Sure, let's solve these multiplication problems step-by-step and reduce the fractions to their lowest forms.
### (i) [tex]\(\frac{2}{7} \times \frac{1}{3}\)[/tex]
1. Multiplication:
[tex]\[
\frac{2}{7} \times \frac{1}{3} = \frac{2 \times 1}{7 \times 3} = \frac{2}{21}
\][/tex]
2. Reduction:
[tex]\(\frac{2}{21}\)[/tex] is already in its simplest form as 2 and 21 have no common factors other than 1.
Result: [tex]\(\frac{2}{21}\)[/tex]
### (iii) [tex]\(\frac{9}{3} \times \frac{5}{5}\)[/tex]
1. Simplify individual fractions:
- [tex]\(\frac{9}{3}\)[/tex] simplifies to 3 because [tex]\(\frac{9 \div 3}{3 \div 3} = \frac{3}{1} = 3\)[/tex].
- [tex]\(\frac{5}{5} = 1\)[/tex].
2. Multiplication:
[tex]\[
3 \times 1 = 3
\][/tex]
Result: 3
### (iv) [tex]\(\frac{9}{5} \times \frac{10}{3} \times \frac{1}{2}\)[/tex]
1. Multiplication:
[tex]\[
\frac{9}{5} \times \frac{10}{3} \times \frac{1}{2} = \frac{9 \times 10 \times 1}{5 \times 3 \times 2} = \frac{90}{30}
\][/tex]
2. Reduction:
[tex]\[
\frac{90}{30} = \frac{90 \div 30}{30 \div 30} = \frac{3}{1} = 3
\][/tex]
Result: 3
### (v) [tex]\(\frac{2}{3} \times 5\frac{1}{5}\)[/tex]
1. Convert the mixed number to an improper fraction:
[tex]\[
5\frac{1}{5} = \frac{5 \times 5 + 1}{5} = \frac{25 + 1}{5} = \frac{26}{5}
\][/tex]
2. Multiplication:
[tex]\[
\frac{2}{3} \times \frac{26}{5} = \frac{2 \times 26}{3 \times 5} = \frac{52}{15}
\][/tex]
3. Reduction:
[tex]\(\frac{52}{15}\)[/tex] is already in its simplest form as 52 and 15 have no common factors other than 1.
Result: [tex]\(\frac{52}{15}\)[/tex]
So, the final results are:
1. [tex]\(\frac{2}{21}\)[/tex]
2. 3
3. 3
4. [tex]\(\frac{52}{15}\)[/tex]
