Time: 40 hours
For example, we use fractions when we make measurements, configure ratios, and calculate proportions. We use decimals and percentages in finance, measurement, and weight. In this course, we also study how to represent data visually, such as with bar graphs, line graphs, or pie charts. Graphs and charts convey data quickly to an audience. We also explore how to interpret data to help you make sense of charts, like those that outline interest rates, so you can calculate how much money you will need to pay off a loan. Math can also be fun: you need to understand statistics to create a winning fantasy football team.
First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.
In this unit, we will discuss some of the basic algebraic properties you may already know, that many math instructors call "common sense" properties. We see uses of these properties every day.
For example, the commutative property tells us we can rearrange the order of the numbers and still get the same result: 3 + 2 = 5, and 2 + 3 = 5. The same is true for multiplication: 2 × 3 = 6, and 3 × 2 = 6.
Other algebraic properties are less intuitive. For example, what happens when we multiply or divide a number by zero? Understanding these number properties will give you the foundation you need for this course.
Completing this unit should take you approximately 4 hours.
To avoid making errors, mathematicians follow a series of steps to simplify expressions that use the four basic operations, grouping symbols, and exponents. We call these steps the "order of operations". In this unit, we explore how to use exponents and grouping symbols to perform mathematical operations in the correct order.
For example, we can use exponents to write out a repeat multiplication, such as 2 × 2 × 2 × 2 × 2, or 25. We also examine the concept of the greatest common factor (GCF), the largest positive integer that divides evenly into a given group of numbers with zero remainder. For example, for the set of numbers 18, 30 and 42, the GCF is 6. We also use the least common multiple (LCM) to determine the smallest number that two numbers can both divide into. For example, for the set of numbers 2 and 6, the LCM is 6. Finally, we learn how to perform mathematical operations with negative numbers.
Completing this unit should take you approximately 7 hours.
Fractions allow us to perform calculations with numbers that are not whole. For example, imagine you baked a pie. If your family eats half the pie for dessert one day, you could use fractions to determine that half a pie remains. If you eat another slice, you could use fractions yet again to see how much is left. We use fractions every day to calculate sale prices, measurements, money, and many other situations. In this unit, we explore how to add, subtract, multiply, divide, and reduce fractions.
Completing this unit should take you approximately 11 hours.
In this unit, we study decimals, which are simply another way to write fractions. For example, think about American currency. One dollar is 100 cents and a quarter is 25 cents, or $0.25 when written as a decimal. We can explain a quarter as being 25/100 of a dollar. This reduces to 1/4, which we read as one-quarter. Decimals are everywhere, just like fractions. We use them in money, in measuring lengths, and in amounts. In this unit, we study how to add, subtract, multiply, and divide decimals, and how to convert between fractions and decimals.
Completing this unit should take you approximately 8 hours.
In this unit, we study ratios and proportions. These are mathematical concepts that we use all the time, probably without even realizing it. For example:
- At the grocery store, have you ever compared unit prices for different packages of the same type of food? That is a ratio.
- When driving 65 mph (miles per hour) on the highway, have you ever determined how long it will take you to get to your destination? That is a proportion.
- In sports, statisticians use proportions to predict an athlete's performance based on what they have accomplished in the past.
In this unit, we explore how to write ratios, set up and solve proportions, and apply proportions to real-world scenarios.
Completing this unit should take you approximately 3 hours.
Now that we have studied fractions and decimals, we are ready to explore percents. Percents are just fractions and decimals written in a different way. For example, we can describe one half in many ways: 0.5 as a decimal, 1/2 as a fraction, and 50% as a percent. These all mean the same thing!
We see percents all the time in the real world, especially in sales at stores. For example, a store might advertise that it is selling clothing at 50% off. So, a $10 shirt would be reduced to $5. A week later, the store may post a sign saying that there is an additional 20% off the sale price of the shirts. How do we determine the new discounted price of the shirt?
We will learn how to answer that question in this unit. We will also convert between percents and fractions or decimals, and learn about percentage increases and decreases. We will explore how to calculate percents in scenarios that you will see in the real world, such as calculating tips at a restaurant or sale prices at a store.
Completing this unit should take you approximately 2 hours.
Once we have gathered data or performed calculations, we have to visualize the information to make sense of it. It is much easier to read a graph or chart than to interpret meaning from a long list of numbers. We use graphs and charts in almost every field. Businesses use graphs and charts to show trends in growth. Politicians use graphs and charts to explain demographics and voting trends in campaigns and elections. Since we use graphs and charts so often, it is important to know how to read and interpret them.
In this unit, we will discuss the different types of graphs and charts that we use in mathematics. We will interpret the results for each type of graph or chart, learn to create charts and graphs, read charts, and work with the measures of central tendency for a data set.
Completing this unit should take you approximately 5 hours.
This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary. It is not meant to replace the course materials!
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Certificate Final Exam
Take this exam if you want to earn a free Course Completion Certificate.
To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.
Once you pass this final exam, you will be awarded a free Course Completion Certificate.
- Receive a grade