Understanding Percentages in 11-Plus Mathematics

Understanding Percentages Percentages are a way of expressing a number as a fraction of 100. They are commonly used in various real-life situations, such as cal...

Understanding Percentages

Percentages are a way of expressing a number as a fraction of 100. They are commonly used in various real-life situations, such as calculating discounts, determining profit and loss, and comparing quantities.

Percentage as 'Parts per Hundred'

When we talk about percentages, we refer to 'parts per hundred'. For example, 25% means 25 parts out of 100. This concept is crucial for understanding how to convert between percentages, fractions, and decimals.

Converting Between Percentages, Fractions, and Decimals

To convert a percentage to a fraction, place the percentage over 100 and simplify if possible. For example:

Worked Example

Convert 40% to a fraction.

Solution:

To convert a percentage to a decimal, divide by 100. For example, 75% as a decimal is 0.75.

Finding Percentages of Amounts

To find a percentage of an amount, multiply the amount by the percentage (as a decimal). For example:

Worked Example

Find 20% of 50.

Solution:

Percentage Increase and Decrease

Percentage increase is calculated by finding the difference between the new and original amount, dividing by the original amount, and then multiplying by 100. Conversely, percentage decrease is found similarly.

Worked Example

Calculate the percentage increase if a price rises from £50 to £60.

Solution:

Solving Problems Involving Percentages

Common problems involving percentages include calculating discounts, profit, and loss. For example, if an item costs £80 and is on a 25% discount:

Worked Example

Find the sale price after a 25% discount.

Solution:

Understanding percentages is essential for success in the 11-plus mathematics exam, as it forms the basis for many practical applications in everyday life.

Related topics:

#percentages #fractions #decimals #problem-solving #11-plus
📚 Category: 11-plus