To determine how much each friend receives when Sahil divides [tex]\( 5 \frac{1}{4} \, \text{kg} \)[/tex] of sweets equally among seven friends, we can follow these steps:
1. Convert the Mixed Number to an Improper Fraction:
- A mixed number consists of a whole number and a fraction. Here, [tex]\( 5 \frac{1}{4} \, \text{kg} \)[/tex] means 5 whole kilograms and [tex]\( \frac{1}{4} \)[/tex] kilogram.
- First, convert the whole part to the same denominator as the fraction part.
[tex]\( 5 = \frac{20}{4} \)[/tex]
- Hence, [tex]\( 5 \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \)[/tex].
2. Divide the Improper Fraction by the Number of Friends:
- Now, divide [tex]\( \frac{21}{4} \, \text{kg} \)[/tex] of sweets by 7 friends.
- The operation involves dividing the numerator by 7 while keeping the same denominator:
[tex]\[
\frac{21}{4} \div 7 = \frac{21}{4} \times \frac{1}{7}
\][/tex]
- This simplifies to:
[tex]\[
\frac{21 \times 1}{4 \times 7} = \frac{21}{28}
\][/tex]
3. Simplify the Fraction:
- Simplify [tex]\( \frac{21}{28} \)[/tex] by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 21 and 28 is 7.
[tex]\[
\frac{21 \div 7}{28 \div 7} = \frac{3}{4}
\][/tex]
Thus, each friend receives [tex]\( \frac{3}{4} \, \text{kg} \)[/tex].
Therefore, the correct option is:
b) [tex]\( \frac{3}{4} \)[/tex]
