Numerical Expression Study Guide

A numerical expression is a mathematical phrase that contains numbers and operational symbols (such as +, -, ×, ÷) without an equal sign. It represents a specific value when the numbers are replaced with actual values and the operations are performed.

Examples of Numerical Expressions

3 + 5
7 × (4 - 2)
12 ÷ 3 + 2
2² + 5 × 3

Key Points to Remember

Numerical expressions do not have an equal sign.
They can contain numbers, operational symbols, and grouping symbols (such as parentheses).
Order of operations (PEMDAS/BODMAS) must be followed to evaluate numerical expressions.

Order of Operations (PEMDAS/BODMAS)

The order of operations specifies the sequence in which different operations should be performed when evaluating numerical expressions. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right) or BODMAS (Brackets, Orders, Division and Multiplication from left to right, Addition and Subtraction from left to right) can be used to remember the order.

Practice Problems

Simplify the following numerical expressions:

8 + 3 × 4
(5 - 2)² + 7
18 ÷ (3 + 1)
4 × 2 + 10 ÷ (5 - 2)

Answers

8 + 3 × 4 = 8 + 12 = 20
(5 - 2)² + 7 = 3² + 7 = 9 + 7 = 16
18 ÷ (3 + 1) = 18 ÷ 4 = 4.5
4 × 2 + 10 ÷ (5 - 2) = 8 + 10 ÷ 3 = 8 + 3.33... ≈ 11.33

◂Math Worksheets and Study Guides Seventh Grade. Fraction Operations

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.