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Which expression is A, in order to have a true equation A=5−113 ?(1 point) Responses A=−123+13 negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction A=123+13 negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=123−13 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=153+13

3 answers

To find the expression that makes the equation \( A = 5 - \frac{113}{3} \) true, we first need to simplify the right side of the equation.

Calculating \( 5 - \frac{113}{3} \):

  1. Convert \( 5 \) to a fraction with a denominator of \( 3 \): \[ 5 = \frac{15}{3} \]

  2. Now subtract \( \frac{113}{3} \) from \( \frac{15}{3} \): \[ \frac{15}{3} - \frac{113}{3} = \frac{15 - 113}{3} = \frac{-98}{3} \]

Now we have \( A = \frac{-98}{3} \). We need to compare this expression with the provided options to find which one is equal to \( -\frac{98}{3} \):

  1. Option 1: \( A = -\frac{123}{3} + \frac{1}{3} \) \[ -\frac{123}{3} + \frac{1}{3} = -\frac{122}{3} \] (Not equal to \(-\frac{98}{3}\))

  2. Option 2: \( A = \frac{123}{3} - \frac{1}{3} \) \[ \frac{123}{3} - \frac{1}{3} = \frac{122}{3} \] (Not equal to \(-\frac{98}{3}\))

  3. Option 3: \( A = \frac{123}{3} - \frac{1}{3} \) (repeated) \[ \frac{123}{3} - \frac{1}{3} = \frac{122}{3} \] (Not equal to \(-\frac{98}{3}\))

  4. Option 4: \( A = \frac{153}{3} \) \[ \frac{153}{3} = 51 \] (Not equal to \(-\frac{98}{3}\))

None of the options seem to correspond to \( -\frac{98}{3} \).

Please check the provided options again, or let me know if I can assist you further!

Which expression is A, in order to have a true equation A=5−11/3 ?(1 point) Responses A=−1 2/3+13 negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction A=1 2/3+13 negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=1 2/3−13 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=15/3+13

To determine which expression for \( A \) makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to simplify the right side:

  1. Calculate \( 5 - \frac{11}{3} \):
    • Convert \( 5 \) to a fraction with a denominator of \( 3 \): \[ 5 = \frac{15}{3} \]
    • Now subtract: \[ \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]

So, we have \( A = \frac{4}{3} \). Now, we need to check each of the provided options to see which one is equal to \( \frac{4}{3} \).

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

    • This option appears to be written incorrectly based on your formatting. Let's assume you meant \( A = -1\frac{2}{3} + \frac{1}{3} \):

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

    • Now perform the addition: \[ -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \quad (\text{Not } \frac{4}{3}) \]

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

    • Convert \( 1\frac{2}{3} \) to an improper fraction: \[ 1\frac{2}{3} = \frac{5}{3} \]
    • Now perform the subtraction: \[ \frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3} \quad (\text{This is equal to } \frac{4}{3}) \]

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

    • This is the same as option 2 and already checks out as \( \frac{4}{3} \).

  4. Option 4: \( A = \frac{15}{3} + \frac{1}{3} \)

    • Calculate: \[ \frac{15}{3} + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \quad (\text{Not } \frac{4}{3}) \]

From the evaluation of the options, Option 2 (or 3): \( A = 1\frac{2}{3} - \frac{1}{3} \) gives the correct result of \( A = \frac{4}{3} \).

So, the correct expression for \( A \) is:

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