Answer :
Sure! Let's solve the question step-by-step:
### 1. Write the percentage equivalent of the following fractions:
a. [tex]\(\frac{1}{4}\)[/tex]: To convert this fraction to a percentage, multiply by 100.
[tex]\[\frac{1}{4} \times 100 = 25\%\][/tex]
b. [tex]\(\frac{2}{3}\)[/tex]: Multiply by 100 to convert to a percentage.
[tex]\[\frac{2}{3} \times 100 = 66.67\%\][/tex]
c. [tex]\(\frac{5}{8}\)[/tex]: Multiply by 100 to convert to a percentage.
[tex]\[\frac{5}{8} \times 100 = 62.5\%\][/tex]
d. [tex]\(1 \frac{4}{5}\)[/tex] is equivalent to [tex]\(\frac{9}{5}\)[/tex]. Multiply by 100.
[tex]\[\frac{9}{5} \times 100 = 180\%\][/tex]
e. [tex]\(4 \frac{9}{10}\)[/tex] is equivalent to [tex]\(\frac{49}{10}\)[/tex]. Multiply by 100.
[tex]\[\frac{49}{10} \times 100 = 490\%\][/tex]
f. [tex]\(3 \frac{7}{8}\)[/tex] is equivalent to [tex]\(\frac{31}{8}\)[/tex]. Multiply by 100.
[tex]\[\frac{31}{8} \times 100 = 387.5\%\][/tex]
### 2. Write the decimal equivalent of the following:
a. [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[0.75\][/tex]
b. [tex]\(80\%\)[/tex]: Convert percentage to a decimal by dividing by 100.
[tex]\[0.80\][/tex]
c. [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[0.2\][/tex]
d. [tex]\(7\%\)[/tex]: Convert percentage to a decimal by dividing by 100.
[tex]\[0.07\][/tex]
e. [tex]\(1 \frac{7}{8}\)[/tex] is equivalent to 1 plus [tex]\(\frac{7}{8}\)[/tex].
[tex]\[1.875\][/tex]
f. [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[0.1667\][/tex]
### 3. Evaluate the following percentages:
a. [tex]\(25\%\)[/tex] of 80:
[tex]\[0.25 \times 80 = 20\][/tex]
b. [tex]\(80\%\)[/tex] of 125:
[tex]\[0.80 \times 125 = 100\][/tex]
c. [tex]\(62.5\%\)[/tex] of 80:
[tex]\[0.625 \times 80 = 50\][/tex]
d. [tex]\(30\%\)[/tex] of 120:
[tex]\[0.30 \times 120 = 36\][/tex]
e. [tex]\(90\%\)[/tex] of 5:
[tex]\[0.90 \times 5 = 4.5\][/tex]
f. [tex]\(25\%\)[/tex] of 30:
[tex]\[0.25 \times 30 = 7.5\][/tex]
### 4. Evaluate the following percentages:
a. [tex]\(17\%\)[/tex] of 50:
[tex]\[0.17 \times 50 = 8.5\][/tex]
b. [tex]\(50\%\)[/tex] of 17:
[tex]\[0.50 \times 17 = 8.5\][/tex]
d. [tex]\(80\%\)[/tex] of 65:
[tex]\[0.80 \times 65 = 52\][/tex]
e. [tex]\(7\%\)[/tex] of 250:
[tex]\[0.07 \times 250 = 17.5\][/tex]
c. [tex]\(65\%\)[/tex] of 80:
[tex]\[0.65 \times 80 = 52\][/tex]
f. [tex]\(250\%\)[/tex] of 7:
[tex]\[2.50 \times 7 = 17.5\][/tex]
### 5. Calculate the number of students with different hair colors in a class of 30 students:
a. Black hair ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 30 = 6\][/tex]
b. Blonde hair ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 30 = 3\][/tex]
c. Brown hair ([tex]\(70\%\)[/tex]):
[tex]\[0.70 \times 30 = 21\][/tex]
### 6. Calculate the number of children preferring each type of meat in a survey of 120 school children:
a. Lamb ([tex]\(55\%\)[/tex]):
[tex]\[0.55 \times 120 = 66\][/tex]
b. Chicken ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 120 = 24\][/tex]
c. Duck ([tex]\(15\%\)[/tex]):
[tex]\[0.15 \times 120 = 18\][/tex]
d. Turkey ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 120 = 12\][/tex]
### 7. Calculate the number of students of each nationality in a school of 220 students:
a. Australian ([tex]\(65\%\)[/tex]):
[tex]\[0.65 \times 220 = 143\][/tex]
b. Pakistani ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 220 = 44\][/tex]
c. Greek ([tex]\(5\%\)[/tex]):
[tex]\[0.05 \times 220 = 11\][/tex]
d. Other nationalities ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 220 = 22\][/tex]
### 8. Calculate the number of each item sold by the shopkeeper, out of 150 items:
a. Newspapers ([tex]\(46\%\)[/tex]):
[tex]\[0.46 \times 150 = 69\][/tex]
b. Pens ([tex]\(24\%\)[/tex]):
[tex]\[0.24 \times 150 = 36\][/tex]
c. Books ([tex]\(12\%\)[/tex]):
[tex]\[0.12 \times 150 = 18\][/tex]
d. Other items ([tex]\(18\%\)[/tex]):
[tex]\[0.18 \times 150 = 27\][/tex]
I hope this breakdown helps you understand how to work out percentages and decimals from fractions, and how to apply percentage calculations to real-world contexts! Let me know if you have any questions.
