2.8. Order of Operations

When more than one operator appears in an expression the order of evaluation depends on the rules of precedence. A complete explanation of precedence can get complicated, but just to get you started:

• Multiplication and division happen before addition and subtraction. So 2 * 3 - 1 yields 5, not 4, and 2 / 3 - 1 yields -1, not 1 (remember that in integer division 2/3 is 0).

• If the operators have the same precedence they are evaluated from left to right. So in the expression minute * 100 / 60, the multiplication happens first, yielding 5900 / 60, which in turn yields 98. If the operations had gone from right to left, the result would be 59 * 1 which is 59, which is wrong.

• Any time you want to override the rules of precedence (or you are not sure what they are) you can use parentheses. Expressions in parentheses are evaluated first, so 2 * (3 - 1) is 4. You can also use parentheses to make an expression easier to read, as in (minute * 100) / 60, even though it doesn’t change the result.

Observe the output of the code below to see how the placement of parentheses can change the result of a calculation.

#include <iostream> using namespace std; int main () { cout << (2 * 3) - 1 << endl; cout << 2 * (3 - 1) << endl; cout << 2 / 3 - 1 << endl; cout << 2 / (3 -1) << endl; }

Q-2: Match the expression to its correct output. Don't forget to consider integer division! Try again!
• (6*4)+1
• 25
• 6*(4+1)
• 30
• (6/4)+1
• 2
• 6/(4+1)
• 1

Note

The following module will walk you through an example of the rules of precedence. Answer the questions in order to check what you remember about the order of operations!

Q-4: Click on ALL PARTS of the expression that get evaluated first. For example, if "1 + 1" gets evaluated first, click on "1", "+", and "1".Try again!

1 + 2 * ( 10 - 2 ) / 4

Once you’ve submitted your answer for Question 3A, click on Question 3B below.

Q-5: Click on ALL PARTS of the expression that get evaluated first. For example, if "1 + 1" gets evaluated first, click on "1", "+", and "1".Try again!

1 + 2 * 8 / 4

Once you’ve submitted your answer for Question 3B, click on Question 3C below.

Q-6: Click on ALL PARTS of the expression that get evaluated first. For example, if "1 + 1" gets evaluated first, click on "1", "+", and "1".Try again!

1 + 16 / 4

Once you’ve submitted your answer for Question 3C, click on Question 3D below.

1 + 5

is the only operation remaining. I’m not going to ask you any questions about it. However, it’s important that you can wrap you head around the fact that the + operator appeared first in the calculation, but it was the last operator to be evaluated. The order of operations can be kind of confusing at times, but I think you’ve got a good grasp of the concept!

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