Question

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?

Answer 1

`4 4/15" miles"`

Explanation:

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"`