Shannon walked ##1 2/3## miles on Wednesday and ##2 3/5## miles on Thursday. What was the total distance, in miles, Shannon walked during those 2 days?

##4 4/15″ miles”##

To calculate the ##color(blue)”total distance”## that Shannon walked we have to ##color(blue)”add”## the distances walked on each day.

That is : ##1 2/3+2 3/5##

One way of doing this is to add the whole numbers together and add the fractions separately.

Now ##1 2/3=1+2/3″ and ” 2 3/5=2+3/5##

##rArr1 2/3+2 3/5=1+2/3+2+3/5##

##=(1+2)+(2/3+3/5)…….. (A)##

Before adding the fractions we require them to have the ##color(blue)”same denominator”##

multiplying ##2/3″ by ” 5/5″ and ” 3/5″ by ” 3/3## will give this.

##(2/3xx5/5)+(3/5xx3/3)=10/15+9/15##

now that we have a ##color(blue)”common denominator”## we can add the numerators together.

##rArr10/15+9/15=(10+9)/15=19/15=1 4/15##

Returning to (A) we obtain the total distance Shannon walked.

That is ##3+1 4/15=3+1+4/15=4 4/15″ miles”##