Ratios and Proportions Worksheets
These are two concepts that people often confuse for one another, even adults in business workplaces. A ratio is just a fraction that indicates how much of a whole value we have. A proportion is an equation that describes the relationship of two ratios. We will explore this more in this series of worksheets that will give students practical hands-on experience with these aspects. We created two clear and distinct types of worksheets that you will see labelled below.
- Fruit Stand Ratios - This is a fun one with real world skills. We provide a very well thought out scenario where proportions come into play and are vital for making a living. Not to mention that you get to count fruit.
- Creating Ratios (Ordered) - We work with guided shapes. Create a ratio that clear spreads out each form of data.
- Creating Ratios (Non- Ordered) - Students have to do a bit of organizing here. The items in the ratios are spread out and student must first order them before deciding on a proper ratio.
- Sentence Based Ratios - A step towards the more moderate. All the problems are very straight forward and should make for a solid introduction to this unit or topic.
- Finish Off the Ratios - Make your own equivalent ratios. 4 sheets in all. Complete the series of equivalent proportions three times per question. 4 versions and 8 pages in all.
- Ratio Word Problems - Very simple straight forward problems. We offer up some fair questions for students. It should help build their confidence for the tougher problems that follow.
- Ratio Sentences and Lacrosse - Many teachers rave about this one. The kids started taking up Lacrosse. It is gaining huge popularity in all of North America. So we made a few problems about it. Just wait for our Justin Bieber problems, just kidding!
- Write the Ratio of the Story - Truly reading within the content (math) area on this one. We mix words with numbers in this one to make sure that students read the problems carefully.
- Write the Ratio of the Story 2 - Same format new story from above. This one is much more straight forward than the past version.
- Three Way Ratios - We work on different forms of notation. We have you restate ratios in a various notations and formats.
- Sales, Stars, and Liquid Ratio Word Problems - Students like the scenarios in this one. Each problem is very realistic and can help steer students towards the answer by just following the given data.
- Compare the Ratios - Less than, greater than, or equal. Hopefully students will breeze through this one. Our hint is to reduce them to their lowest form and then go from there.
- Story Based Ratio Problems - A nice set that mimics national learning standards. A very simpole walk into the world of ratios in everyday life. Great for new comers to ratios.
- Writing Ratios Worksheet - Very introductory based. Two sentence ratios that need to be visualized.
- Reducing Ratios - As simple as it gets in this skill set. Find a common denominator and go for it! This should be a quick one for you.
- Make a Proportion - A deep thinking activity. This is a really neat one. We ask students to find two equivalent proportions from a group of random numbers.
- Shopping with Proportions - This one really hits home with kids for some reason. This introduces students to the concept of unit price which really is just a proportion. WOW! Proportions can save you money, who would have thought!
- Proportion Word Problems (Simple) - Everyday problems all people are faced with regularly. We start thinking about unit price and how it affects us when we buy extra products.
- Proportion Word Problems (Hard) - These can be difficult for anyone. These problems are difficult for even adults at first. They can be tricky. Take your time.
- Are the Ratios Proportional? - Find an equal proportion or create one. We make students apply higher levels of thinking with this one. They may need to create their on proportions.
- Solving for the Missing Proportions - Solve for x over 4 versions here. There are 4 versions of this in the download. That should provide students with a great deal of practice to help improve their skills.
- Horizontal Proportions - We change the typical format to work on the skill more. I just realized that the author on this one must have had crazy eights infiltrate his/her head. See if you get what I mean.
- Using Proportions to Solve Word Problems - These can be a bit wordy like national exams. This is the first time that we add unneeded data to see if students can sift through the data to find the main and critical data.
- Solving Proportions with Decimals - Who would have thought introducing a dot makes it that much harder? Decimals definitely help step up the level of difficulty here.
How Do We Use Ratios and Proportions?
Ratio and proportions are two mathematical principles that are often used interchangeably. However, there is a slight difference between the two terms.
It might be tough to envision how you might use math concepts in everyday life. Ratios, which make up logical relationships between different elements, are excellent illustrations of math in action. Groceries, cooking, and traveling about are typical, real-life circumstances in which ratios and proportions are used frequently and necessary for accurate, cost-effective execution.
