Question

1. Write these percentage as fractions and decimals:
A) 60%
B) 240%
C) $$12{\displaystyle \frac{1}{2}}\mathrm{\%}$$
D) $$55{\displaystyle \frac{2}{3}}\mathrm{\%}$$
2. Write these numbers as percentage:
i) ${\displaystyle \frac{3}{4}}$
ii) ${\displaystyle \frac{21}{40}}$
iii) 0.0087
iv) 0.375
v) 1.07

Answer 1

Hint: We will first get to know how we convert a percentage into fraction and thus decimal and then apply all that to part 1 of question and then learn how to convert numbers into percentage and then apply that to part 2 of question.

Complete step-by-step solution:
We know that Number is equal to the given percentage divided by 100.
So, we have: $Number={\displaystyle \frac{Percentage}{100}}$.
So, to convert the percentage into fractions and decimals, we will require to divide the given percentage quantity by 100 and then to get percentage from number, we will multiply it by 100 to obtain percentage.
Part 1:
Here, we need to convert percentage into numbers.
So, we will use $Number={\displaystyle \frac{Percentage}{100}}$.
A) We are given 60%.
So, $Number={\displaystyle \frac{Percentage}{100}}={\displaystyle \frac{60}{100}}$
Simplifying the RHS, we will get:-
$Number={\displaystyle \frac{6}{10}}={\displaystyle \frac{3}{5}}=0.6$
Hence, 60 % is ${\displaystyle \frac{3}{5}}$ as a fraction and 0.6 as decimals.
B) We are given 240%.
So, $Number={\displaystyle \frac{Percentage}{100}}={\displaystyle \frac{240}{100}}$
Simplifying the RHS, we will get:-
$Number={\displaystyle \frac{24}{10}}={\displaystyle \frac{12}{5}}=2.4$
Hence, 240 % is ${\displaystyle \frac{12}{5}}$ as a fraction and 2.4 as decimals.
C) We are given $$12{\displaystyle \frac{1}{2}}\mathrm{\%}$$.
We will first convert into an improper fraction from the given mixed fraction.
So, we get: $$12{\displaystyle \frac{1}{2}}\mathrm{\%}={\displaystyle \frac{2\times 12+1}{2}}\mathrm{\%}={\displaystyle \frac{25}{2}}\mathrm{\%}$$
Now, $Number={\displaystyle \frac{Percentage}{100}}={\displaystyle \frac{{\displaystyle \frac{25}{2}}}{100}}$
Simplifying the RHS, we will get:-
$$Number={\displaystyle \frac{25}{200}}={\displaystyle \frac{1}{8}}=0.125$$
Hence, $$12{\displaystyle \frac{1}{2}}\mathrm{\%}$$ is ${\displaystyle \frac{1}{8}}$ as a fraction and 0.125 as decimals.
D) We are given $$55{\displaystyle \frac{2}{3}}\mathrm{\%}$$.
We will first convert into an improper fraction from the given mixed fraction.
So, we get: $$55{\displaystyle \frac{2}{3}}\mathrm{\%}={\displaystyle \frac{3\times 55+2}{3}}\mathrm{\%}={\displaystyle \frac{167}{3}}\mathrm{\%}$$
Now, $Number={\displaystyle \frac{Percentage}{100}}={\displaystyle \frac{{\displaystyle \frac{167}{3}}}{100}}$
Simplifying the RHS, we will get:-
$$Number={\displaystyle \frac{167}{300}}=0.55\bar{6}$$
Hence, $$55{\displaystyle \frac{2}{3}}\mathrm{\%}$$ is ${\displaystyle \frac{167}{300}}$ as fraction and $$0.55\bar{6}$$ as decimals.
Part 2:
Here, we need to convert percentage into numbers.
So, we will use $Percentage=Number\times 100$.
i) We are given ${\displaystyle \frac{3}{4}}$.
So, $Percentage=Number\times 100={\displaystyle \frac{3}{4}}\times 100$
Simplifying the RHS, we will get:-
$Percentage=3\times 25=75\mathrm{\%}$
Hence, ${\displaystyle \frac{3}{4}}$ is equivalent to 75%.
ii) We are given ${\displaystyle \frac{21}{40}}$.
So, $Percentage=Number\times 100={\displaystyle \frac{21}{40}}\times 100$
Simplifying the RHS, we will get:-
$Percentage=21\times 2.5=52.5\mathrm{\%}$
Hence, ${\displaystyle \frac{21}{40}}$ is equivalent to 52.5%.
iii) We are given 0.0087.
So, $Percentage=Number\times 100=0.0087\times 100$
Simplifying the RHS, we will get:-
$Percentage=0.87\mathrm{\%}$
Hence, 0.0087 is equivalent to 0.87%.
iv) We are given 0.375.
So, $Percentage=Number\times 100=0.375\times 100$
Simplifying the RHS, we will get:-
$Percentage=37.5\mathrm{\%}$
Hence, 0.375 is equivalent to 37.5%.
v) We are given 1.07.
So, $Percentage=Number\times 100=1.07\times 100$
Simplifying the RHS, we will get:-
$Percentage=107\mathrm{\%}$
Hence, 1.07 is equivalent to 107%.

Note: The students must commit to the formula: $Number={\displaystyle \frac{Percentage}{100}}$ because both the questions 1 and 2 can be solved using this formula only by molding it a bit.
The students must note that the word “percent” refers to ‘per cent’ which means “per 100”. So, to convert a percentage into a number, we divide it by 100 because present represents a quantity per 100. Similarly, we can do vice versa.
The students must note that there is a bit of difference between “percentage” and “percent”. Percentage is the resultant obtained by multiplying some quantity by percent. For example:- 50% of 10 kites is 5 kites: “5 kites” is the percentage. But we use both of these words as the same only.