Understanding Ratios, Percentages, and Averages with Simple Animations

A ratio compares two or more quantities. Let's look at a simple example with red and blue circles.Here we have three red circles and six blue circles. We can write this as a ratio in two ways.Both three to six and three over six represent the same ratio. But we can make this simpler.To simplify a ratio, we divide both numbers by their greatest common factor.For three to six, both numbers can be divided by three.Let's look at another example. Six to nine can also be divided by three.And four to six can be divided by two to get two to three.Ratios are used everywhere, including cooking! Let's look at a simple recipe ratio.This recipe uses three parts flour to one part sugar, written as three to one.Ratios are all around us! Here are some common examples we use every day.Now that we understand what ratios are, we can move on to working with them in different ways.Now that we understand ratios, let's learn how to convert them to percentages.Let's start with the ratio one to two. To convert this to a percentage, we first write it as a division problem.When we divide one by two, we get zero point five.To convert this to a percentage, we multiply by one hundred.Let's visualize this with a pie chart. Fifty percent represents half of the whole.Let's try another example. Convert the ratio three to four to a percentage.First, we write three divided by four, which equals zero point seven five.Multiply by one hundred to get seventy-five percent.In the pie chart, seventy-five percent fills three quarters of the circle.Let's explore the three main types of averages using this set of numbers.The mean average is found by adding all numbers and dividing by how many numbers there are.First, we add all numbers: two plus three plus three plus four plus eight equals twenty.Next, we count how many numbers we have, which is five.Finally, we divide twenty by five to get our mean average of four.For the median, we first arrange numbers in order from smallest to largest.The median is the middle number when the data is ordered. In this case, it's three.The mode is the most frequently occurring number in our dataset.In our set, three appears twice, while all other numbers appear only once. Therefore, three is our mode.Let's understand when to use each type of average.The mean is best for evenly distributed data, like test scores.The median is most useful when dealing with outliers, such as house prices in a neighborhood.The mode works best for categorical data, like finding the most popular choice.Let's calculate the mean temperature for this week using our daily readings.We'll add each temperature one by one.Now we divide the total by the number of days to get our mean average.Remember the three steps: add all values, count the total items, and divide to find the mean.Let's explore how to use percentages for shopping discounts.To calculate thirty percent off forty dollars, first convert the percentage to a decimal.Multiply forty by zero point three to find the discount amount of twelve dollars.Subtract twelve from forty to get the final price of twenty-eight dollars.Next, let's look at mixing paint using ratios. A one to three ratio means one part paint to three parts water.Now, let's calculate a class average from test scores.Add all scores to get six hundred and ten, divide by seven students, for an average of eighty-seven point one four.Here's a practice problem for you. Pause the video and try to solve it.Finally, let's review when to use each calculation method.Let's wrap up with some key takeaways about using math in everyday life.Thanks for learning about real-world math applications with Spark.E!