To solve the equation [tex]\(\frac{r}{5} = \frac{4}{7}\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
\frac{r}{5} = \frac{4}{7}
\][/tex]
2. Cross-multiply to eliminate the fractions. This involves multiplying both sides of the equation by the denominators of the fractions. Doing so yields:
[tex]\[
r \cdot 7 = 5 \cdot 4
\][/tex]
3. Perform the multiplication on both sides:
[tex]\[
7r = 20
\][/tex]
4. Solve for [tex]\(r\)[/tex] by isolating [tex]\(r\)[/tex]. To do this, divide both sides of the equation by 7:
[tex]\[
r = \frac{20}{7}
\][/tex]
5. Simplify the fraction if necessary. In this case, dividing 20 by 7 gives:
[tex]\[
r \approx 2.857142857142857
\][/tex]
Therefore, the value of [tex]\(r\)[/tex] is approximately [tex]\(2.857142857142857\)[/tex].
In summary, the solution to the equation [tex]\(\frac{r}{5} = \frac{4}{7}\)[/tex] is:
[tex]\[
r = \frac{20}{7} \approx 2.857142857142857
\][/tex]
To verify, you can check that:
[tex]\[
20 = 7r \quad \text{when} \quad r = 2.857142857142857
\][/tex]
