Answer :
Let's solve the given problems step by step by converting the units to make the calculations easier.
Express the first quantity as a percentage of the second quantity:
a. 15 cm, 3 m
Convert 3 m to cm: [tex]3 \text{ m} = 300 \text{ cm}[/tex].
Calculate the percentage: [tex]\frac{15}{300} \times 100 = 5\%[/tex].
b. 1.5 kg, 900 g
Convert 1.5 kg to grams: [tex]1.5 \text{ kg} = 1500 \text{ g}[/tex].
Calculate the percentage: [tex]\frac{1500}{900} \times 100 = 166.67\%[/tex].
c. 45 minutes, 1.5 hours
Convert 1.5 hours to minutes: [tex]1.5 \text{ hours} = 90 \text{ minutes}[/tex].
Calculate the percentage: [tex]\frac{45}{90} \times 100 = 50\%[/tex].
d. 335 cm, 5.5 m
Convert 5.5 m to cm: [tex]5.5 \text{ m} = 550 \text{ cm}[/tex].
Calculate the percentage: [tex]\frac{335}{550} \times 100 \approx 60.91\%[/tex].
e. 1 year, 6 months
Convert 1 year to months: [tex]1 \text{ year} = 12 \text{ months}[/tex].
Calculate the percentage: [tex]\frac{12}{6} \times 100 = 200\%[/tex].
f. 1 litre, 15 millilitres
Convert 1 litre to millilitres: [tex]1 \text{ litre} = 1000 \text{ ml}[/tex].
Calculate the percentage: [tex]\frac{1000}{15} \times 100 \approx 6666.67\%[/tex].
g. 500 g, 2 kg
Convert 2 kg to grams: [tex]2 \text{ kg} = 2000 \text{ g}[/tex].
Calculate the percentage: [tex]\frac{500}{2000} \times 100 = 25\%[/tex].
Given 105 students in a class with 35 girls, find the percentage of:
a. Boys
Number of boys: [tex]105 - 35 = 70[/tex].
Percentage of boys: [tex]\frac{70}{105} \times 100 \approx 66.67\%[/tex].
b. Girls
Percentage of girls: [tex]\frac{35}{105} \times 100 \approx 33.33\%[/tex].
Find 1/6 percent of 2/3:
Convert 1/6 percent to a decimal: [tex]\frac{1}{6} \times \frac{1}{100} = \frac{1}{600}[/tex].
Multiply by 2/3: [tex]\frac{1}{600} \times \frac{2}{3} = \frac{2}{1800} = \frac{1}{900}[/tex].
So, 1/6 percent of 2/3 is [tex]\frac{1}{900}[/tex].
