The area of a sheet of paper is 623`7/10` sq. cm. If its length is 29`7/10` cm, find its width.

Answer

To find the width of the sheet of paper given its area and length, we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
The area of the sheet of paper is given as \( 623 \frac{7}{10} \) sq. cm. To convert this to an improper fraction:

\[ 623 \frac{7}{10} = \frac{623 \times 10 + 7}{10} = \frac{6230 + 7}{10} = \frac{6237}{10} \text{ sq. cm} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator, then place that result over the denominator.

### Step 2: Convert the length to an improper fraction
The length is given as \( 29 \frac{7}{10} \) cm. We convert this in the same way:

\[ 29 \frac{7}{10} = \frac{29 \times 10 + 7}{10} = \frac{290 + 7}{10} = \frac{297}{10} \text{ cm} \]

**Hint:** Use the same method as in Step 1 to convert the mixed number for length to an improper fraction.

### Step 3: Use the formula for area
The formula for the area of a rectangle is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

To find the width, we rearrange this formula:

\[ \text{Width} = \frac{\text{Area}}{\text{Length}} \]

### Step 4: Substitute the values
Now we substitute the values we found for area and length:

\[ \text{Width} = \frac{\frac{6237}{10}}{\frac{297}{10}} \]

### Step 5: Simplify the division of fractions
Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \text{Width} = \frac{6237}{10} \times \frac{10}{297} \]

The \(10\) in the numerator and denominator cancels out:

\[ \text{Width} = \frac{6237}{297} \]

### Step 6: Simplify the fraction
Now we need to simplify \( \frac{6237}{297} \). We can check for common factors. Both numbers can be divided by 3:

\[ 6237 \div 3 = 2079 \quad \text{and} \quad 297 \div 3 = 99 \]

So, we have:

\[ \text{Width} = \frac{2079}{99} \]

Next, we can simplify this further by dividing both by 9:

\[ 2079 \div 9 = 231 \quad \text{and} \quad 99 \div 9 = 11 \]

Thus, we have:

\[ \text{Width} = \frac{231}{11} \]

### Step 7: Perform the division
Now we divide:

\[ 231 \div 11 = 21 \]

So, the width of the sheet of paper is:

\[ \text{Width} = 21 \text{ cm} \]

**Final Answer:** The width of the sheet of paper is \( 21 \text{ cm} \).

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