Jordan planned to practice ice skating for 30 hours in a month. He practiced for $7\frac{3}{4}$ hours in the first week and $3\frac{1}{2}$ hours in the second week. We need to find how many more hours he needs to practice to reach his goal.

1. Problem Description

Jordan planned to practice ice skating for 30 hours in a month. He practiced for $7\frac{3}{4}$ hours in the first week and $3\frac{1}{2}$ hours in the second week. We need to find how many more hours he needs to practice to reach his goal.

2. Solution Steps

First, we calculate the total number of hours Jordan practiced in the first two weeks:

$7\frac{3}{4} + 3\frac{1}{2}$

We can rewrite the mixed numbers as improper fractions:

$7\frac{3}{4} = \frac{7 \times 4 + 3}{4} = \frac{28+3}{4} = \frac{31}{4}$

$3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6+1}{2} = \frac{7}{2}$

Now we add the two fractions:

$\frac{31}{4} + \frac{7}{2}$

To add the fractions, we need a common denominator. The least common denominator of 4 and 2 is

4. So we rewrite $\frac{7}{2}$ as $\frac{7 \times 2}{2 \times 2} = \frac{14}{4}$.

$\frac{31}{4} + \frac{14}{4} = \frac{31+14}{4} = \frac{45}{4}$

Now we convert $\frac{45}{4}$ back to a mixed number:

$\frac{45}{4} = 11\frac{1}{4}$

So, Jordan practiced $11\frac{1}{4}$ hours in the first two weeks.

Next, we need to find how many more hours Jordan needs to practice to reach his goal of 30 hours. We subtract the hours he already practiced from his goal:

$30 - 11\frac{1}{4}$

We can rewrite 30 as $29\frac{4}{4}$, so we have:

$29\frac{4}{4} - 11\frac{1}{4} = (29-11) + (\frac{4}{4} - \frac{1}{4}) = 18 + \frac{3}{4} = 18\frac{3}{4}$

3. Final Answer

$18\frac{3}{4}$