To solve [tex]\(15 \div 6 \frac{2}{3}\)[/tex], we need to follow a sequence of steps for converting and dividing fractions.
1. Convert the mixed number to an improper fraction:
- [tex]\(6 \frac{2}{3}\)[/tex] can be written as an improper fraction.
[tex]\[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3} \][/tex]
2. Invert the divisor and multiply:
- Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\[ 15 \div \frac{20}{3} = 15 \times \frac{3}{20} \][/tex]
3. Perform the multiplication:
- Multiply the numerators and the denominators.
[tex]\[ 15 \times \frac{3}{20} = \frac{15 \times 3}{20} = \frac{45}{20} \][/tex]
4. Simplify the fraction:
- Simplify [tex]\(\frac{45}{20}\)[/tex].
[tex]\[ \frac{45}{20} = \frac{45 \div 5}{20 \div 5} = \frac{9}{4} \][/tex]
5. Convert to a decimal:
- [tex]\(\frac{9}{4} = 2.25\)[/tex]
Since [tex]\( \frac{9}{4} = 2.25 \)[/tex], we check the options and no option directly states 2.25. However, we find the simplified fraction which is [tex]\( \frac{9}{4} \)[/tex].
Upon reviewing the options provided:
A. [tex]\( \frac{21}{4} \)[/tex]
B. [tex]\( 100 \frac{1}{4} \)[/tex]
C. [tex]\( \frac{23}{4} \)[/tex]
D. [tex]\( 100 \)[/tex]
None of these options directly match, [tex]\( \frac{9}{4} \)[/tex] is not among them which is equivalent to 2.25.
Clearly, none of the options (A, B, C, D) correctly match the simplified fraction [tex]\(\frac{9}{4}\)[/tex].
