OCR GCSE Maths: Integer Calculations and Order of Operations

Mastering Integer Calculations and Order of Operations (OCR GCSE Maths)

This tutorial will equip you with the skills to confidently tackle integer calculations without a calculator, focusing on:

• Understanding Integer Operations: Sums, differences, products, and quotients involving positive and negative integers.
• The Power of BIDMAS: Unlocking the order of operations and its role in achieving accurate results.
• Verifying Your Answers: Techniques like inverse operations and estimation to ensure you've got it right.

1. The Basics of Integer Operations

• Adding Integers:

  • When signs are the same, add the numbers and keep the sign.
  • When signs are different, subtract the smaller number from the larger and keep the sign of the larger number.

  Example:
  * 5 + 3 = 8 * -5 + (-3) = -8 * 5 + (-3) = 2 * -5 + 3 = -2

• Subtracting Integers: Change subtraction to addition of the opposite number.

  Example: * 5 - 3 = 5 + (-3) = 2 * -5 - 3 = -5 + (-3) = -8 * 5 - (-3) = 5 + 3 = 8 * -5 - (-3) = -5 + 3 = -2

• Multiplying and Dividing Integers:

  • If signs are the same, the answer is positive.
  • If signs are different, the answer is negative.

  Example: * 5 x 3 = 15 * -5 x (-3) = 15 * 5 x (-3) = -15 * -5 x 3 = -15 * 5 / 3 = 1.67 (approximately) * -5 / (-3) = 1.67 (approximately) * 5 / (-3) = -1.67 (approximately) * -5 / 3 = -1.67 (approximately)

2. The Importance of BIDMAS

BIDMAS stands for Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This order ensures that calculations are performed in a consistent manner, leading to accurate results.

3. Putting it All Together: Examples

• Example 1:

  • Calculate: 3 + 4 x 5 - 2
  • Solution:
    • 4 x 5 = 20 (Multiplication first)
    • 3 + 20 = 23
    • 23 - 2 = 21
  • Therefore, 3 + 4 x 5 - 2 = 21

• Example 2:

  • Calculate: 2 x (5 - 3) + 8 / 2
  • Solution:
    • 5 - 3 = 2 (Brackets first)
    • 2 x 2 = 4 (Multiplication next)
    • 8 / 2 = 4 (Division next)
    • 4 + 4 = 8 (Addition last)
  • Therefore, 2 x (5 - 3) + 8 / 2 = 8

4. Verifying Your Answers

• Inverse Operations: Check your answer by using the opposite operation.

  • Example: If you multiplied by 3, divide the answer by 3 to check.

• Estimation: Round numbers to the nearest whole number and perform the calculation mentally to get an approximate answer. This can help you quickly identify if your exact answer is reasonable.

5. Practice Makes Perfect

The key to mastering integer calculations and order of operations is consistent practice. Work through various problems, gradually increasing the complexity. Don't be afraid to ask for help or refer back to this tutorial if you need guidance. Good luck!