Question

How do you know if the pair 4/3 and 8/6 form a proportion?

Answer 1

If you divide one into the other and the answer is 1 then they are of the same ratio.

Explanation:

Write in faction format `" "4/3"; "8/6`

`color(blue)("The test process")`

`4/3-:8/6`

`color(green)(4/3xxcolor(red)(6/8)" "=" "(4xxcolor(red)(6))/(3xxcolor(red)(8))" "=" "(color(red)(6)xx4)/(3xxcolor(red)(8)))`

`" "=" "color(green)((color(red)(6))/3xx4/(color(red)(8))" "=" "2xx1/2`

`" "=" "1`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("A different test")`

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

`color(green)(4/3color(red)(xx1) " "=" "4/3color(red)(xx2/2)" "=" "8/6`

Thus it is true that `4/3-=8/6`

Where `-=` means 'proportional to'