*Monday 2 June 2025* *Mathematics* 🥏🎲🥏🎲🥏🎲 *Key Words* Combined operations – are numerical expressions in which multiple operations (addition, subtraction, multiplication or division) are displayed with parentheses. Addition – is an operation that finds the total number when two or more numbers are put together. In other words, addition is the process to find the sum of two or more numbers symbolized by (+). Subtraction – is a mathematical operation that tells us the difference between two numbers it is symbolized by (–). Multiplication – is the process of finding the number (product) obtained by repeated additions of a specified number and it is symbolized by (×). Division – is splitting into equal parts or groups and it is the result of “fair sharing”, it is symbolised by (/ or ÷). Order of Operations Suppose you are asked to evaluate an expression that looks something like this; 8 + 4 × 3 ÷ 2 =? The expression above contains three operations. Can you name them? When an expression contains many operations, we must be careful of what order we do the operations in. For example, if we do all the operations as we would read them (from left to right), we would get the following: 8 + 4 × 3 ÷ 2 = 8 + 12 ÷ 2 = 8 + 6 = 14 However, in a few minutes, we will see why the correct answer is actually 14. The reason for this surprising result is the Order of Operations. The Order of Operations states that you do some things, like multiplication, before others, like addition and subtraction. Here are the rules in the Order of Operations: • Do everything inside of brackets first. • Multiplication and division, performing them left to right. • Addition and subtraction, performing them left to right. Example 1 Evaluate 8 + 4 × 3 ÷ 2 =? Solution 8 + 4 × 3 ÷ 2 = 12 × 3 ÷ 2 = 36 ÷ 2 = 18 (wrong answer) In Example 1, we divided first and then multiplied (left to right). So, it turns out that we were lucky and followed the order of operations without knowing it! In the future, we will always follow the rule above rather than guessing. Let us apply Order of Operations at our example, 8 + 4 × 3 ÷ 2 Multiply 4 and 3 first to get 12 = 8 + 12 ÷ 2 Divide 12 by 2 to get = 8 + 6 Lastly, add 8 and 6 = 14 (correct answer) Example 2 2 + 4 × 3 − 1 =? Solution 2 + 4 × 3 − 1 = 2 + 12 − 1 (× first) = 14 − 1 (+ and − next, so we do + first) = 13 Example 3 9 − 6 + 1 =? Solution 9 − 6 + 1 = 3 + 1 (left to right, as + and − have the same priority) = 4. From the Order of Operations, we see that the division and multiplication must be done before the addition. We also know that we multiply before dividing in this case because the multiplication sign comes first when we read the expression from left to right. *Exercise 1* Solve the following in the right order. 1. 5 × 5 + 9 2. 4+ 2 × 8 + 3 3. 54 + 8 × 7 4. 12 + 2 × 8 + 6 5. 8 + 25 ÷ 5+ 2 6. 3 × 10− 8+ 2 7. 120 − 2 × 8 − 4 8. 63+ 8 × 5 ÷ 8 9. 80 + 18 ÷ 2 × 18 – 7 10. 4 × 4 + 9 – 9 + 1 https://whatsapp.com/channel/0029VacyWp52kNFk9c6opU3Z