### 1. Write the percentage equivalent of the following fractions:
a. [tex]\(\frac{1}{4}\)[/tex]: To convert this fraction to a percentage, multiply by 100.
[tex]\[\frac{1}{4} \times 100 = 25\%\][/tex]
b. [tex]\(\frac{2}{3}\)[/tex]: Multiply by 100 to convert to a percentage.
[tex]\[\frac{2}{3} \times 100 = 66.67\%\][/tex]
c. [tex]\(\frac{5}{8}\)[/tex]: Multiply by 100 to convert to a percentage.
[tex]\[\frac{5}{8} \times 100 = 62.5\%\][/tex]
d. [tex]\(1 \frac{4}{5}\)[/tex] is equivalent to [tex]\(\frac{9}{5}\)[/tex]. Multiply by 100.
[tex]\[\frac{9}{5} \times 100 = 180\%\][/tex]
e. [tex]\(4 \frac{9}{10}\)[/tex] is equivalent to [tex]\(\frac{49}{10}\)[/tex]. Multiply by 100.
[tex]\[\frac{49}{10} \times 100 = 490\%\][/tex]
f. [tex]\(3 \frac{7}{8}\)[/tex] is equivalent to [tex]\(\frac{31}{8}\)[/tex]. Multiply by 100.
[tex]\[\frac{31}{8} \times 100 = 387.5\%\][/tex]
### 2. Write the decimal equivalent of the following:
a. [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[0.75\][/tex]
b. [tex]\(80\%\)[/tex]: Convert percentage to a decimal by dividing by 100.
[tex]\[0.80\][/tex]
c. [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[0.2\][/tex]
d. [tex]\(7\%\)[/tex]: Convert percentage to a decimal by dividing by 100.
[tex]\[0.07\][/tex]
e. [tex]\(1 \frac{7}{8}\)[/tex] is equivalent to 1 plus [tex]\(\frac{7}{8}\)[/tex].
[tex]\[1.875\][/tex]
f. [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[0.1667\][/tex]
### 3. Evaluate the following percentages:
a. [tex]\(25\%\)[/tex] of 80:
[tex]\[0.25 \times 80 = 20\][/tex]
b. [tex]\(80\%\)[/tex] of 125:
[tex]\[0.80 \times 125 = 100\][/tex]
c. [tex]\(62.5\%\)[/tex] of 80:
[tex]\[0.625 \times 80 = 50\][/tex]
d. [tex]\(30\%\)[/tex] of 120:
[tex]\[0.30 \times 120 = 36\][/tex]
e. [tex]\(90\%\)[/tex] of 5:
[tex]\[0.90 \times 5 = 4.5\][/tex]
f. [tex]\(25\%\)[/tex] of 30:
[tex]\[0.25 \times 30 = 7.5\][/tex]
### 4. Evaluate the following percentages:
a. [tex]\(17\%\)[/tex] of 50:
[tex]\[0.17 \times 50 = 8.5\][/tex]
b. [tex]\(50\%\)[/tex] of 17:
[tex]\[0.50 \times 17 = 8.5\][/tex]
d. [tex]\(80\%\)[/tex] of 65:
[tex]\[0.80 \times 65 = 52\][/tex]
e. [tex]\(7\%\)[/tex] of 250:
[tex]\[0.07 \times 250 = 17.5\][/tex]
c. [tex]\(65\%\)[/tex] of 80:
[tex]\[0.65 \times 80 = 52\][/tex]
f. [tex]\(250\%\)[/tex] of 7:
[tex]\[2.50 \times 7 = 17.5\][/tex]
### 5. Calculate the number of students with different hair colors in a class of 30 students:
a. Black hair ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 30 = 6\][/tex]
b. Blonde hair ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 30 = 3\][/tex]
c. Brown hair ([tex]\(70\%\)[/tex]):
[tex]\[0.70 \times 30 = 21\][/tex]
### 6. Calculate the number of children preferring each type of meat in a survey of 120 school children:
a. Lamb ([tex]\(55\%\)[/tex]):
[tex]\[0.55 \times 120 = 66\][/tex]
b. Chicken ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 120 = 24\][/tex]
c. Duck ([tex]\(15\%\)[/tex]):
[tex]\[0.15 \times 120 = 18\][/tex]
d. Turkey ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 120 = 12\][/tex]
### 7. Calculate the number of students of each nationality in a school of 220 students:
a. Australian ([tex]\(65\%\)[/tex]):
[tex]\[0.65 \times 220 = 143\][/tex]
b. Pakistani ([tex]\(20\%\)[/tex]):
[tex]\[0.20 \times 220 = 44\][/tex]
c. Greek ([tex]\(5\%\)[/tex]):
[tex]\[0.05 \times 220 = 11\][/tex]
d. Other nationalities ([tex]\(10\%\)[/tex]):
[tex]\[0.10 \times 220 = 22\][/tex]
### 8. Calculate the number of each item sold by the shopkeeper, out of 150 items:
a. Newspapers ([tex]\(46\%\)[/tex]):
[tex]\[0.46 \times 150 = 69\][/tex]
b. Pens ([tex]\(24\%\)[/tex]):
[tex]\[0.24 \times 150 = 36\][/tex]
c. Books ([tex]\(12\%\)[/tex]):
[tex]\[0.12 \times 150 = 18\][/tex]
d. Other items ([tex]\(18\%\)[/tex]):
[tex]\[0.18 \times 150 = 27\][/tex]
I hope this breakdown helps you understand how to work out percentages and decimals from fractions, and how to apply percentage calculations to real-world contexts! Let me know if you have any questions.