Questions: Determine the solution to the following: 1/2 - 5/32 Answer must be a proper fraction in lowest terms.

$Determine the solution to the following: 1/2 - 5/32 Answer must be a proper fraction in lowest terms.$

Transcript text: Determine the solution to the following: \[ \frac{1}{2}-\frac{5}{32} \] Answer must be a proper fraction in lowest terms. $\square$

Solution

Solution Steps

To solve the given problem, we need to subtract the fractions $\frac{1}{2}$ and $\frac{5}{32}$. First, find a common denominator for the fractions. Then, convert each fraction to have this common denominator and perform the subtraction. Finally, simplify the resulting fraction to its lowest terms.

Step 1: Find a Common Denominator

To subtract the fractions $\frac{1}{2}$ and $\frac{5}{32}$, we first need to find a common denominator. The least common multiple (LCM) of 2 and 32 is 32.

Step 2: Convert Fractions to Common Denominator

Convert $\frac{1}{2}$ to a fraction with a denominator of 32: \[ \frac{1}{2} = \frac{1 \times 16}{2 \times 16} = \frac{16}{32} \]

The fraction $\frac{5}{32}$ already has the denominator 32.

Step 3: Subtract the Fractions

Subtract the fractions: \[ \frac{16}{32} - \frac{5}{32} = \frac{16 - 5}{32} = \frac{11}{32} \]

Step 4: Simplify the Fraction

The fraction $\frac{11}{32}$ is already in its lowest terms since 11 and 32 have no common factors other than 1.