Question

How do you add `\frac { 3} { 10} + \frac { 7} { 15}`?

Answer 1

Convert both terms to have the same denominator, then add the numerators after conversion to get `color(green)(23/30)`

Explanation:

`color(red)(3/10)+color(blue)(7/15)`

`color(white)("XXX")=color(red)(9/30) + color(blue)(14/30)`

`color(white)("XXX")=(color(red)9+color(blue)(14))/(color(green)(30))`

`color(white)("XXX")=color(green)(23/30)`

Answer 2

Expanding Alan P's solution

Explanation:

Multiply by 1 and you do not change the value. However, 1 comes in many forms. So you can change the way a fraction looks without changing its overall value.

`color(green)([3/10color(red)(xx1)]color(white)(.)" "+" "[7/15color(red)(xx1)])`

`color(green)([3/10color(red)(xx3/3)]" "+" "[7/15color(red)(xx2/2)])`

`" "[9/30]" "+" "[14/30]`

`" "(9+14)/30`

`" "23/30`
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`color(blue)("Footnote")`

23 is a prime number so `23/30` can not be simplified further.