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Which of the following fractions is the smallest: rac23, rac69, rac73, rac83?

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps
  1. Identify the fractions.

    The given fractions are 23,69,73,83\frac{2}{3}, \frac{6}{9}, \frac{7}{3}, \frac{8}{3}.

  2. Simplify the fractions to their lowest terms.

    23\frac{2}{3} 69=6÷39÷3=23\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} 73\frac{7}{3} 83\frac{8}{3}
  3. Compare the fractions.

    After simplification, the fractions are 23,23,73,83\frac{2}{3}, \frac{2}{3}, \frac{7}{3}, \frac{8}{3}.
    All these fractions have a common denominator of 3. When fractions have the same denominator, the smallest fraction is the one with the smallest numerator.
    Comparing the numerators (2, 2, 7, 8), the smallest numerator is 2.
    Therefore, the smallest fraction is 23\frac{2}{3}.

  4. Select the correct option.

    The options are:
    (A) 23\frac{2}{3}
    (B) 73\frac{7}{3}
    (C) 83\frac{8}{3}
    (D) 69\frac{6}{9}

    Both 23\frac{2}{3} and 69\frac{6}{9} are equal to the smallest value. Since 23\frac{2}{3} is the simplest form and is given as option (A), we select (A).

    The final answer is (A)23\boxed{\text{(A)} \frac{2}{3}}.

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