Sure! Let's go through the step-by-step solution for each part of the question:
### Part (i): [tex]\(20 \times \frac{4}{5}\)[/tex]
1. Multiply the whole number by the numerator of the fraction:
[tex]\[
20 \times 4 = 80
\][/tex]
2. Write this result over the original denominator of the fraction:
[tex]\[
\frac{80}{5}
\][/tex]
3. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):
[tex]\[
\text{GCD of 80 and 5 is 5.}
\][/tex]
[tex]\[
\frac{80 \div 5}{5 \div 5} = \frac{16}{1}
\][/tex]
4. Convert the resulting fraction into a mixed number (if necessary):
Since the numerator [tex]\(16\)[/tex] is greater than the denominator [tex]\(1\)[/tex], we can convert it to a mixed number:
[tex]\[
\frac{16}{1} \text{ is equivalent to } 16.
\][/tex]
So, the final result for [tex]\(20 \times \frac{4}{5}\)[/tex] is:
[tex]\[
16
\][/tex]
### Part (ii): [tex]\(15 \times \frac{1}{3}\)[/tex]
1. Multiply the whole number by the numerator of the fraction:
[tex]\[
15 \times 1 = 15
\][/tex]
2. Write this result over the original denominator of the fraction:
[tex]\[
\frac{15}{3}
\][/tex]
3. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):
[tex]\[
\text{GCD of 15 and 3 is 3.}
\][/tex]
[tex]\[
\frac{15 \div 3}{3 \div 3} = \frac{5}{1}
\][/tex]
4. Convert the resulting fraction into a mixed number (if necessary):
Since the numerator [tex]\(5\)[/tex] is greater than the denominator [tex]\(1\)[/tex], we can convert it to a mixed number:
[tex]\[
\frac{5}{1} \text{ is equivalent to } 5.
\][/tex]
So, the final result for [tex]\(15 \times \frac{1}{3}\)[/tex] is:
[tex]\[
5
\][/tex]
In summary:
- [tex]\(20 \times \frac{4}{5} = 16\)[/tex]
- [tex]\(15 \times \frac{1}{3} = 5\)[/tex]
