Which expression is A, in order to have a true equation $A=5-\frac {11}{3}$ ? (1 pc

$A=1\frac {2}{3}+\frac {1}{3}$
$A=1\frac {2}{3}-\frac {1}{3}$
$A=\frac {15}{3}+\frac {1}{3}$
$A=-1\frac {2}{3}+\frac {1}{3}$

1 answer

To find the expression for \( A \) such that it satisfies the equation \( A = 5 - \frac{11}{3} \), we first need to simplify the right-hand side.

Starting with the calculation:

\[ 5 - \frac{11}{3} \]

First, we express 5 as a fraction with a denominator of 3:

\[ 5 = \frac{15}{3} \]

Now we can rewrite the equation:

\[ A = \frac{15}{3} - \frac{11}{3} \]

Next, subtract the fractions:

\[ A = \frac{15 - 11}{3} = \frac{4}{3} \]

So, \( A = \frac{4}{3} \).

Next, we evaluate each of the provided expressions to see which one equals \( \frac{4}{3} \).

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

Convert \( 1\frac{2}{3} \) to an improper fraction:

\[ 1\frac{2}{3} = \frac{3 \cdot 1 + 2}{3} = \frac{5}{3} \]

Now calculate:

\[ A = \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \quad (\text{not equal to } \frac{4}{3}) \]

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

Using \( 1\frac{2}{3} = \frac{5}{3} \):

\[ A = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \quad (\text{this equals } \frac{4}{3}) \]

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

Calculate:

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

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

Convert \( -1\frac{2}{3} \) to an improper fraction:

\[ -1\frac{2}{3} = -\frac{3 \cdot 1 + 2}{3} = -\frac{5}{3} \]

Now calculate:

\[ A = -\frac{5}{3} + \frac{1}{3} = -\frac{5}{3} + \frac{1}{3} = -\frac{4}{3} \quad (\text{not equal to } \frac{4}{3}) \]

The only expression that equals \( \frac{4}{3} \) is:

\[ A = 1\frac{2}{3} - \frac{1}{3} \]

Thus, the correct answer is:

\[ \boxed{1\frac{2}{3} - \frac{1}{3}} \]