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which expression is A. in order to have a true equation A=5-11/3

A=1 2/3+1/3
A=15/3+1/3
A=-1 2/3+1/3
A=1 2/3-1/3

1 answer

To determine which expression is equal to \( A \) in the equation \( A = 5 - \frac{11}{3} \), we first need to simplify \( A \).

  1. Calculate \( 5 - \frac{11}{3} \):
    • Convert \( 5 \) to a fraction: \( 5 = \frac{15}{3} \).
    • Now, perform the subtraction: \[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]

Now that we know \( A = \frac{4}{3} \), we can compare it with the options provided:

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

    • Convert to improper fraction:
      \[ 1 \frac{2}{3} = \frac{5}{3} \]
    • Therefore:
      \[ A = \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \]

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

    • Same result as before: \( A = 2 \).

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

    • Adding these gives:
      \[ A = \frac{15 + 1}{3} = \frac{16}{3} \]

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

    • Convert to improper fraction:
      \[ -1 \frac{2}{3} = -\frac{5}{3} \]
    • Therefore:
      \[ A = -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \]

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

    • Again, convert to improper fraction:
      \[ 1 \frac{2}{3} = \frac{5}{3} \]
    • So:
      \[ A = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \]

From this analysis, the option that gives us \( A = \frac{4}{3} \) is:

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