Final answer:
Jake's total distance travelled to go from home to Dairy Queen and then to the movie theater is 2/3 of a mile. This is found by converting the distances to a common denominator, adding them, and simplifying the result.
Step-by-step explanation:
Jake wants to travel from his home to Dairy Queen, which is 2/5 of a mile away, and then continue to the movie theater, which is an additional 4/15 of a mile from Dairy Queen. To find the total distance Jake will travel, we need to add these two distances together.
To add fractions, they must have the same denominator. The denominators here are 5 and 15. We can convert 2/5 to a fraction with a denominator of 15 by multiplying both the numerator and the denominator by 3, giving us 6/15. Now we can add the two fractions:
Distance = 6/15 (from home to Dairy Queen) + 4/15 (from Dairy Queen to movie theater)
Distance = (6/15 + 4/15)
Distance = 10/15 miles
However, 10/15 can be simplified by dividing both the numerator and the denominator by 5, giving us 2/3. So, the total distance Jake will have to travel is 2/3 of a mile.
Therefore, none of the provided options a) 10/15 miles, b) 6/15 miles, c) 8/15 miles, or d) 12/15 miles are correct. The correct answer is not listed among the options.