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...
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.
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.
To convert a percentage to a fraction, place the percentage over 100 and simplify if possible. For 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.
To find a percentage of an amount, multiply the amount by the percentage (as a decimal). For example:
Find 20% of 50.
Solution:
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.
Calculate the percentage increase if a price rises from £50 to £60.
Solution:
Common problems involving percentages include calculating discounts, profit, and loss. For example, if an item costs £80 and is on a 25% discount:
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.