To find the area of each strip when a sheet of paper with an area of [tex]\( 42 \frac{1}{4} \, \text{cm}^2 \)[/tex] is cut into 13 equal strips, follow these steps:
1. Convert Mixed Number to Improper Fraction:
- The total area of the sheet is given as [tex]\( 42 \frac{1}{4} \, \text{cm}^2 \)[/tex].
- First, convert [tex]\( 42 \frac{1}{4} \)[/tex] to an improper fraction.
- [tex]\( 42 \frac{1}{4} = 42 + \frac{1}{4} = \frac{42 \times 4}{4} + \frac{1}{4} = \frac{168}{4} + \frac{1}{4} = \frac{169}{4} \)[/tex].
2. Divide the Total Area by the Number of Strips:
- The total area of the paper is [tex]\( \frac{169}{4} \, \text{cm}^2 \)[/tex].
- There are 13 strips.
- To find the area of each strip, divide the total area by the number of strips:
[tex]\[
\frac{169}{4} \div 13
\][/tex]
3. Perform the Division:
- To divide by 13, you can multiply by the reciprocal of 13:
[tex]\[
\frac{169}{4} \div 13 = \frac{169}{4} \times \frac{1}{13} = \frac{169 \times 1}{4 \times 13} = \frac{169}{52}
\][/tex]
4. Simplify the Fraction:
- Simplify [tex]\( \frac{169}{52} \)[/tex]. By dividing the numerator and denominator by their greatest common divisor:
[tex]\[
\frac{169}{52} = \frac{169 \div 13}{52 \div 13} = \frac{13}{4}
\][/tex]
5. Convert to Decimal Form:
- This fraction can be converted to a decimal:
[tex]\[
\frac{13}{4} = 3.25
\][/tex]
So, the area of each strip is [tex]\( 3.25 \, \text{cm}^2 \)[/tex].