Here we'll mention what ratios and proportions are, all the while highlighting their differences. We'll also shed some light on the uses of ratios and proportions in real life.
What are Ratios and Proportions?
A ratio expresses the relationship of 2 variables using the mathematical operation: division. Meanwhile, a proportion is the equivalency of two ratios.
Ratios can be expressed in several ways, for instance, a : b or a/b and is usually written as a is to b
A proportion, on the contrary, is a mathematical expression that states that 2 ratios are comparable. A proportion is expressed in this format: a: b : : c : d, and is written as a is to b as c is to d. And it can be expressed like this as well: a/b = c/d where c and d are ≠ 0.
Many people think they are one and the same. The fact is they are very different.
A ratio is just a fraction like 3/4. It can come many forms such as 3 out of 4 equal parts or 3:4, but fundamentally it is a fraction.
A proportion,on the other hand, is an equation that relates 2 ratios. Such as:
Real-Life Uses of This Math
Ratios and proportions are used in everyday life in a variety of ways. They help in recognizing patterns and making informed decisions.
1. Cooking Recipes
Ratios are used in cooking. The proportions of various ingredients in recipes are critical to creating the most delectable dishes. For instance, to make the delicious Alfredo sauce, you should mix 1 cup of milk with 1/2 a cup of cream, one teaspoon of chopped garlic, 1/4 a cup of shredded cheese, and salt and pepper to taste. The quantity of these ingredients can be explained through this math as well.
2. Grocery Shopping
The grocery store is a space bursting with the use of ratios in real life. You can easily compare the price of two different products using this type of math. For instance, if a 5-ounce bag of chips costs $4 and a 10-ounce bag of chips costs $5. Each ounce of chips is significantly cheaper, so the 10-ounce bag is the better bargain. You may show the link between quantity and size by dividing the total number of ounces of chips in a bag by the price.
3. Earnings Per Day
They are particularly helpful for those who get paid daily. For instance, if a worker earns $600 a day. It means he'll earn $1200 in two days and $2400 in four days. The pattern and link seen between the number of days and the sum of cash generated are easily discernible. The amount of money received increases as the duration increases. This validates the use of proportions in everyday life.
4. Road Trips
Another instance where ratios can be used is when traveling to a distant location. For example, in case you are going on a road trip from Los Angeles to San Deigo, you would need to travel up to 120 miles. If you are traveling by car and driving at a speed of 60 miles per hour, keeping in mind the speed and distance ratio, it may take up to 2 hours to reach San Diego.
Businesses employ different ratios to analyze their company's performance. Some of them include the debt-to-equity ratio, current assets ratio, dividend payout ratio, and more. Here we'll mention how businesses use them for their benefit.
1. Financial Statements Review
Interpreting financial accounts is critical for firm stakeholders. This form of math aid in comprehending the comparability of this data. Moreover, it aids in forecasting future figures from balance sheets and income statements.
As per the perspectives of managers and investors, this type of data can aid in understanding and estimating the firm's future profitability and operations. Ratios derived from historical financial analysis aid in predicting future finances and budgets.
3. Decision Making
Ratios give critical information about a company's current performance and resource use. It assists the firm in forecasting and planning ahead, setting new goals, and focusing on other markets.
4. More Effective Communication
This type of data is vital for reporting the firm's financial results to its stakeholders. Ratios make large and complex numbers easier to grasp. More often than not, figures may be deceiving, causing investors to lose faith, but ratios help investors recognize the firm's position after comparison, allowing them to continue investing in the business.
5. Trend Line
They can provide the trend line that tells whether or not a firm can perform over time. Businesses obtain data from previous financial periods to create trend lines that may be used to analyze and assess the company's outcomes and any potential issues that cannot be discovered through a one-year ratio study.
6. Company Performance
Ratios are useful in determining a firm's ability to create profit. Return on Equity and Return on Asset ratios indicate how much money the business can produce over its investments, whereas net profit and operating profit ratios indicate the firm's potential to create a revenue through sales and operational efficiency.
To Sum Up
Ratios and proportions are a fundamental part of mathematics. However, understanding how they work is not only beneficial when an individual is solving math equations. They can aid in many other activities and tasks, be it every day or business.