Hello!
The answer is:
She still needs to ride
[tex]1\frac{9}{10}miles[/tex]
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:
[tex]TotalDistance=RiddenDistance+x[/tex]
Remember that:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]
Also, if we need to add/substract fractions we must remember that:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]
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.
[tex]\frac{a}{b}=c.r[/tex]
Where:
[tex]a=numerator\\b=denominator\\c=WholePart\\r=NextWholeNumber[/tex]
So,
[tex]\frac{a}{b}=c\frac{r}{b}[/tex]
Then, substituting the given information into the equation, we have:
[tex]4\frac{1}{2} =2\frac{3}{5} +x\\\\x=(4\frac{1}{2}) -(2\frac{3}{5})=4+\frac{1}{2}-2-\frac{3}{5}=2+\frac{1}{2}-\frac{3}{5}\\\\x=2+\frac{1}{2}-\frac{3}{5}=2+\frac{5-6}{10}=2-\frac{1}{10}\\\\x=2-\frac{1}{10}=\frac{20-1}{10}=\frac{19}{10}[/tex]
So, she still need to ride [tex]\frac{19}{10}miles[/tex]
or
[tex]1\frac{9}{10}miles[/tex]
To prove if the answer is reasoable, let's substituite the obtained value into the equation and check if the equation is satisfied:
[tex]4\frac{1}{2}=2\frac{3}{5}+1\frac{9}{10}[/tex]
[tex]4\frac{1}{2}=\frac{13}{5}+\frac{19}{10}[/tex]
[tex]4\frac{1}{2}=\frac{9}{2}[/tex]
[tex]4\frac{1}{2}=4\frac{1}{2}[/tex]
Have a nice day!
