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Number - Percentage of a Quantity and Percentage Change

Grade 6IB

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

🔑Concepts

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A percentage is a way of expressing a number as a fraction of 100100. The symbol used is %\%.

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To find the percentage of a specific quantity, you convert the percentage into a fraction or decimal and multiply it by the quantity. For example, 20%20\% of xx is calculated as 20100×x\frac{20}{100} \times x.

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Percentage change describes the relationship between an old value and a new value. It is always calculated relative to the original (initial) amount.

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A percentage increase occurs when the final value is greater than the original value, while a percentage decrease occurs when the final value is smaller.

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To convert a fraction to a percentage, multiply the fraction by 100100 and add the %\% sign. For example, 14×100=25%\frac{1}{4} \times 100 = 25\%.

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To convert a decimal to a percentage, multiply by 100100. For example, 0.75×100=75%0.75 \times 100 = 75\%.

📐Formulae

Percentage of a Quantity=Percentage100×Total Quantity\text{Percentage of a Quantity} = \frac{\text{Percentage}}{100} \times \text{Total Quantity}

Percentage Change=New Value−Original ValueOriginal Value×100%\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%

Percentage Increase=IncreaseOriginal Value×100%\text{Percentage Increase} = \frac{\text{Increase}}{\text{Original Value}} \times 100\%

Percentage Decrease=DecreaseOriginal Value×100%\text{Percentage Decrease} = \frac{\text{Decrease}}{\text{Original Value}} \times 100\%

💡Examples

Problem 1:

Calculate 15%15\% of 12001200 students in a school.

Solution:

15100×1200=15×12=180\frac{15}{100} \times 1200 = 15 \times 12 = 180

Explanation:

To find the percentage of a quantity, divide the percentage by 100100 and multiply by the total quantity. Here, 15100\frac{15}{100} simplifies to 0.150.15. Multiplying 0.150.15 by 12001200 gives 180180 students.

Problem 2:

A video game originally cost Rs 8080. The price was reduced to Rs 6060. Find the percentage decrease.

Solution:

Step 1: Find the decrease in price. 80−6020\begin{array}{r} 80 \\ - 60 \\ \hline 20 \end{array} Step 2: Use the percentage decrease formula. Percentage Decrease=2080×100%=14×100%=25%\text{Percentage Decrease} = \frac{20}{80} \times 100\% = \frac{1}{4} \times 100\% = 25\%

Explanation:

First, subtract the new price from the original price to find the amount of decrease (Rs 2020). Then, divide this decrease by the original price (Rs 8080) and multiply by 100100 to get the percentage.

Problem 3:

A plant grew from 2020 cm to 2525 cm in one week. What is the percentage increase in its height?

Solution:

Step 1: Find the increase in height. 25−205\begin{array}{r} 25 \\ - 20 \\ \hline 5 \end{array} Step 2: Use the percentage increase formula. Percentage Increase=520×100%=0.25×100%=25%\text{Percentage Increase} = \frac{5}{20} \times 100\% = 0.25 \times 100\% = 25\%

Explanation:

First, calculate the actual growth by subtracting the initial height from the final height (55 cm). Then, divide the growth by the original height (2020 cm). Finally, multiply by 100100 to convert the fraction to a percentage.