Work these problems with the techniques you've read about in this chapter so far. Then check your answer by solving them with your calculator. If you have any problem go back and review the information just outlined.
Q. `2(1)/(3)-3(3)/(5)`=___________

Answer

To solve the problem \( 2\frac{1}{3} - 3\frac{3}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 2\frac{1}{3} \):
\[ 2\frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = \frac{7}{3} \]

For \( 3\frac{3}{5} \):
\[ 3\frac{3}{5} = 3 \times 5 + 3 = 15 + 3 = \frac{18}{5} \]

### Step 2: Set Up the Subtraction
Now we can rewrite the expression:
\[ \frac{7}{3} - \frac{18}{5} \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators (3 and 5). The LCM of 3 and 5 is 15.

### Step 4: Convert Each Fraction to Have the Same Denominator
Now, we convert each fraction to have the common denominator of 15.

For \( \frac{7}{3} \):
\[ \frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \]

For \( \frac{18}{5} \):
\[ \frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15} \]

### Step 5: Perform the Subtraction
Now we can subtract the two fractions:
\[ \frac{35}{15} - \frac{54}{15} = \frac{35 - 54}{15} = \frac{-19}{15} \]

### Final Answer
Thus, the result of \( 2\frac{1}{3} - 3\frac{3}{5} \) is:
\[ \frac{-19}{15} \]

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