NEKG33 Mathematical methods for economists

Chapter 1 : Day 01: Real numbers and fractions

By Lund University

Do you remember your high school algebra (adding fractions and all that fun stuff)? If not, lets do a review! We focus on real numbers, rules for real numbers and fractions. Pay particular attention to the distributive law and the quadratic identities.

Number systems

This section introduces different types of numbers: natural numbers, integers, rational numbers and real numbers with a focus on the real numbers. We look at addition and multiplication as binary operations on the real numbers and ≤ as binary relation on the real numbers.


The real number system

Problem: Number systems

Rules of algebra

This section contains the basic rules of algebra. We will cover the commutative and the associative laws of addition and multiplication. We will also look at the four types of inequalities. Next, we have all the sign rules, manipulating addition and multiplication of positive and negative numbers. We cover a bunch rules related to the numbers zero and one (for example, multiplying any number by zero will take it to zero). The distributive law is one of the most important rules in algebra and we will cover this law as well as extensions of the distributive law dealing with quadratic identities. We can often use quadratic identities “in reverse” to factorize and algebraic expression, that is, decomposing the expression into a product of expressions.

Commutative and associative laws



Zero and one rules

Distributive law and quadratic identities

Rules of algebra: problems

Algebra exercises. Try to do as many as possible

Problem: Commutative and associative

Problem: Inequalities

Problem: Percent

Problem: Sign rules

Problem: Factor expressions

Problem: Factor expressions

Problem: Factor expressions

Problem: Zero rules

Problem: Quadratic identities

Problem: Quadratic identities with three terms

Problem: Quadratic identities

Problem: Square sum of three terms

Fractions and powers with integer exponents

We have two separate topics in this section: fractions and powers. In this section, we only consider powers where the exponent is an integer. This course assumes that you are familiar with fractions and that you know how to add, multiply and divide fractions. The focus here is instead to provide you with a complete list all the rules related to fractions and a bunch of problems allowing you to refresh your skills. The same is true for powers. It is assumed that you know the basic power rules such as multiplying two powers with the same base.


Powers with integer exponent

Powers, rules

Fractions and integer powers: Problems

Exercises on fractions and powers

Problem: Simplify fractions

Problem: Simplify fractions

Problem: Power rules, integer powers

Problem: Power rules, integer powers

Problem: Integer powers

Problem: Percent and growth

Problem: Understanding negative exponents and 0^0