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
Inequalities
Sign-rules
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.
Fractions
Powers with integer exponent
Powers, rules
Fractions and integer powers: Problems
Exercises on fractions and powers