing and error-prone. Always multiply both sides by the reciprocal $\frac{9}{4}$ to isolate x cleanly.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

What's the difference between coefficient and reciprocal?

The coefficient is the number multiplying x (here it's $\frac{4}{9}$ ). The reciprocal flips the fraction: $\frac{4}{9}$ becomes $\frac{9}{4}$ . We multiply by the reciprocal to cancel out the coefficient!

Why can't I just move the fraction to the other side?

You can, but you'd be dividing by $\frac{4}{9}$ , which means multiplying by its reciprocal anyway! It's clearer to multiply both sides by $\frac{9}{4}$ directly.

How do I multiply 18 by 9/4 without a calculator?

Think of it as $\frac{18 \times 9}{4} = \frac{162}{4}$ . Since 162 ÷ 4 = 40.5, you can also calculate $18 \times 2.25 = 40.5$ (because $\frac{9}{4} = 2.25$ ).

What if my answer doesn't look right?

Always check by substituting back! If $\frac{4}{9} \times 40.5$ equals 18, then x = 40.5 is correct. Don't trust your intuition—trust the math!

Can x be bigger than the number on the right side?

Absolutely! When the coefficient is a proper fraction (less than 1), like $\frac{4}{9}$ , the solution will be larger than the constant term. This makes perfect sense mathematically.

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