Of course! Let's break down each problem step by step.
### Problem 3: Pillows with Cotton
#### Given:
- Amount of cotton needed to make one pillow: [tex]\( 1 \frac{2}{3} \)[/tex] kg
- Total amount of cotton available: [tex]\( 11 \frac{2}{3} \)[/tex] kg
#### Step-by-step Solution:
1. Convert Mixed Numbers to Improper Fractions:
- [tex]\( 1 \frac{2}{3} \)[/tex] can be written as [tex]\( \frac{5}{3} \)[/tex] kg
- [tex]\( 11 \frac{2}{3} \)[/tex] can be written as [tex]\( \frac{35}{3} \)[/tex] kg
2. Calculate the Number of Pillows:
- To find out how many pillows Rina can make, we divide the total cotton by the amount needed for one pillow:
[tex]\[
\frac{\text{Total Cotton}}{\text{Cotton per Pillow}} = \frac{\frac{35}{3}}{\frac{5}{3}}
\][/tex]
- Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\frac{35}{3} \times \frac{3}{5} = 35 \times \frac{1}{5} = 7
\][/tex]
Thus, Rina can make 7 pillows with [tex]\( 11 \frac{2}{3} \)[/tex] kg of cotton.
### Problem 4: Sweets in Boxes
#### Given:
- Amount of sweets in one box: [tex]\( \frac{1}{4} \)[/tex] kg
- Total amount of sweets available: [tex]\( 2 \frac{3}{4} \)[/tex] kg
#### Step-by-step Solution:
1. Convert Mixed Number to Improper Fraction:
- [tex]\( 2 \frac{3}{4} \)[/tex] can be written as [tex]\( \frac{11}{4} \)[/tex] kg
2. Calculate the Number of Boxes:
- To find out how many boxes are needed to contain all the sweets, we divide the total sweets by the amount per box:
[tex]\[
\frac{\text{Total Sweets}}{\text{Sweets per Box}} = \frac{\frac{11}{4}}{\frac{1}{4}}
\][/tex]
- Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\frac{11}{4} \times 4 = 11
\][/tex]
Thus, 11 boxes are needed to contain [tex]\( 2 \frac{3}{4} \)[/tex] kg of sweets.
To summarize:
- Rina can make 7 pillows with [tex]\( 11 \frac{2}{3} \)[/tex] kg of cotton.
- 11 boxes are needed to contain [tex]\( 2 \frac{3}{4} \)[/tex] kg of sweets.
