Evaluate Numerical Expressions - Integers

Introduction

This worksheet provides focused, interactive practice on evaluating numerical expressions involving integers. Learners apply standard order-of-operations rules to solve expressions accurately and confidently.

Quick Revision: What Is a Numerical Expression

A numerical expression is a mathematical statement made up of numbers and arithmetic operations such as addition (+), subtraction (−), multiplication (✕), and division (÷).

Numerical expressions do not include variables. Their values are found by evaluating the operations according to established arithmetic rules.

Examples of Numerical Expressions

• 6 − (2 + 7) ✕ 12 ÷ 4
• 5 − 16 ÷ 8 ✕ [(2 + 6) + 7]
• 215 + 4 ✕ (90 ÷ 10) − (7 + 5)

How to Evaluate a Numerical Expression

To evaluate a numerical expression correctly, you must follow the order of operations.

The commonly used rules are DMAS, BODMAS, and PEMDAS. Although the names differ, the underlying logic is the same.

DMAS Rule

DMAS is a simplified version of BODMAS that applies when there are no brackets or exponents. It follows:

• Division & Multiplication (left to right)
• Addition & Subtraction (left to right)

BODMAS Rule

BODMAS stands for:

• Brackets – Innermost parentheses() first, then brackets[], and then braces{}
• Orders – Square roots, exponents or powers
• Division & Multiplication (left to right)
• Addition & Subtraction (left to right)

PEMDAS Rule

PEMDAS is commonly used in the United States and follows this order:

• Parentheses
• Exponents
• Multiplication & Division (left to right)
• Addition & Subtraction (left to right)

Key Takeaways Before You Start

• Always solve expressions inside brackets or parentheses first
• Multiplication and division come before addition and subtraction
• When operations have the same priority, solve from left to right
• Following the order of operations ensures correct results every time

Worksheet Structure

This worksheet is divided into two sections to gradually increase complexity.

• 24 medium-sized numerical expression problems
• 12 long-sized numerical expression problems

Configuration Options

Before generating the worksheet, learners can customize the difficulty level.

• Choose problems with smaller numbers
• Choose problems with larger numbers

This flexibility allows targeted practice based on skill level.

Skills Developed Through This Worksheet

• Accurate application of order-of-operations rules
• Improved confidence with integer arithmetic
• Stronger logical and sequential thinking
• Preparation for algebra and advanced mathematics

Online, Interactive, and Self-Correcting

This is a fully online worksheet that runs directly in the browser.

Learners enter their answers into input fields and receive instant feedback, helping them identify and correct mistakes quickly. No printing or downloading is required.