What per cent of `7(1)/(3)` m is `5(1)/(2)` m ?

Answer

To find what percent of \(7 \frac{1}{3}\) m is \(5 \frac{1}{2}\) m, we can follow these steps:

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

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

- For \(5 \frac{1}{2}\):
\[ 5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = \frac{11}{2} \]

### Step 2: Set Up the Percentage Formula
The formula to find the percentage is:
\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
Here, the part is \(5 \frac{1}{2}\) m and the whole is \(7 \frac{1}{3}\) m. Substituting the improper fractions:
\[ \text{Percentage} = \left( \frac{\frac{11}{2}}{\frac{22}{3}} \right) \times 100 \]

### Step 3: Simplify the Fraction
To simplify \(\frac{\frac{11}{2}}{\frac{22}{3}}\), we multiply by the reciprocal of the denominator:
\[ \frac{11}{2} \times \frac{3}{22} = \frac{11 \times 3}{2 \times 22} = \frac{33}{44} \]

### Step 4: Reduce the Fraction
Now, we can simplify \(\frac{33}{44}\):
\[ \frac{33 \div 11}{44 \div 11} = \frac{3}{4} \]

### Step 5: Calculate the Percentage
Now we substitute back into the percentage formula:
\[ \text{Percentage} = \frac{3}{4} \times 100 \]
Calculating this gives:
\[ \frac{3 \times 100}{4} = \frac{300}{4} = 75 \]

### Final Answer
Thus, \(5 \frac{1}{2}\) m is \(75\%\) of \(7 \frac{1}{3}\) m.

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