Sure, let's solve the equation [tex]\(\frac{9r}{7} = \frac{3}{4}\)[/tex] step-by-step.
1. Isolate the variable [tex]\(r\)[/tex]:
We start by eliminating the fraction on the left side of the equation. To do this, we can multiply both sides of the equation by 7 to clear the denominator:
[tex]\[
\frac{9r}{7} \times 7 = \frac{3}{4} \times 7
\][/tex]
This simplifies to:
[tex]\[
9r = \frac{21}{4}
\][/tex]
2. Solve for [tex]\(r\)[/tex]:
Next, we want to isolate [tex]\(r\)[/tex] by dividing both sides by 9:
[tex]\[
r = \frac{\frac{21}{4}}{9}
\][/tex]
Simplifying the right-hand side, we can write the division as multiplication by the reciprocal of 9:
[tex]\[
r = \frac{21}{4} \times \frac{1}{9}
\][/tex]
3. Simplify the fraction:
Now, we multiply the numerators together and the denominators together:
[tex]\[
r = \frac{21 \times 1}{4 \times 9} = \frac{21}{36}
\][/tex]
4. Reduce the fraction to its simplest form:
We can simplify [tex]\(\frac{21}{36}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{21 \div 3}{36 \div 3} = \frac{7}{12}
\][/tex]
Therefore, the value of [tex]\(r\)[/tex] is:
[tex]\[
r = \frac{7}{12}
\][/tex]
In decimal form, this fraction is approximately [tex]\(0.5833333333333334\)[/tex].
