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

2 Answers
Jul 14, 2016

Answer:

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.

Jul 14, 2016

Answer:

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#