Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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].
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].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.