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

Question

A=1 2/3+13

A=1 2/3−13

A=1 5/3+13

A=−1 2/3+13

Answer 1

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

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

So, we have: \[ A = \frac{4}{3} \]

Next, let's convert \( \frac{4}{3} \) into a mixed number: \[ \frac{4}{3} = 1 \frac{1}{3} \]

Now, we will evaluate each expression for \( A \):

1. \( A = 1 \frac{2}{3} + 13 \):

   • Convert \( 1 \frac{2}{3} \): \[ 1 \frac{2}{3} = \frac{5}{3} \]
   • Now, add \( 13 \): \[ \frac{5}{3} + 13 = \frac{5}{3} + \frac{39}{3} = \frac{44}{3} \]
   • This does not equal \( \frac{4}{3} \).

2. \( A = 1 \frac{2}{3} - 13 \):

   • Continue with \( \frac{5}{3} \): \[ \frac{5}{3} - 13 = \frac{5}{3} - \frac{39}{3} = \frac{5 - 39}{3} = \frac{-34}{3} \]
   • This does not equal \( \frac{4}{3} \).

3. \( A = 1 \frac{5}{3} + 13 \):

   • Convert \( 1 \frac{5}{3} \): \[ 1 \frac{5}{3} = \frac{8}{3} \]
   • Now, add \( 13 \): \[ \frac{8}{3} + 13 = \frac{8}{3} + \frac{39}{3} = \frac{47}{3} \]
   • This does not equal \( \frac{4}{3} \).

4. \( A = -1 \frac{2}{3} + 13 \):

   • Convert \( -1 \frac{2}{3} \): \[ -1 \frac{2}{3} = -\frac{5}{3} \]
   • Now, add \( 13 \): \[ -\frac{5}{3} + 13 = -\frac{5}{3} + \frac{39}{3} = \frac{34}{3} \]
   • This does not equal \( \frac{4}{3} \).

None of the expressions for \( A \) resulted in \( \frac{4}{3} \). There might have been a misunderstanding with the expressions. To find a mix of a fraction or integer equivalent to \( A = 1 \frac{1}{3} \) from the given expressions, you can review or adjust that list based on specified values.

Answer 2

can you explain the answer more simpler and make the answer more visable

Answer 3

Sure! Let's simplify the explanation and clarify the steps.

We start with the equation: \[ A = 5 - \frac{11}{3} \]

Step 1: Simplify the Right Side

Convert \( 5 \) to a fraction with a denominator of \( 3 \): \[ 5 = \frac{15}{3} \] Now, perform the subtraction: \[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]

Step 2: Convert \( \frac{4}{3} \) to a Mixed Number

\(\frac{4}{3}\) can be expressed as a mixed number: \[ \frac{4}{3} = 1 \frac{1}{3} \]

Now we are looking for an expression for \( A \) that equals \( 1 \frac{1}{3} \) (or \( \frac{4}{3} \)).

Step 3: Evaluate Each Expression

Let’s evaluate each expression one by one:

1. \( A = 1 \frac{2}{3} + 13 \):

   • Convert \( 1 \frac{2}{3} \) to an improper fraction: \[ 1 \frac{2}{3} = \frac{5}{3} \]
   • Calculate: \[ \frac{5}{3} + 13 = \frac{5}{3} + \frac{39}{3} = \frac{44}{3} \quad (\text{not } \frac{4}{3}) \]

2. \( A = 1 \frac{2}{3} - 13 \):

   • Continue with \( 1 \frac{2}{3} = \frac{5}{3} \):
   • Calculate: \[ \frac{5}{3} - 13 = \frac{5}{3} - \frac{39}{3} = \frac{-34}{3} \quad (\text{not } \frac{4}{3}) \]

3. \( A = 1 \frac{5}{3} + 13 \):

   • Convert \( 1 \frac{5}{3} \): \[ 1 \frac{5}{3} = \frac{8}{3} \]
   • Calculate: \[ \frac{8}{3} + 13 = \frac{8}{3} + \frac{39}{3} = \frac{47}{3} \quad (\text{not } \frac{4}{3}) \]

4. \( A = -1 \frac{2}{3} + 13 \):

   • Convert \( -1 \frac{2}{3} \): \[ -1 \frac{2}{3} = -\frac{5}{3} \]
   • Calculate: \[ -\frac{5}{3} + 13 = -\frac{5}{3} + \frac{39}{3} = \frac{34}{3} \quad (\text{not } \frac{4}{3}) \]

Conclusion

None of the provided expressions match \( A = \frac{4}{3} \) or \( 1 \frac{1}{3} \).

If you're looking for an expression that equals \( \frac{4}{3} \), none of the listed options work. If you need to clarify or correct the expressions provided, it would help to identify one that truly equals \( 1 \frac{1}{3} \).