2. Select all the groups of numbers that are ordered correctly from least to greatest. \( -5,-4.3,-\frac{7}{2}, 1 \frac{3}{4} \) \( -1 \frac{2}{3},-1.75,-\frac{5}{7},-0.3 \) \( -15.3,-15 \frac{5}{8},-15 \frac{2}{7},-15 \) \( -2.8,-\frac{4}{5},-\frac{3}{4}, 2.8 \) \( -2 \frac{1}{2},-\frac{7}{3},-2 \frac{1}{4},-2 \frac{1}{10} \)
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Bonus Knowledge
To tackle the challenge of ordering numbers from least to greatest, let’s first transform everything to a standard numerical form for clarity. The first group: \( -5, -4.3, -\frac{7}{2} \) (which is -3.5), and \( 1 \frac{3}{4} \) (which is 1.75) correctly arranges as \( -5 < -4.3 < -3.5 < 1.75 \). Now, the second group contains \( -1 \frac{2}{3} \) (approximately -1.67), \( -1.75 \), \( -\frac{5}{7} \) (approximately -0.71), and \( -0.3 \), which can be transformed to \( -1.75 < -1.67 < -0.71 < -0.3 \); so this one is incorrect. In the third group, we see that \( -15.3, -15 \frac{5}{8} \) (which is -15.625), \( -15 \frac{2}{7} \) (approximately -15.285), and \( -15 \); here, we crisscross between -15.3, which comes first, leading to an incorrect order as well. As for the fourth group \( -2.8, -\frac{4}{5} \) (which is approximately -0.8), \( -\frac{3}{4} \) (approximately -0.75), and \( 2.8 \), this one also falls under incorrect structure. Lastly, the fifth set: \( -2 \frac{1}{2} \) (or -2.5), \( -\frac{7}{3} \) (over -2.33), \( -2 \frac{1}{4} \) (-2.25), and \( -2 \frac{1}{10} \) (which is -2.1) also shuffles in an incorrect way. Therefore, the only correctly ordered group from least to greatest is the first!
