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

Other useful links

AMC-AIME Program at Cheenta

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

Other useful links

AMC-AIME Program at Cheenta

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