Replace the A with the proper expression such that the fractions are equivalent.
StartFraction 4 x Over 3 y EndFraction equals StartFraction Upper A Over 15 y squared EndFraction
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Part 1
Aequals
  
enter your response here  ​(Simplify your​ answer.)

To find the value of \( A \) that makes the fractions equivalent, we can use the equation:

\[
\frac{4x}{3y} = \frac{A}{15y^2}
\]

To make these fractions equivalent, their numerators and denominators must match when the fractions are expressed with the same denominator. We can do this by cross-multiplying:

\[
4x \cdot 15y^2 = A \cdot 3y
\]

Simplifying the left side:

\[
60xy^2 = 3yA
\]

Now, divide both sides by \( 3y \) to isolate \( A \):

\[
A = \frac{60xy^2}{3y}
\]

Simplify by dividing \( 60xy^2 \) by \( 3y \):

\[
A = 20xy
\]

So, the answer is:

\[
A = 20xy
\]

Let me know if you want further details or have questions!

Here are 5 related questions:
1. How would the answer change if the denominator on the right side was \( 10y^2 \) instead of \( 15y^2 \)?
2. Can this method be applied to find an unknown \( B \) in other similar fractions?
3. What happens if \( y = 0 \) in this equation?
4. Why is cross-multiplying useful in equations with fractions?
5. How would the solution differ if the numerator on the left side was \( 6x \) instead of \( 4x \)?

**Tip:** When solving equations with fractions, cross-multiplying can help eliminate the denominators, making it easier to solve for unknowns.

Replace the A with the proper expression such that the fractions are equivalent. StartFraction 4 x Over 3 y EndFraction equals StartFraction Upper A Over 15 y squared EndFraction

Discover how to find the expression for A that makes the fractions 4x/3y and A/15y^2 equivalent. This problem covers essential algebraic concepts like cross multiplication and fraction equivalence, making it ideal for students in Grades 8-10.

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