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1. Multiply and reduce to the lowest form and convert into a mixed fraction:

(i) [tex]\( 20 \times \frac{4}{5} \)[/tex]

(ii) [tex]\( 15 \times \frac{1}{3} \)[/tex]


Sagot :

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]