# Numeric expressions We can combine numbers in many different ways; We can write them with positive and negative signs, with parentheses, brackets and braces, with signs of addition, subtraction, multiplication, division and exponents. In mathematics these combinations of numbers and operational symbols are called numerical expressions.

A numerical expression is a set of numbers combined with operation signs (addition, subtraction, multiplication, and division) or with exponents. A numeric expression can also contain parentheses, brackets, and braces.

### Examples of numerical expressions

• (33 – 8) + 25
• -15 + 7
• 82 - 7 ∙ (3 - 1)
• 3 + 15 - 5 ∙ (6) + 22

## Order of operations

When you have a large number of numbers with operation signs, parentheses, brackets, braces, and exponents, there must be a certain order to perform the calculations:

1. Perform the operations in parentheses, brackets and braces.
2. Carry out the operations with exponents.
3. Make the products (multiplication) and quotients (division) from left to right in the same way as the expression is read.
4. Perform addition and subtraction from left to right.

### Exercises

1. Evaluate the numerical term of the following expression following the order of operation: 82 + 7 ∙ (6 + 3) ÷ 9 - 8
• First step: Solve parentheses

82 + 7 ∙ 9 ÷ 9 - 8 =

• Second step: Solve operations with exponents

64 + 7 ∙ 9 ÷ 9 - 8 =

• Third step: Solve the products and quotients

64 + 63 ÷ 9 - 8 =

64 + 7 – 8 =

• Fourth step: Solve addition and subtraction

71 - 8 =

63

1. Evaluate the numerical term of the following expression following the order of operation: (10)2 ÷ (14 + 9 ∙ 4) - 2 ∙ 2
• First step: Solve parentheses

(10)2 ÷ (14 + 36) - 2 ∙ 2 =

(10)2 ÷ 50 - 2 ∙ 2 =

• Second step: Solve operations with exponents

100 ÷ 50 - 2 ∙ 2 =

• Third step: Solve the products and quotients

2 - 2 ∙ 2 =

2 - 4 =

• Fourth step: Solve addition and subtraction

-2