Question

How do you know if the pair 6/9 and 2/3 form a proportion?

Answer 1

They are proportions, see explanation.

Explanation:

First, set them both equal to each other.

`6/9 = 2/3`

Then, cross multiply. Follow this method: `a/b=c/d` = `ad = bc`.

`6(3) = 9(2)`

`18 = 18`

`18` does equal `18`, so the two fractions do show a proportion.

Another way to look at is to set both fractions equal and see what happened to one fraction to get to the other.

`2/3 = 6/9`

`(2times3)/(3times3) = 6/9`

`6/9 = 6/9`

We found that you can multiply `3/3` to `2/3` to get the other fraction or divide `3/3` from `6/9` to get the other fraction. These both represent proportions.

Answer 2

See explanation

Explanation:

To investigate if`" "6/9-=2/3" "` ( `-=` means 'equivalent to')

`color(blue)("Consider the left hand side (LHS)")`

Using the property of ratios
Divide top and bottom by 3 giving

`(6-:3)/(9-:3) = 2/3`

`color(blue)("Comparing shows that "LHS-=RHS)`

Thus it is true that `6/9-=2/3`