ClassX Video Lessons Subjects Algebra Introduction to ratios | Ratios, proportions, units, and rates | Pre-Algebra
Hey there! Today, we’re going to learn about something called ratios. Ratios are a cool way to compare different things and see how they relate to each other. Let’s dive in and explore what ratios are, how to simplify them, and how to use them in real-life situations!
A ratio is a way to compare two or more things. Imagine you have 10 horses and 5 dogs. You can show the ratio of horses to dogs in a few different ways:
Here, the first number (10) is for horses, and the second number (5) is for dogs.
To make a ratio simpler, you can divide both numbers by their greatest common divisor (GCD). For our horses and dogs, the GCD is 5. So, divide both numbers by 5:
Now, the simplified ratio is 2:1, meaning there are 2 horses for every 1 dog.
If you switch the order of the numbers in a ratio, the meaning changes. For example, if you want to find the ratio of dogs to horses, it would be:
Ratios can compare more than two things. Suppose you have 20 apples, 40 oranges, and 60 strawberries. The ratio of apples to oranges to strawberries is:
To simplify, find the GCD, which is 20, and divide each number by 20:
This means for every 1 apple, there are 2 oranges and 3 strawberries.
Sometimes, you know the ratio and the total number of items, and you need to find the quantities. For example, if the ratio of boys to girls in a class is 2:3 and there are 40 students total, here’s how you find the number of girls:
So, there are 24 girls in the class.
For more complex ratios, like sheep, chickens, and pigs with a ratio of 2:5:10, follow these steps:
Understanding ratios helps you compare things and solve problems about how different items relate to each other. Whether you’re dealing with simple or complex ratios, the basic ideas stay the same, making it easier to understand and analyze relationships between quantities. Keep practicing, and you’ll be a ratio expert in no time!
Let’s go on a scavenger hunt around your home or classroom! Find pairs of objects and write down their ratios. For example, if you find 8 pencils and 4 erasers, the ratio is 8:4. Simplify the ratios you find and share them with your classmates!
Imagine you’re a chef! Create a simple recipe using ratios. For example, if you’re making a fruit salad, you might use a ratio of 2:3:5 for apples, bananas, and grapes. Write down your recipe and explain how you used ratios to decide the quantities.
Use colored pencils or markers to create a piece of art based on a given ratio. For instance, if the ratio is 3:2:1, use 3 parts blue, 2 parts red, and 1 part yellow. Display your artwork and explain how you used the ratio to decide on the colors.
Work in pairs to create and solve word problems involving ratios. For example, if a zoo has a ratio of 4 lions to 6 tigers, how many tigers are there if there are 20 lions? Exchange problems with another pair and solve them together!
Organize a relay race where each team must solve a ratio problem before passing the baton. For example, if the ratio of red to blue marbles is 3:2 and there are 15 red marbles, how many blue marbles are there? The first team to solve all problems and finish the race wins!
Ratios – A ratio is a comparison of two quantities by division. – Example sentence: The ratio of apples to oranges in the basket is 3 to 2.
Compare – To compare means to examine the differences between numbers or quantities. – Example sentence: We can compare the fractions 1/2 and 3/4 to see which is larger.
Simplify – To simplify means to make a mathematical expression easier to understand by reducing it to its simplest form. – Example sentence: You can simplify the fraction 4/8 to 1/2.
Fraction – A fraction represents a part of a whole or a division of quantities. – Example sentence: The fraction 3/5 shows that we have three parts out of five equal parts.
Common – In math, common refers to something shared by two or more numbers, like a common factor. – Example sentence: The numbers 6 and 9 have a common factor of 3.
Divisor – A divisor is a number by which another number is divided. – Example sentence: In the division 15 ÷ 3, the number 3 is the divisor.
Quantities – Quantities refer to amounts or numbers of things. – Example sentence: We measured the quantities of flour and sugar needed for the recipe.
Students – Students are individuals who are learning, especially in a school setting. – Example sentence: The students worked together to solve the algebra problem.
Groups – Groups are sets of people or things that are considered together. – Example sentence: We divided the class into groups to work on the math project.
Relationships – In math, relationships describe how numbers or quantities are connected. – Example sentence: The relationship between the variables x and y can be shown in a graph.
