krit.club logo

Fractions in Disguise - Fractions as Percentages

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

A percentage is a fraction where the denominator is always 100100. The symbol used for percentage is %\%.

•

The word 'percent' comes from the Latin 'per centum', meaning 'by the hundred'.

•

To convert a fraction into a percentage, multiply the fraction by 100100 and append the %\% sign. For example, ab=(ab×100)%\frac{a}{b} = \left( \frac{a}{b} \times 100 \right)\%.

•

To convert a percentage into a fraction, remove the %\% sign and divide the number by 100100, then simplify the fraction to its lowest terms: x%=x100x\% = \frac{x}{100}.

•

Percentages are 'fractions in disguise' because they represent parts of a whole, just like fractions and decimals. For example, 0.250.25, 14\frac{1}{4}, and 25%25\% all represent the same value.

•

When comparing two quantities with different totals, converting them to percentages makes comparison easier.

📐Formulae

Percentage=ValueTotal Value×100\text{Percentage} = \frac{\text{Value}}{\text{Total Value}} \times 100

x%=x100x\% = \frac{x}{100}

Fraction to Percentage: ab→(ab×100)%\text{Fraction to Percentage: } \frac{a}{b} \rightarrow \left( \frac{a}{b} \times 100 \right)\%

Decimal to Percentage: d→(d×100)%\text{Decimal to Percentage: } d \rightarrow (d \times 100)\%

💡Examples

Problem 1:

Convert the fraction 45\frac{4}{5} into a percentage.

Solution:

45×100=4×20=80%\frac{4}{5} \times 100 = 4 \times 20 = 80\%

Explanation:

To convert a fraction to a percentage, we multiply by 100100. Here, 55 divides 100100 exactly 2020 times, and 4×20=804 \times 20 = 80.

Problem 2:

A student scored 340340 marks out of 400400 in an exam. Find the percentage of marks obtained.

Solution:

Percentage=(340400×100)%=3404%=85%\text{Percentage} = \left( \frac{340}{400} \times 100 \right)\% = \frac{340}{4}\% = 85\%

Explanation:

We use the formula Obtained MarksTotal Marks×100\frac{\text{Obtained Marks}}{\text{Total Marks}} \times 100 to find the percentage.

Problem 3:

Convert 37.5%37.5\% into a fraction in its simplest form.

Solution:

37.5%=37.5100=3751000=3837.5\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}

Explanation:

First, we remove the percent sign and divide by 100100. To remove the decimal, we multiply numerator and denominator by 1010. Finally, we simplify by dividing both by their greatest common divisor, 125125.

Problem 4:

Out of a total budget of ₹5000₹ 5000, a person spent ₹1250₹ 1250 on groceries. Calculate the remaining amount and find what percentage of the total budget is left.

Solution:

First, calculate the remaining amount: 5000−12503750\begin{array}{r} 5000 \\ -1250 \\ \hline 3750 \end{array} Remaining Percentage: (37505000×100)%=3755%=75%\left( \frac{3750}{5000} \times 100 \right)\% = \frac{375}{5}\% = 75\%

Explanation:

We subtract the spent amount from the total to find the remainder (₹3750₹ 3750). Then, we express this remainder as a fraction of the total and multiply by 100100 to get the percentage.