`7(1)/(3)-(5)/(9) "of" 4(1)/(5)=?`

Options

A. `5`
B. `3`
C. `21`
D. `7`

Answer

To solve the expression \( 7 \frac{1}{3} - \frac{5}{9} \text{ of } 4 \frac{1}{5} \), we will follow these steps:

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

- For \( 7 \frac{1}{3} \):
\[ 7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} \]

- For \( 4 \frac{1}{5} \):
\[ 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \]

### Step 2: Rewrite the Expression
Now, we can rewrite the original expression using the improper fractions:
\[ \frac{22}{3} - \frac{5}{9} \text{ of } \frac{21}{5} \]

### Step 3: Calculate the "of" (Multiplication)
Next, we interpret "of" as multiplication:
\[ \frac{5}{9} \text{ of } \frac{21}{5} = \frac{5}{9} \times \frac{21}{5} \]
The \( 5 \) in the numerator and denominator cancels out:
\[ = \frac{21}{9} \]

### Step 4: Rewrite the Expression Again
Now we have:
\[ \frac{22}{3} - \frac{21}{9} \]

### Step 5: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple of \( 3 \) and \( 9 \) is \( 9 \).

- Convert \( \frac{22}{3} \) to have a denominator of \( 9 \):
\[ \frac{22}{3} = \frac{22 \times 3}{3 \times 3} = \frac{66}{9} \]

### Step 6: Perform the Subtraction
Now we can perform the subtraction:
\[ \frac{66}{9} - \frac{21}{9} = \frac{66 - 21}{9} = \frac{45}{9} \]

### Step 7: Simplify the Result
Finally, simplify \( \frac{45}{9} \):
\[ \frac{45}{9} = 5 \]

### Final Answer
Thus, the answer to the expression \( 7 \frac{1}{3} - \frac{5}{9} \text{ of } 4 \frac{1}{5} \) is \( 5 \).

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