A solution consists of 2/3 of substance G and the rest is substance F .Express substance G as a fraction of substance F in the solution

Mathematics

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Answer

21\frac{2}{1}

Step-by-step solution

3 steps

  1. Determine the fraction of substance G in the solution.

    Given that substance G makes up 23\frac{2}{3} of the solution.

  2. Determine the fraction of substance F in the solution.

    The rest of the solution is substance F. So,

    Fraction of F=1−Fraction of G\text{Fraction of F} = 1 - \text{Fraction of G} Fraction of F=1−23\text{Fraction of F} = 1 - \frac{2}{3} Fraction of F=33−23\text{Fraction of F} = \frac{3}{3} - \frac{2}{3} Fraction of F=13\text{Fraction of F} = \frac{1}{3}

  3. Express substance G as a fraction of substance F.

    This means we need to find the ratio Fraction of GFraction of F\frac{\text{Fraction of G}}{\text{Fraction of F}}.

    Fraction of GFraction of F=2313\frac{\text{Fraction of G}}{\text{Fraction of F}} = \frac{\frac{2}{3}}{\frac{1}{3}}

    To simplify, multiply the numerator by the reciprocal of the denominator:

    2313=23×31\frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2}{3} \times \frac{3}{1} 2313=2×33×1\frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2 \times 3}{3 \times 1} 2313=63\frac{\frac{2}{3}}{\frac{1}{3}} = \frac{6}{3} 2313=2\frac{\frac{2}{3}}{\frac{1}{3}} = 2

    So, substance G is 2 times substance F. As a fraction, this can be written as 21\frac{2}{1}.

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