Question

Nance is riding her bike to a friend's house 4 1/2 miles away. She's ridden 2 3/5 miles so far, How much farther does she need to ride?

Answer 1

19/10 miles

Step-by-step explanation:

The situation is sketched below

The remaining distance is

`4(1)/(2)-2(3)/(5)`

which can be rewritten as

`4+(1)/(2)-2-(3)/(5)`
`2+(1)/(2)-(3)/(5)`

We subtract the fractions 1/2 and 3/5.

`(1)/(2)\cdot(5)/(5)-(3)/(5)\cdot(2)/(2)`
`=(5)/(10)-(6)/(10)=-(1)/(10)`

Therefore now our expression becomes

`2+(1)/(2)-(3)/(5)=2-(1)/(10)`

which can be further rewritten as

`2\cdot(10)/(10)-(1)/(10)`
`=(20)/(10)-(1)/(10)`
`=(19)/(10)`

which is our answer!