Question

How do you subtract `\frac { 17} { 21} - \frac { 4} { 6}`?

Answer 1

`1/7` find a common denominator subtract the numerators and divide out any common factors.

Explanation:

21 can be factored into `7xx3`
6 can be factored into `2 xx 3`

7 and 2 are the uncommon factors

multiply `17/21 xx 2/2 = 34/42`

multiply `4/6 xx 7/7 = 28/42` subtract gives

`=(34-28)/42= 6/42 = 1/7`

Note :
In case you noticed that `4/6=2/3`:

`17/21-2/3xx7/7=17/21-14/21=3/21=1/7`

Answer 2

`17/21-4/6=1/7`

Explanation:

A fraction structure is `("count")/("size indicator")->("numerator")/("denominator")`

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

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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 value.

`color(green)([17/21color(red)(xx1)]-[4/6color(red)(xx1)])" "->" "color(green)([17/21color(red)(xx2/2)]-[4/6color(red)(xx7/7)])`

`" "[ 34/42] - [28/42]`

`" "=6/42 -= (6-:6)/(42-:6) = 1/7`