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An introduction to comparing quantities using ratios and understanding the relationship between two numbers.
Have you ever wondered why a tiny model car looks exactly like the real thing, just smaller? It’s not magic—it’s the power of ratios!
A ratio is a way to compare two quantities by using division. It tells us how much of one thing there is compared to another. For example, if you have blue marbles and red marbles, you are comparing the count of blue to red. Ratios help us keep things in proportion, whether we are mixing paint, following a recipe, or designing a skyscraper. The order of the numbers matters! If we say the ratio of dogs to cats is to , it means for every dogs, there is cat. If we switched it to to , the meaning changes completely!
Let's look at a simple comparison. 1. Imagine a bowl with bananas and apples. 2. To find the ratio of bananas to apples, identify the first quantity () and the second (). 3. Write it out: to .
Quick Check
If a backpack contains 10 pens and 3 pencils, what is the ratio of pencils to pens?
Answer
3 to 10
In mathematics, we can write the same ratio in three different ways. They all represent the same relationship! 1. Using the word 'to': to 2. Using a colon: 3. As a fraction:
When writing a ratio as a fraction, the first number mentioned is the numerator (top), and the second is the denominator (bottom). Even though it looks like a fraction, we still read it as "3 to 4" when discussing ratios.
A recipe for lemonade uses cups of lemon juice for every cups of water. 1. Identify the parts: (juice) and (water). 2. Write in colon form: . 3. Write in fraction form: . 4. You can even simplify this ratio just like a fraction: . This means for every cup of juice, you need cups of water.
Quick Check
Write the ratio 5:9 in the other two common forms.
Answer
5 to 9 and 5/9
Ratios aren't just for math class; they are everywhere! Architects use them for scale models. If a model house has a ratio of , every inch on the model represents inches on the real house. In sports, we use ratios to compare wins to losses. If a team has a win-loss ratio of , they win three times for every one time they lose. Understanding these relationships allows us to predict outcomes and scale things up or down without losing the original balance.
You are mixing 'Ocean Blue' paint. The instructions say to mix parts blue paint with part white paint and parts green paint. 1. What is the ratio of blue paint to the total number of parts? 2. First, find the total: total parts. 3. The ratio of blue to total is . 4. In fraction form, this is , which simplifies to . This tells you that exactly half of your mixture is blue paint!
A classroom has boys and girls. What is the ratio of girls to boys?
Which of these is NOT a standard way to write the ratio of to ?
The ratio represents the same relationship as the ratio .
Review Tomorrow
In 24 hours, try to recall the three different ways to write a ratio using the numbers 5 and 11.
Practice Activity
Find a food package in your kitchen and look at the 'Servings per Container' and 'Serving Size'. Try to write the ratio of calories to one serving.