What should be subtracted from `(-5)/(7)` to get `( 2)/(3)` ?

Options

A. `(1)/(3)`
B. `(-1)/(21)`
C. `(-29)/(21)`
D. `(1)/(21)`

Answer

To solve the problem of what should be subtracted from \(-\frac{5}{7}\) to get \(\frac{2}{3}\), we can set up the equation as follows:

Let \(x\) be the number that needs to be subtracted. According to the problem, we have:

\[ -\frac{5}{7} - x = \frac{2}{3} \]

### Step 1: Rearranging the Equation
To find \(x\), we can rearrange the equation to isolate \(x\):

\[ -x = \frac{2}{3} + \frac{5}{7} \]

### Step 2: Finding a Common Denominator
Next, we need to add the fractions \(\frac{2}{3}\) and \(\frac{5}{7}\). To do this, we need a common denominator. The least common multiple (LCM) of 3 and 7 is 21.

### Step 3: Converting Fractions
Now, we convert both fractions to have the common denominator of 21:

\[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]
\[ \frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21} \]

### Step 4: Adding the Fractions
Now we can add the two fractions:

\[ -\frac{5}{7} - x = \frac{14}{21} + \frac{15}{21} = \frac{29}{21} \]

### Step 5: Solving for \(x\)
Now we have:

\[ -x = \frac{29}{21} \]

To find \(x\), we multiply both sides by -1:

\[ x = -\frac{29}{21} \]

### Final Answer
Thus, the number that should be subtracted from \(-\frac{5}{7}\) to get \(\frac{2}{3}\) is:

\[ \boxed{-\frac{29}{21}} \]

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