24. Change each algebraic fraction into an equivalent fraction with the denominator of $$ 24 a $$ $$ \frac{7 a}{3 b^{2}} $$

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UpStudy AI · Accepted Answer

To change
$$
\frac{7a}{3b^2}
$$
into an equivalent fraction with denominator $$24a$$, we need to multiply the fraction by a form of 1 that will convert the denominator as desired.

1. Write the equation for the multiplier:
   $$
   3b^2 \times \text{(multiplier)} = 24a.
   $$
   Solving for the multiplier:
   $$
   \text{multiplier} = \frac{24a}{3b^2} = \frac{8a}{b^2}.
   $$

2. Multiply numerator and denominator by $$\frac{8a}{b^2}$$:
   $$
   \frac{7a}{3b^2} = \frac{7a}{3b^2} \times \frac{8a}{b^2} = \frac{7a \times \frac{8a}{b^2}}{3b^2 \times \frac{8a}{b^2}}.
   $$

3. Simplify the denominator:
   $$
   3b^2 \times \frac{8a}{b^2} = 24a.
   $$

4. Simplify the numerator:
   $$
   7a \times \frac{8a}{b^2} = \frac{56a^2}{b^2}.
   $$

Thus, the fraction with the denominator $$24a$$ is
$$
\frac{56a^2/b^2}{24a} \quad \text{or} \quad \frac{56a^2}{24ab^2}.
$$

This is the equivalent fraction with denominator $$24a$$.
To change $$\frac{7a}{3b^{2}}$$ to an equivalent fraction with denominator $$24a$$, multiply numerator and denominator by $$\frac{8a}{b^{2}}$$. The resulting fraction is $$\frac{56a^{2}}{24ab^{2}}$$.

24. Change each algebraic fraction into an equivalent fraction with the denominator of \( 24 a \) \( \frac{7 a}{3 b^{2}} \)

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