Question

Ada lives 12 4/5 miles from her aunt's house. she lives 17 3/8 miles from her grandmother's house. how many more miles does jada live from her grandmother's house than her aunt's house?

Answer 1

`4 (23)/(40)\; \rm miles`

Explanation:

To find how many more miles Ada lives from her grandmother's house than her aunt's house, we need to subtract the distance to her aunt's house from the distance to her grandmother's house.

Ada lives 17 3/8 miles from her grandmother's house.

Ada lives 12 4/5 miles from her aunt's house.

Convert both mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

`17 (3)/(8)=(17 \cdot 8+3)/(8)=(139)/(8)`

`12 (4)/(5)=(12 \cdot 5+4)/(5)=(64)/(5)`

As both improper fractions have a different denominator, we need to change both fractions into equivalent fractions with the same denominator. To do this, find the least common multiple (LCM) of the denominators, 8 and 5.

The LCM of 8 and 5 is 40. Therefore, convert the fractions into their equivalent fractions (with 40 as their denominator) by multiplying the numerator and denominator by the same number:

`(139)/(8)=(139 \cdot 5)/(8 \cdot 5)=(695)/(40)`

`(64)/(5)=(64 \cdot 8)/(5 \cdot 8)=(512)/(40)`

Now the fractions have the same denominator, we can carry out the subtraction by simply subtracting the numerators:

`(695)/(40)-(512)/(40)=(695-512)/(40)=(183)/(40)`

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

`183 / 40=4\;\rm remainder \;23`

The mixed number answer is the whole number and the remainder divided by the denominator:

`4 (23)/(40)`

Therefore, Ada lives 4 23/40 miles more from her grandmother's house than her aunt's house.