A person walked a dog [tex]\frac{2}{3}[/tex] of a mile on Thursday and [tex]\frac{5}{7}[/tex] of a mile on Friday. What total number of miles did the person walk the dog?

A. [tex]\frac{7}{10}[/tex]
B. [tex]\frac{10}{21}[/tex]
C. [tex]1 \frac{3}{10}[/tex]
D. [tex]1 \frac{8}{21}[/tex]



Answer :

To determine the total number of miles walked by the person in two days, we first need to add the distances walked on Thursday and Friday.

1. Distance walked on Thursday: [tex]\(\frac{2}{3}\)[/tex] mile

2. Distance walked on Friday: [tex]\(\frac{5}{7}\)[/tex] mile

We start by converting each fraction into a decimal to facilitate addition:

[tex]\[ \frac{2}{3} \approx 0.6666666666666666 \][/tex]

[tex]\[ \frac{5}{7} \approx 0.7142857142857143 \][/tex]

Next, we add these decimal values to find the total distance:

[tex]\[ 0.6666666666666666 + 0.7142857142857143 \approx 1.380952380952381 \][/tex]

To return to fraction form and simplify, we recognize that [tex]\(1.380952380952381\)[/tex] can be written as:

[tex]\[ 1 \frac{380952380952381}{1000000000000000} \][/tex]

Which is better simplified to the fraction [tex]\( \frac{29}{21} \)[/tex].

We should convert [tex]\( \frac{29}{21} \)[/tex] to a mixed number:
[tex]\[ \frac{29}{21} = 1 \frac{8}{21} \][/tex]

Therefore, the total number of miles the person walked the dog is:

[tex]\[ \boxed{1 \frac{8}{21}} \][/tex]
Hence, the correct answer is option D: [tex]\(1 \frac{8}{21}\)[/tex].