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Which expression is A, in order to have a true equation A= 5 – 11/3?

A. A= 1 2/3 – 1/3
B. A= -1 2/3 + 1/3
C. A= 15/3 + 1/3
D. A= 1 2/3 + 1/3

1 answer

To find which expression equals \( A = 5 - \frac{11}{3} \), we first need to simplify \( 5 - \frac{11}{3} \).

  1. Convert \( 5 \) into a fraction that has the same denominator as \( \frac{11}{3} \): \[ 5 = \frac{15}{3} \]

  2. Now perform the subtraction: \[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]

Now that we know \( A = \frac{4}{3} \) (which can also be expressed as \( 1 \frac{1}{3} \) or \( 1.33 \)), we need to evaluate each expression given in the options and see which one equals \( \frac{4}{3} \).

A. \( A = 1 \frac{2}{3} - \frac{1}{3} \):

  • Convert \( 1 \frac{2}{3} \) to an improper fraction: \( 1 \frac{2}{3} = \frac{5}{3} \)
  • Now calculate: \[ A = \frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3} \]

B. \( A = -1 \frac{2}{3} + \frac{1}{3} \):

  • Convert \( -1 \frac{2}{3} \) to an improper fraction: \( -1 \frac{2}{3} = -\frac{5}{3} \)
  • Now calculate: \[ A = -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \quad \text{(not equal to } \frac{4}{3}\text{)} \]

C. \( A = \frac{15}{3} + \frac{1}{3} \):

  • Now calculate: \[ A = \frac{15}{3} + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \quad \text{(not equal to } \frac{4}{3}\text{)} \]

D. \( A = 1 \frac{2}{3} + \frac{1}{3} \):

  • Convert \( 1 \frac{2}{3} \) to an improper fraction: \( 1 \frac{2}{3} = \frac{5}{3} \)
  • Now calculate: \[ A = \frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2 \quad \text{(not equal to } \frac{4}{3}\text{)} \]

Based on the evaluations, the expression that equals \( A = \frac{4}{3} \) is:

A. \( A = 1 \frac{2}{3} - \frac{1}{3} \).