Decimals and Percentages

This lesson covers key decimal and percentage skills for AQA GCSE Mathematics. You will learn how to perform operations with decimals, calculate percentages of amounts, find percentage increase and decrease, and express one quantity as a percentage of another. These skills are essential for both exam papers and real-life applications.

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Operations with Decimals

Adding and Subtracting Decimals

Line up the decimal points and add/subtract as with whole numbers.

Worked Example: Calculate 3.47 + 12.6

   3.47
+ 12.60
-------
  16.07

Answer: 16.07

Multiplying Decimals

Method: Ignore the decimal points, multiply as whole numbers, then put the decimal point back in.

Worked Example: Calculate 2.3 x 0.14

Step 1: 23 x 14 = 322

Step 2: Count the total number of decimal places in the original numbers:

• 2.3 has 1 decimal place
• 0.14 has 2 decimal places
• Total = 3 decimal places

Step 3: Place the decimal point: 0.322

Dividing Decimals

To divide by a decimal, multiply both numbers by a power of 10 to make the divisor a whole number.

Worked Example: Calculate 4.56 divided by 0.3

Step 1: Multiply both by 10: 45.6 divided by 3