Question

Solve for the variable in the following proportion.
1/4 is to 1 1/4 as 2 is to b

Answer 1

To solve for \( b \) in the proportion \( \frac{1}{4} : 1 \frac{1}{4} = 2 : b \), we first convert \( 1 \frac{1}{4} \) to an improper fraction:

\[
1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}
\]

Now we rewrite the proportion:

\[
\frac{1}{4} : \frac{5}{4} = 2 : b
\]

Using the property of proportions, we can write the equation:

\[
\frac{\frac{1}{4}}{\frac{5}{4}} = \frac{2}{b}
\]

To simplify the left side, we multiply by the reciprocal of the denominator:

\[
\frac{1}{4} \times \frac{4}{5} = \frac{1 \times 4}{4 \times 5} = \frac{1}{5}
\]

Now we have the equation:

\[
\frac{1}{5} = \frac{2}{b}
\]

Cross-multiplying gives:

\[
1 \cdot b = 2 \cdot 5
\]

Therefore:

\[
b = 10
\]

Thus, the value of \( b \) is:

\[
\boxed{10}
\]