Question

Order the tions from least to greatest.

a) −21/4, −17/2, −23/5, −14/3
b) −17/2, −14/3, −23/5, −21/4
c) −23/5, −21/4, −14/3, −17/2
d) −17/2, −21/4, −14/3, −23/5

Answer 1

To order the fractions from least to greatest, we convert them to decimals and then arrange them considering their negative values. The correct order is −17/2, −21/4, −23/5, −14/3, which is option c).

Step-by-step explanation:

To order the fractions from least to greatest, we can compare each fraction by finding a common denominator or converting them to decimal form to see which is larger. It's important to remember that since all fractions in question are negative, a fraction with a larger absolute value will be smaller when considering their negative values.

1. Convert each fraction to decimal:
   • −21/4 = -5.25
   • −17/2 = -8.5
   • −23/5 = -4.6
   • −14/3 = -4.⅓3(continuing decimal)
2. Order the decimals from least to greatest, keeping in mind their negative values make the ranking opposite to their absolute values:
   • -8.5 (−17/2)
   • -5.25 (−21/4)
   • -4.6 (−23/5)
   • -4.⅓3(−14/3)
3. Now write the original fractions in order from least to greatest based on their decimal equivalents:

The correct ordered sequence is −17/2, −21/4, −23/5, −14/3, which corresponds to option c).