Answer :

Final answer:

The expression with the greatest value is 138 \/ 14, which approximately equals 9.86, as it has the smallest denominator compared to the value of the numerators in the other options.Therefore the correct option is A.

Explanation:

The student asks which expression has the greatest value out of the following options:

  • a. 138 \/ 14
  • b. 138 \/ 116
  • c. 23 \/ 14
  • d. 23 \/ 116

To find the answer, we need to perform the division for each expression. Since 138 and 23 are the numerators in these expressions, the greatest value will come from the one with the smallest denominator because the value of a fraction increases as the denominator decreases. Performing the calculations:

  1. 138 \/ 14 equals approximately 9.86
  2. 138 \/ 116 equals approximately 1.19
  3. 23 \/ 14 equals approximately 1.64
  4. 23 \/ 116 equals approximately 0.20

Therefore, the expression with the greatest value is a. 138 \/ 14, which approximately equals 9.86.

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