Question

Nance is riding her bike to a friend’s house 4 and 1/2 miles away. She’s ridden 2 and 3/5 miles. How much farther does she need to ride. Estimate, and then compute. Explain how you know your answer is reasonable.

Answer 1

Hello!

The answer is:

She still needs to ride

`1(9)/(10)miles`

Why?

From the statement, we know that Nance's friend is 4 1/2 miles away and she only has ridden 2 3/5 miles.

So, let be "x" the distance that she still need to ride to get to her friend's house.

The equation will be:

`TotalDistance=RiddenDistance+x`

Remember that:

`a(b)/(c)=a+(b)/(c)`

Also, if we need to add/substract fractions we must remember that:

`(a)/(b)+(c)/(d)=(ad+bc)/(bd)`

If we need to switch fractions to mixed numbers, we need to:

- Perform the division

- Keep the whole number and make a fraction with the aproximated next whole number (remainder) as numerator, and the original denominator. We need to use the remainder to approximate to the next whole number.

`(a)/(b)=c.r`

Where:

`a=numerator\\b=denominator\\c=WholePart\\r=NextWholeNumber`

So,

`(a)/(b)=c(r)/(b)`

Then, substituting the given information into the equation, we have:

`4(1)/(2) =2(3)/(5) +x\\\\x=(4(1)/(2)) -(2(3)/(5))=4+(1)/(2)-2-(3)/(5)=2+(1)/(2)-(3)/(5)\\\\x=2+(1)/(2)-(3)/(5)=2+(5-6)/(10)=2-(1)/(10)\\\\x=2-(1)/(10)=(20-1)/(10)=(19)/(10)`

So, she still need to ride
`(19)/(10)miles`

or

`1(9)/(10)miles`

To prove if the answer is reasoable, let's substituite the obtained value into the equation and check if the equation is satisfied:

`4(1)/(2)=2(3)/(5)+1(9)/(10)`

`4(1)/(2)=(13)/(5)+(19)/(10)`

`4(1)/(2)=(9)/(2)`

`4(1)/(2)=4(1)/(2)`

Have a nice day!