Question

at the beginning of practice today, bryces soccer team spent $\frac{1}{2}$ of an hour doing warm - up exercises and another $\frac{3}{4}$ of an hour doing drills. then they played a practice game for the last $1\frac{3}{4}$ hours of practice. in all, how much time did bryces soccer team spend practicing today?
$\frac{square}{square}$ hours
fraction
mixed number
whole number

Explanation:

Step1: Convert to common denominator

To add the fractions, we first convert \(\frac{1}{2}\) to a fraction with denominator 4. \(\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}\)

Step2: Add warm - up and drill time

Add the time for warm - up (\(\frac{2}{4}\) hour) and drills (\(\frac{3}{4}\) hour): \(\frac{2}{4}+\frac{3}{4}=\frac{2 + 3}{4}=\frac{5}{4}\)

Step3: Add practice game time

Now add the time for the practice game (\(1\frac{3}{4}=\frac{1\times4+3}{4}=\frac{7}{4}\) hours) to the previous sum: \(\frac{5}{4}+\frac{7}{4}=\frac{5 + 7}{4}=\frac{12}{4}=3\) (Wait, but let's check again. Wait, \(\frac{5}{4}+\frac{7}{4}=\frac{12}{4} = 3\)? Wait, no, wait: \(\frac{1}{2}\) hour is 30 minutes, \(\frac{3}{4}\) hour is 45 minutes, \(1\frac{3}{4}\) hours is 1 hour and 45 minutes. 30+45 = 75 minutes (which is \(\frac{5}{4}\) hours or 1 hour and 15 minutes), then 1 hour 15 minutes+1 hour 45 minutes = 3 hours. But let's do fraction addition correctly:

Wait, \(\frac{1}{2}+\frac{3}{4}+1\frac{3}{4}\)

First, \(\frac{1}{2}=\frac{2}{4}\), so \(\frac{2}{4}+\frac{3}{4}=\frac{5}{4}\), then \(\frac{5}{4}+1\frac{3}{4}=\frac{5}{4}+\frac{7}{4}=\frac{12}{4}=3\). Wait, but the problem's answer box is a fraction. Wait, maybe I made a mistake. Wait, no, 3 is a whole number, which can be written as \(\frac{3}{1}\), but maybe the problem expects a mixed number or fraction. Wait, let's re - calculate:

\(\frac{1}{2}+\frac{3}{4}+1\frac{3}{4}=\frac{2}{4}+\frac{3}{4}+\frac{7}{4}=\frac{2 + 3+7}{4}=\frac{12}{4}=3=\frac{3}{1}\)

Answer:

\(\frac{3}{1}\) hours (or 3 hours, but in fraction form \(\frac{3}{1}\))