You live 35 1/3 miles from your grandmother's house. You're workplace is 7 2/5 miles from your grandmother's house. If you drive by your grandmother's home on the way to work one morning, what is the total number of miles you drove that morning? Write your answer as a mixed number.
27 14/15
looks to me like you subtracted instead of adding.
35 1/3 + 7 2/5 = 42 11/15
To find the total number of miles you drove that morning, you need to add the distance from your home to your grandmother's house and the distance from your grandmother's house to your workplace.
First, let's add the distance from your home to your grandmother's house. You live 35 1/3 miles away. To add a mixed number, you need to convert it to an improper fraction.
35 1/3 as an improper fraction is (35 * 3 + 1) / 3 = 106/3.
Next, let's add the distance from your grandmother's house to your workplace. It is 7 2/5 miles away. To add a mixed number, you need to convert it to an improper fraction.
7 2/5 as an improper fraction is (7 * 5 + 2) / 5 = 37/5.
Now, add the two fractions together:
106/3 + 37/5
To add fractions, you need a common denominator. The least common multiple (LCM) of 3 and 5 is 15.
Convert both fractions to have a denominator of 15:
(106/3) * (5/5) = 530/15
(37/5) * (3/3) = 111/15
Now, add the two fractions:
530/15 + 111/15 = 641/15
Finally, convert the improper fraction back to a mixed number:
641/15 as a mixed number is 42 11/15.
Therefore, the total number of miles you drove that morning is 42 11/15 miles.