About parentheses

Using the parentheses, you can group operations in an expression to change the order in which they are performed. Without parentheses, operations are performed in the following order: multiplication/division, addition/subtraction, and relational operations (greater than, less than, not equal to, and so on).

• For example, the expression, 4 + 6 / 2, provides the answer 7, and not 5, because division is performed before addition. When a mathematical expression contains operators that have the same rank, operations are performed left to right. For example, in the expression, 2 + 6 / 3 * 5 – 9, division and multiplication are first performed before the addition and subtraction. The first operation divides 6 by 3, which produces 2. The second operation multiplies 2 by 5, which produces 10. In the third operation, add 2 to 10, which produces 12. In the fourth operation, subtract 9 from 12 to produce 3 as the answer.

By using parentheses, you can change the order of operations in an expression. That is, operations in parentheses are performed first, then operations outside the parentheses are performed.

• For example, the expression, (2 + 6 / 3) * 5 – 9, results in an answer of 11, while the expression, (2 + 6 / 3) * (5 – 9), results in –16 as the answer.

You can also embed parentheses, where operations in the deepest parentheses are performed first.

• For example, the expression, ( (7 + 3) / 2) * 3, contains embedded parentheses. From the example, the first operation is 7 + 3, the second operation is 10 / 2, and the third operation is 5 * 3, which results in 15 as the answer.