Evaluate numerical expressions

Key Notes :

To evaluate an expression with multiple operations, you can follow the order of operations:

1. Perform operations inside parentheses and brackets. Start with the operations in the inner parentheses or brackets, evaluating the expression from the  inside  out.
2. Evaluate the exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

Order of operations:

How can you simplify an expression like this one?

2×5+(14–6)÷2²–1

It’s important to follow the order of operations! Otherwise, you might get the wrong answer. The order of operations tells you which steps to do first.

What is the order of operations?

1. Perform operations inside parentheses.
2. Evaluate exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

Let’s try an example!

The steps below show how to simplify an expression using the order of operations.

Let’s try it for 2 × 5 + ( 14 – 6 ) ÷ 2 ² – 1 .

Perform operations inside parentheses.

2 × 5 + ( 14 – 6 ) ÷ 2 ² – 1

2 × 5 + 8 ÷ 2 ² – 1

Evaluate exponents.

2 × 5 + 8 ÷ 2 ² – 1

2 × 5 + 8 ÷ 4 – 1

3. Multiply and divide from left to right. Start with 2×5, since it’s farther left.

×5+8÷4–1

10+8÷4–1

Now do 8÷4.

10+8÷4–1

10+2–1

4. Add and subtract from left to right. Start with 10+2, since it’s farther left.

10+2–1

12–1

Almost there!

12–1

11

So, 2 × 5 + ( 14 – 6 ) ÷ 2 ² – 1 = 11 !

How can you remember the order of operations?

Say PEMDAS:

• Parentheses
• Exponents
• Multiply or Divide (from left to right)
• Add or Subtract (from left to right)

Or, you can also remember Please Excuse My Dear Aunt Sally.

Learn with an example

Try some practice problems!