Question

How do write in simplest form given `7/10-2/15`?

Answer 1

`17/30`

Explanation:

In order to add or subtract fractions, we have to have common denominators.

1. List multiples of both numbers.

   `10: 10,20,ul 30,40 ....`
   `15: 15,ul 30,45,60 ....`

2. Look for the smallest underlined number (known as the least common multiple, or LCM). This is your common denominator.

   Common denominator: `30`

3. Multiply the numerator and denominator by the factor that it would take to get to your common denominator…like this:

`7/10 *3/3 = 21/30`

and, `2/15 *2/2 = 4/30`

Now we have both of our fractions with common denominators, so we can subtract! Remember, in a subtraction problem, the numerators subtract but the denominators stay the same. It looks like this:

`7/10-2/15=21/30-4/30=17/30`

Answer 2

`17/30`

Explanation:

`color(blue)("Initial thoughts")`

Known: `" "2xx15=30" "` and `" "3xx10=30` so both the 'denominators' will divide exactly into 30.

A fraction consist of `" "("numerator")/("denominator")" "->" "("count")/("size indicator")`

You can not directly add or subtract the counts unless the size indicators are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Making the denominators (size indicators) the same")`

`color(brown)("Multiply by 1 and you do not change the value. However 1 comes in many forms")`

`" "[7/10color(red)(xx1)]" " -" "[2/15color(red)(xx1)]`

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

`" "21/30" "-" "4/30`

`" "17/30`