What number multiplied by the numerator and added to the denominator of two thirds
 makes the resulting fraction equivalent to four thirds
​?
Question content area bottom
Part 1
The number is 
  
enter your response here.

We are given that we need to find a number \( x \) such that when it is multiplied by the numerator of the fraction \( \frac{2}{3} \) and added to the denominator, the resulting fraction equals \( \frac{4}{3} \). 

Let's set up the equation based on the given information:

\[
\frac{x \cdot 2}{x + 3} = \frac{4}{3}
\]

### Step-by-step solution:

1. Multiply both sides by \( 3(x + 3) \) to eliminate the denominators:

\[
3(x \cdot 2) = 4(x + 3)
\]

2. Simplify the equation:

\[
6x = 4x + 12
\]

3. Subtract \( 4x \) from both sides:

\[
2x = 12
\]

4. Divide by 2:

\[
x = 6
\]

So, the number is \( 6 \).

Do you want further details or have any questions? Here are some related questions to practice:

1. What number multiplied by the numerator and added to the denominator of \( \frac{3}{5} \) makes the resulting fraction \( \frac{7}{5} \)?
2. Solve for \( x \): \( \frac{x \cdot 4}{x + 2} = \frac{8}{5} \).
3. How do you set up a similar equation for \( \frac{1}{2} \) and the resulting fraction being \( \frac{5}{6} \)?
4. What is the process to cross-multiply fractions in equations?
5. Can you derive the equation for a general fraction \( \frac{a}{b} \) and another fraction \( \frac{c}{d} \)?

Tip: Always check your solution by plugging the value of \( x \) back into the original equation.

What number multiplied by the numerator and added to the denominator of two thirds makes the resulting fraction equivalent to four thirds?

This math problem involves finding a number that, when multiplied by the numerator of 2/3 and added to the denominator, makes the fraction equal to 4/3. Learn how to solve this rational equation with step-by-step instructions, suitable for Grades 7-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation