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AMC 8 2019 Problem 3 | Ordering Problem

Try this beautiful Problem based on Ordering of fraction from AMC 8 2019.

Ordering Problem - AMC 8 2019 Problem 3


Which of the following is the correct order of the fractions \frac{15}{11}, \frac{19}{15}, and \frac{17}{13}, from least to greatest?

  • \frac{15}{11}<\frac{17}{13}<\frac{19}{15}
  • \frac{15}{11}<\frac{19}{15}<\frac{17}{13}
  • \frac{17}{13}<\frac{19}{15}<\frac{15}{11}
  • \frac{19}{15}<\frac{15}{11}<\frac{17}{13}
  • \frac{19}{15}<\frac{17}{13}<\frac{15}{11}

Key Concepts


Fraction

Greatest Common Divisor

Ordering in Fraction

Suggested Book | Source | Answer


AMC 8 2019 Problem 3

\frac{19}{15}<\frac{17}{13}<\frac{15}{11}

Try with Hints


First try to make all the denominators equal

\frac{15}{11}, \frac{19}{15}, \frac{17}{13}

=\frac{15 \cdot 15 \cdot 13}{11 \cdot 15 \cdot 13}, \frac{19 \cdot 11 \cdot 13}{15 \cdot 11 \cdot 13}, \frac{17 \cdot 11 \cdot 15}{13 \cdot 11 \cdot 15}

=\frac{2925}{2145}, \frac{2717}{2145}, \frac{2805}{2145}

Now, Try compare numerator

We have, 2717<2805<2925

so , \frac{19}{15}<\frac{17}{13}<\frac{15}{11} is the right order

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Try this beautiful Problem based on Ordering of fraction from AMC 8 2019.

Ordering Problem - AMC 8 2019 Problem 3


Which of the following is the correct order of the fractions \frac{15}{11}, \frac{19}{15}, and \frac{17}{13}, from least to greatest?

  • \frac{15}{11}<\frac{17}{13}<\frac{19}{15}
  • \frac{15}{11}<\frac{19}{15}<\frac{17}{13}
  • \frac{17}{13}<\frac{19}{15}<\frac{15}{11}
  • \frac{19}{15}<\frac{15}{11}<\frac{17}{13}
  • \frac{19}{15}<\frac{17}{13}<\frac{15}{11}

Key Concepts


Fraction

Greatest Common Divisor

Ordering in Fraction

Suggested Book | Source | Answer


AMC 8 2019 Problem 3

\frac{19}{15}<\frac{17}{13}<\frac{15}{11}

Try with Hints


First try to make all the denominators equal

\frac{15}{11}, \frac{19}{15}, \frac{17}{13}

=\frac{15 \cdot 15 \cdot 13}{11 \cdot 15 \cdot 13}, \frac{19 \cdot 11 \cdot 13}{15 \cdot 11 \cdot 13}, \frac{17 \cdot 11 \cdot 15}{13 \cdot 11 \cdot 15}

=\frac{2925}{2145}, \frac{2717}{2145}, \frac{2805}{2145}

Now, Try compare numerator

We have, 2717<2805<2925

so , \frac{19}{15}<\frac{17}{13}<\frac{15}{11} is the right order

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