Brandon is running errands for his mother.
It is
1
4
mile from his house to the library and
2
3
mile from the library to the grocery store.
Brandon claims that he walks a total of
11
12
mile if he goes from his house to the library to the grocery store.
Which of the following shows whether Brandon is correct and why?
A.
Yes; the correct distance is
11
12
mile, because
1
4
+
2
3
=
3
12
+
8
12
=
11
12
.
B.
No; the correct distance is
10
12
mile, because
1
4
+
2
3
=
4
12
+
6
12
=
10
12
.
C.
No; the correct distance is 1 mile, because
1
4
+
2
3
=
4
12
+
8
12
=
12
12
=
1
.
D.
No; the correct distance is
1
1
12
miles, because
1
4
+
2
3
=
4
12
+
9
12
=
13
12
=
1
1
12
.
A. looks good
To determine whether Brandon is correct, we need to calculate the total distance he walks if he goes from his house to the library to the grocery store.
According to the given information, the distance from Brandon's house to the library is 1/4 mile, and the distance from the library to the grocery store is 2/3 mile.
To find the total distance, we need to add these two distances together:
1/4 + 2/3
To add fractions with different denominators, we need to find a common denominator. In this case, the smallest common denominator is 12 because it is divisible by both 4 and 3.
Converting 1/4 to a fraction with a denominator of 12:
1/4 * 3/3 = 3/12
Now, adding the fractions:
3/12 + 2/3 = 3/12 + 8/12 = 11/12
So, the correct distance is 11/12 mile.
Therefore, option A is correct because it shows that Brandon is correct.