order of operations
Reading Passage 1
Following the Order of Operations
When a math problem has many steps, we need to solve it in the right order. The order of operations is a list of rules that tells us how to do this. It helps us know what to do first, next, and last.
Look at this expression:
3 + 2(4 − 1)² − 6 ÷ 3
First, solve what is inside the parentheses: (4 − 1) = 3. Now the problem is 3 + 2 × 3² − 6 ÷ 3.
Next, do the exponent. That means 3 × 3 = 9. Now it looks like this: 3 + 2 × 9 − 6 ÷ 3
Now do multiplication and division, from left to right. 2 × 9 = 18, and 6 ÷ 3 = 2. Now the problem is 3 + 18 − 2.
Last, do addition and subtraction. 3 + 18 = 21, then 21 − 2 = 19.
The order of operations helps you know how to do problems in the right steps. That way, you always know what to do next.
Reading Passage 2
Following the Order of Operations
When a math expression has more than one operation, solving it in the right order is important. We use a set of rules called the order of operations to help us do that. These rules tell us where to start and what to do next so everyone solves the problem the same way.
Let’s look at this expression:
3 + 2(4 − 1)² − 6 ÷ 3
First, we solve anything inside parentheses. Here, we see (4 − 1), which equals 3. So the expression becomes 3 + 2 × 3² − 6 ÷ 3.
Next, we handle exponents. The 3² means 3 times 3, which is 9. Now the expression is 3 + 2 × 9 − 6 ÷ 3.
After that, we move to multiplication and division, working from left to right. 2 × 9 = 18 and 6 ÷ 3 = 2, so now we have 3 + 18 − 2.
Last, we do addition and subtraction. 3 + 18 = 21, and then 21 − 2 = 19.
By using the order of operations, we made sure each part of the expression was solved in the correct sequence. This helps keep expressions clear and consistent. Each step follows the last one and depends on the operations around it. That’s why the order of operations is important in understanding how expressions work.
When you face expressions that have many steps, using these rules helps you make sense of the whole problem.
Reading Passage 3
Following the Order of Operations
When evaluating expressions with many steps, the order of operations ensures consistency and clarity. These rules explain the order in which to handle parentheses, exponents, multiplication, division, addition, and subtraction.
Take this expression:
3 + 2(4 − 1)² − 6 ÷ 3
Start with the parentheses: (4 − 1) equals 3. Now we have 3 + 2 × 3² − 6 ÷ 3.
Next, apply the exponent: 3² equals 9. Now the expression is 3 + 2 × 9 − 6 ÷ 3.
Then complete multiplication and division, in order from left to right: 2 × 9 = 18, and 6 ÷ 3 = 2. This simplifies the expression to 3 + 18 − 2.
Finally, perform addition and subtraction from left to right: 3 + 18 = 21, then 21 − 2 = 19.
Using the order of operations allows us to approach complex expressions with confidence. Each operation builds on the last, and the correct sequence ensures the expression’s meaning is preserved. This structure helps mathematicians communicate their thinking clearly and avoids confusion.