Solve 2/5x = 3/8: Unraveling the Fraction Equation

Q: What exactly is a reciprocal and how do I find it?

A reciprocal is simply flipping the fraction upside down! For $ \frac{2}{5} $, the reciprocal is $ \frac{5}{2} $. When you multiply a number by its reciprocal, you always get 1.

Q: Why multiply by the reciprocal instead of dividing?

Dividing by a fraction means multiplying by its reciprocal anyway! So $ x ÷ \frac{2}{5} = x \times \frac{5}{2} $. It's faster to go straight to multiplication.

Q: How do I multiply fractions like 5/2 × 3/8?

Multiply straight across: numerator × numerator and denominator × denominator. So $ \frac{5}{2} \times \frac{3}{8} = \frac{5 \times 3}{2 \times 8} = \frac{15}{16} $

Q: What if I get a mixed number or improper fraction?

For equations, keep your answer as an improper fraction in lowest terms. Mixed numbers are harder to verify and work with in further calculations.

Fraction Equations with Reciprocal Multiplication

Solve for X:

$\frac{2}{5}x=\frac{3}{8}$

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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

00:07 We'll multiply by the reciprocal fraction to eliminate the fraction

00:20 We'll reduce what we can

00:27 We'll make sure to multiply numerator by numerator and denominator by denominator

00:31 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:

$\frac{2}{5}x=\frac{3}{8}$

Step-by-step solution

To solve the equation $\frac{2}{5}x = \frac{3}{8}$ , we need to isolate $x$ . We can achieve this by multiplying both sides by the reciprocal of $\frac{2}{5}$ .

Step 1: Multiply both sides by $\frac{5}{2}$ , which is the reciprocal of $\frac{2}{5}$ :

$\frac{5}{2} \times \frac{2}{5}x = \frac{5}{2} \times \frac{3}{8}$

Step 2: Simplify the left side. The $\frac{5}{2}$ and $\frac{2}{5}$ cancel each other out:

$x = \frac{5 \times 3}{2 \times 8}$

Step 3: Simplify the right side by multiplying the numerators and denominators:

$x = \frac{15}{16}$

Therefore, the solution to the equation is $\boxed{\frac{15}{16}}$ , which matches choice 3.

Final Answer

$\frac{15}{16}$

Key Points to Remember

Essential concepts to master this topic

Reciprocal Rule: To isolate x, multiply by the reciprocal of the coefficient
Technique: $\frac{2}{5}x = \frac{3}{8}$ becomes $x = \frac{5}{2} \times \frac{3}{8} = \frac{15}{16}$
Check: Substitute back: $\frac{2}{5} \times \frac{15}{16} = \frac{30}{80} = \frac{3}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the coefficient instead of multiplying by its reciprocal
Don't divide both sides by $\frac{2}{5}$ = multiplying by 5 then dividing by 2! This creates messy calculations and often leads to errors. Always multiply by the reciprocal $\frac{5}{2}$ in one clean step.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

What exactly is a reciprocal and how do I find it?

A reciprocal is simply flipping the fraction upside down! For $\frac{2}{5}$ , the reciprocal is $\frac{5}{2}$ . When you multiply a number by its reciprocal, you always get 1.

Why multiply by the reciprocal instead of dividing?

Dividing by a fraction means multiplying by its reciprocal anyway! So $x ÷ \frac{2}{5} = x \times \frac{5}{2}$ . It's faster to go straight to multiplication.

How do I multiply fractions like 5/2 × 3/8?

Multiply straight across: numerator × numerator and denominator × denominator. So $\frac{5}{2} \times \frac{3}{8} = \frac{5 \times 3}{2 \times 8} = \frac{15}{16}$

Do I need to simplify my final answer?

Yes! Always check if your fraction can be simplified by finding common factors. In this case, $\frac{15}{16}$ is already in lowest terms since 15 and 16 share no common factors.

What if I get a mixed number or improper fraction?

For equations, keep your answer as an improper fraction in lowest terms. Mixed numbers are harder to verify and work with in further calculations.

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