To solve the equation [tex]\(\frac{30}{29} = \frac{60}{\square}\)[/tex], we need to find the value of the missing denominator.
Step-by-Step Solution:
1. Write Down the Proportion:
We are given [tex]\(\frac{30}{29} = \frac{60}{\square}\)[/tex].
2. Set Up the Equation Using Cross Multiplication:
According to the property of proportions, if [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], then [tex]\(a \cdot d = b \cdot c\)[/tex].
Applying this property here:
[tex]\[
30 \cdot \square = 29 \cdot 60
\][/tex]
3. Solve for the Missing Denominator:
We need to isolate the variable (the missing denominator). To do this, divide both sides of the equation by 30:
[tex]\[
\square = \frac{29 \cdot 60}{30}
\][/tex]
4. Perform the Multiplication and Division:
Calculate the numerator:
[tex]\[
29 \cdot 60 = 1740
\][/tex]
Then divide the result by 30:
[tex]\[
\frac{1740}{30} = 58
\][/tex]
So, the missing denominator is [tex]\(58\)[/tex].
Therefore, [tex]\(\frac{30}{29} = \frac{60}{58}\)[/tex].
