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# How do you know if the pair $\dfrac{6}{9}$ and $\dfrac{2}{3}$ form a proportion?

Last updated date: 17th Jul 2024
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Hint: In this question, we are given two fractions and we have to find if they are proportional or not. Proportional means that one fraction is a multiple of the other fraction, that is, if we multiply one fraction by some number and we get the other fraction, then we can say that the two fractions form a pair of proportions. For example, if one fraction is $\dfrac{a}{b}$ and the other fraction is $\dfrac{{2a}}{{2b}}$ , then these two fractions form a proportion as on simplifying the second fraction, we get the first fraction as the answer. This way we can solve the given question.
We are given two fractions $\dfrac{6}{9}$ and $\dfrac{2}{3}$ , $\dfrac{6}{9}$ can be written as $\dfrac{6}{9} = \dfrac{{2 \times 3}}{{3 \times 3}}$
$\dfrac{6}{9} = \dfrac{2}{3}$
Hence, the pair $\dfrac{6}{9}$ and $\dfrac{2}{3}$ forms a proportion.
$\dfrac{6}{9} = \dfrac{2}{3} \\ \Rightarrow 6 \times 3 = 2 \times 9 \\ \Rightarrow 18 = 18 \\$