Question

an expression is shown.
$5\frac{9}{16} - 2\frac{1}{2}$
what is the value of the expression?
a. $3\frac{1}{16}$
b. $3\frac{1}{14}$
c. $3\frac{8}{14}$
d. $3\frac{8}{16}$

Explanation:

Step1: Convert mixed numbers to improper fractions (or adjust fractions for subtraction)

First, look at the fractional parts. The denominators are 16 and 2. We need a common denominator, which is 16. So convert \(2\frac{1}{2}\) to a fraction with denominator 16. \(2\frac{1}{2}=2 + \frac{1\times8}{2\times8}=2\frac{8}{16}\) (since \(\frac{1}{2}=\frac{8}{16}\) when we multiply numerator and denominator by 8 to get denominator 16).

Step2: Subtract the mixed numbers

Now subtract the whole numbers and the fractional parts separately. The whole numbers: \(5 - 2 = 3\). The fractional parts: \(\frac{9}{16}-\frac{8}{16}=\frac{1}{16}\). Then combine the whole number and the fractional part: \(3+\frac{1}{16}=3\frac{1}{16}\).

Answer:

A. \(3\frac{1}{16}\)