Sure, let's solve the equation step-by-step:
We are given the equation:
[tex]\[
\frac{r}{5} = \frac{4}{7}
\][/tex]
Our goal is to find the value of [tex]\( r \)[/tex]. Here's the detailed process:
1. Cross Multiply: To remove the fractions, we can use cross-multiplication. Cross-multiplying means to multiply the numerator of one fraction by the denominator of the other fraction.
[tex]\[
r \cdot 7 = 4 \cdot 5
\][/tex]
This simplifies to:
[tex]\[
7r = 20
\][/tex]
2. Solve for [tex]\( r \)[/tex]: Now, we need to isolate [tex]\( r \)[/tex]. To do that, we'll divide both sides of the equation by 7:
[tex]\[
r = \frac{20}{7}
\][/tex]
3. Simplify the Fraction: While [tex]\(\frac{20}{7}\)[/tex] is already in simplest form, we can convert it to a decimal to see the numerical value more clearly.
[tex]\[
\frac{20}{7} \approx 2.857142857142857
\][/tex]
So, the value of [tex]\( r \)[/tex] is approximately [tex]\( 2.857142857142857 \)[/tex].
Hence, the solution for [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{20}{7} \approx 2.857142857142857
\][/tex]
