To solve the equation [tex]\(\frac{4}{r} = \frac{5}{7}\)[/tex] for [tex]\(r\)[/tex], follow these steps:
1. Set up the equation:
[tex]\[\frac{4}{r} = \frac{5}{7}\][/tex]
2. Cross-multiply to solve for [tex]\(r\)[/tex]:
Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction. Thus, we get:
[tex]\[4 \times 7 = 5 \times r\][/tex]
3. Simplify the resulting equation:
[tex]\[28 = 5r\][/tex]
4. Isolate [tex]\(r\)[/tex] by dividing both sides of the equation by 5:
[tex]\[\frac{28}{5} = r\][/tex]
5. Simplify the fraction to get the value of [tex]\(r\)[/tex]:
[tex]\[r = 5.6\][/tex]
Hence, the solution to the equation [tex]\(\frac{4}{r} = \frac{5}{7}\)[/tex] is:
[tex]\[r = 5.6\][/tex]
