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Verified Answer :

To determine the equivalent expressions for the given expression which is 3ab:27ab = 1:9 , we can simplify the choices and see whether they are equal with the original.

1:9 = 1:9  EQUAL

9a:81a = 1:9 EQUAL 

a:b NOT EQUAL

a:3b NOT EQUAL

2:18 = 1:9 EQUAL

3b:27a = NOT EQUAL

SociometricStar

Answer:

1:9, 9a:81a and 2:18

Step-by-step explanation:

We have been given the ratio 3ab:27ab.

We can write the ratio a:b in fraction form as \(\frac{a}{b}\)

So, the given ratio can be written as

\(\frac{3ab}{27ab}\)

Now, 27 can be written as 27 =3 × 9

\(\frac{3ab}{3\times9ab}\)

Now, cancel the common terms in numerator and denominator.

\(\frac{1}{9}\)

We can write this in ratio form as 1:9

Now, we'll see the equivalent ratio of 1:9 from the given options.

9a:81a = 1:9

2:18 = 1:9

Therefore, the correct options are

1:9, 9a:81a and 2:18

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