Question

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Card sort rational numbers: order from least to greatest.


10, 15, 8, 23, 11, 5, 3, 22, 2, -1, -3, -7.7, -23, -22 3/8, -7, -8/3, -1/4, 9/8, -31/3, -6, -2.5, 0, -10, -5 5/6, -2, 1, -9, -4, -1.125, 1/4, 2.5, 8/3, 22 3/8, 31/3, 5 5/6, and 7.7

Answer 1

3/8 < -31/3 < -7.7 < -7 < -6 < -3 < -8/3 < -2.5 < -1 < -1/4 < 0 < 9/8 < 2 < 3 < 5 < 8 < 10 < 11 < 15 < 22 < 23

Showing Work

Using the given inputs:

10 15 8 23 11 5 3 22 2 -1 -3 -7.7 -23 -22 3/8 -7 -8/3 -1/4 9/8 -31/3 -6 -2.5 0

Rewriting these inputs as decimals:

10 15 8 23 11 5 3 22 2 -1 -3 -7.7 -23 -22 3/8 -7 -8/3 -1/4 9/8 -31/3 -6 -2.5 0

10 15 8 23 11 5 3 22 2 -1 -3 -7.7 -23 -22.375 -7 -2.666667 -0.25 1.125 -10.333333 -6 -2.5 0

Sorting this table by decimal values in order from least to greatest:

-23 -22 3/8 -31/3 -7.7 -7 -6 -3 -8/3 -2.5 -1 -1/4 0 9/8 2 3 5 8 10 11 15 22 23

-23 < -22.375 < -10.333333 < -7.7 < -7 < -6 < -3 < -2.666667 < -2.5 < -1 < -0.25 < 0 < 1.125 < 2 < 3 < 5 < 8 < 10 < 11 < 15 < 22 < 23

Therefore, the sorted inputs in order from least to greatest is:

-23 < -22 3/8 < -31/3 < -7.7 < -7 < -6 < -3 < -8/3 < -2.5 < -1 < -1/4 < 0 < 9/8 < 2 < 3 < 5 < 8 < 10 < 11 < 15 < 22 < 23

Explanation: