Question

The distance from Will's house to a park is 1 9/10 miles. Will

leaves his house and walks 2/5 mile toward the park. About
how much farther does he have to walk to reach the park?

Answer 1

`\boxed{1(1)/(2)\;miles}`

Explanation:

Convert 1 9/10 to an improper fraction and then the calculation becomes simpler

`1 (9)/(10 ) = ( 1 \cdot 10 + 9)/(10) = (19)/(10)\\\\`

Since Will has already walked 2/5 of a mile to the park, the remaining distance

`= (19)/(10) - (2)/(5)\\\\`

Make the denominators the same by multiplying both the numerator and denominator of 2. This does not change the original value of 2/5

`\frac {2 * 2}{5 * 2} = (4)/(10)\\\\`

Therefore the remaining distance is

`(19)/(10) - (2)/(5)\\\\\\= (19)/(10) - (4)/(10)`

Since the denominator is the same we can simply subtract the numerator terms and use 10 as the denominator for the result:

`= (19-4)/(10) = (15)/(10) \\\\`

Dividing numerator and denominator by 5 reduces it to the lowest fraction

`(15 / 5)/(10 / 5) = (3)/(2) = 1(1)/(2) \\\\`

So Will needs to travel a further
`1(1)/(2)` miles to reach the park