Question

weekly exercise
number of hours
0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1
melissa kept track of the amount of time she spent exercising last week on a line plot. in hours, what is the total amount of time that she exercised?
a 4 1/8 hours
b 4 1/2 hours
c 5 1/2 hours
d 5 2/3 hours

Explanation:

Step1: Count X's per hour

• At $\frac{1}{4}$: 2 X's. Total: $2\times\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$
• At $\frac{3}{4}$: 1 X. Total: $1\times\frac{3}{4}=\frac{3}{4}$
• At $\frac{7}{8}$: 1 X. Total: $1\times\frac{7}{8}=\frac{7}{8}$
• At 1: 2 X's. Total: $2\times1 = 2$

Step2: Convert to eighths

• $\frac{1}{2}=\frac{4}{8}$, $\frac{3}{4}=\frac{6}{8}$, $2=\frac{16}{8}$

Step3: Sum all fractions

• $\frac{4}{8}+\frac{6}{8}+\frac{7}{8}+\frac{16}{8}=\frac{4 + 6+7 + 16}{8}=\frac{33}{8}=4\frac{1}{8}$? Wait, wait, missed $\frac{1}{4}$ was 2, $\frac{3}{4}$ 1, $\frac{7}{8}$ 1, 1 two times? Wait, recheck line plot:

Wait, original line plot:

• $\frac{1}{4}$: two X's (so $2\times\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$)
• $\frac{3}{4}$: one X ($\frac{3}{4}$)
• $\frac{7}{8}$: one X ($\frac{7}{8}$)
• 1: two X's ($2\times1 = 2$)

Wait, no, maybe I missed other X's. Wait the line plot has:

• At $\frac{1}{4}$: two X's (so 2 times $\frac{1}{4}$)
• At $\frac{3}{4}$: one X (1 times $\frac{3}{4}$)
• At $\frac{7}{8}$: one X (1 times $\frac{7}{8}$)
• At 1: two X's (2 times 1)

Wait, no, maybe the X's are:
Wait the line plot labels: 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1.
Looking at X positions:

• $\frac{1}{4}$: two X's (so 2 * 1/4)
• $\frac{3}{4}$: one X (1 * 3/4)
• $\frac{7}{8}$: one X (1 * 7/8)
• 1: two X's (2 * 1)

Wait, no, maybe I miscounted. Wait the user's line plot:
"X" at 1/4 (two X's), 3/4 (one), 7/8 (one), 1 (two). Wait, no, let's list all X's:

• 1/4: 2 X's
• 3/4: 1 X
• 7/8: 1 X
• 1: 2 X's

Wait, but maybe I missed 3/8? No, the X's are:
Wait the line plot:
First two X's at 1/4, then one at 3/4, one at 7/8, two at 1. Wait, no, original problem's line plot:
Wait the user's image:
Melissa's line plot:

• At $\frac{1}{4}$: two X's (so 2 * 1/4)
• At $\frac{3}{4}$: one X (1 * 3/4)
• At $\frac{7}{8}$: one X (1 * 7/8)
• At 1: two X's (2 * 1)

Wait, no, maybe I made a mistake. Let's recalculate:
2*(1/4) = 1/2
1*(3/4) = 3/4
1*(7/8) = 7/8
2*(1) = 2
Now convert all to eighths:
1/2 = 4/8
3/4 = 6/8
7/8 = 7/8
2 = 16/8
Sum: 4 + 6 + 7 + 16 = 33/8 = 4 1/8? But option A is 4 1/8. Wait, but let's check again. Wait, maybe the X's are:
Wait, the line plot:

• $\frac{1}{4}$: 2 X's (2*(1/4) = 1/2)
• $\frac{3}{4}$: 1 X (3/4)
• $\frac{7}{8}$: 1 X (7/8)
• 1: 2 X's (2*1 = 2)

Wait, but maybe there's another X? Wait the original problem's line plot:
Looking at the image, the X's are:

• Two at 1/4
• One at 3/4
• One at 7/8
• Two at 1

Wait, no, maybe I missed the X at 3/8? No, the labels are 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1. So the X positions:

• 1/4: two X's
• 3/4: one X
• 7/8: one X
• 1: two X's

Wait, but let's sum again:
2*(1/4) = 0.5
1*(3/4) = 0.75
1*(7/8) = 0.875
2*(1) = 2
Total: 0.5 + 0.75 = 1.25; 1.25 + 0.875 = 2.125; 2.125 + 2 = 4.125 = 4 1/8, which is option A. Wait, but maybe I miscounted X's. Wait, maybe the X's are:

• At 1/4: 2
• At 3/4: 1
• At 7/8: 1
• At 1: 2

Yes, that's 2+1+1+2=6 X's. Let's confirm:
2*(1/4) = 1/2
1*(3/4) = 3/4
1*(7/8) = 7/8
2*(1) = 2
Convert to eighths:
1/2 = 4/8
3/4 = 6/8
7/8 = 7/8
2 = 16/8
Sum: 4 + 6 + 7 + 16 = 33/8 = 4 1/8. So the answer is A.

Answer:

A. $4\frac{1}{8}$ hours