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Compare two quantities with ratios. These worksheets feature basic and intermediate-level ratio activities.
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6th Grade ratio worksheets are used to give students a good understanding of how to deal with ratio and proportion problems. The questions in these worksheets range from simple interpretation sums to word problems that require analysis.
Ratios are used very frequently in daily life. It is good for young minds to have a clear foundation of this concept. By solving the problems in 6th grade ratio worksheets, children can increase their speed and accuracy. Questions are structured in a way to improve a student's logical and analytical abilities. These 6th grade math worksheets are provided with answer keys with step-by-step solutions to help students in case they get stuck while solving a question.
6th Grade math ratio worksheets are easy to use and available in PDF format that is free to download, enabling students to access quality education offline.
Explore more topics at Cuemath's Math Worksheets .
A ratio is a comparison between two or more numbers. Help learners discover how to identify and record ratios and use the greatest common factors to find the simplified equivalent ratios with this practice worksheet. Colorful graphics help students connect concepts to strategies. Designed for sixth graders, this math worksheet supports students as they learn to write and simplify ratios. For more practice with this skill, check out the Writing Ratios worksheet next!
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Understanding ratios is crucial for solving problems relating to proportions and percents. Math Games makes reviewing this higher-level math skill a breeze, with our suite of enjoyable educational games that students won’t want to stop playing!
Our free resources include mobile-compatible game apps, PDF worksheets, an online textbook and more. Students can use these tools to blend study with play as they practice:
Help the kids in your life look forward to reviewing math! Our games are tailored to a variety of grade levels and become easier or more challenging depending on how well users are playing. Select one of the skills listed above to check them out!
A ratio says how much of one thing there is compared to another thing.
Ratios can be shown in different ways:
Use the ":" to separate the values: | 3 : 1 | |
Or we can use the word "to": | 3 to 1 | |
Or write it like a fraction: |
A ratio can be scaled up:
Using ratios.
The trick with ratios is to always multiply or divide the numbers by the same value .
is the same as ×2 ×2 |
So the ratio of flour to milk is 3 : 2
To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:
3 ×4 : 2 ×4 = 12 : 8
In other words, 12 cups of flour and 8 cups of milk .
The ratio is still the same, so the pancakes should be just as yummy.
The examples so far have been "part-to-part" (comparing one part to another part).
But a ratio can also show a part compared to the whole lot .
Part-to-Part:
The ratio of boys to girls is 2:3 or 2 / 3
The ratio of girls to boys is 3:2 or 3 / 2
Part-to-Whole:
The ratio of boys to all pups is 2:5 or 2 / 5
The ratio of girls to all pups is 3:5 or 3 / 5
We can use ratios to scale drawings up or down (by multiplying or dividing).
The height to width ratio of the Indian Flag is So for every (inches, meters, whatever) of height | |
If we made the flag 20 inches high, it should be 30 inches wide. If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3) |
This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is
1500 : 2000
What is that ratio when we draw it at 1/10th normal size?
1500 : 2000 | = 1500 : 2000 | |
= |
We can make any reduction/enlargement we want that way.
Allie measured her foot and it was 21cm long, and then she measured her Mother's foot, and it was 24cm long. |
"I must have big feet, my foot is nearly as long as my Mom's!"
But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.
In a table this is:
Allie | Mom | |
Length of Foot: | 21cm | 24cm |
Height: | 133cm | 152cm |
The "foot-to-height" ratio in fraction style is:
Allie: | Mom: |
We can simplify those fractions like this:
And we get this (please check that the calcs are correct):
"Oh!" she said, "the Ratios are the same".
"So my foot is only as big as it should be for my height, and is not really too big."
You can practice your ratio skills by Making Some Chocolate Crispies
Helping with Math
Ratios are one way of comparing amounts of things. Ratios can tell us how much bigger, or smaller, one thing is than another. In other words, ratios show how much of one thing we have in relation to another thing.
In this Ratio and Proportion section you will find additional guidance on direct proportion , help with simplifying ratios , and guidance on using ratio and proportion .
Note: You can also get to these pages by using the menu towards the top of this page.
Ratio and proportion worksheet: simplifying ratios(1 of 2), ratio and proportion worksheet: writing ratios(2 of 2), ratio and proportion worksheet: writing ratios(1 of 2), changing recipe quantities worksheet, ratio and rates worksheet, writing ratio worksheet, example of ratio.
In the example below we are trying to get purple paint by mixing cans of red and blue paint.
4 parts blue paint | |
3 parts red paint |
The ratio of blue to red paint is 4:3
There are three ways that ratios are commonly written:
When writing ratios be careful to write the numbers in the same order as the words (or things) to which they refer.
You will find more ratio and proportion worksheets here
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Explore this compilation of printable ratio worksheets with a range of ratio problems to understand the concept of ratio. These pdf worksheets cover key skills like ratio of part to part, equivalent ratios, writing ratios in three different ways, and much more. Each worksheet is aligned with common core curriculum. Our free worksheets are a great place to make a head start!
Finding Ratios
Access these worksheets on ratio of part to part and ratio of part to whole to provide practice to 6th grade and 7th grade students. Look at the pictures and express them as ratios.
Equivalent Ratios
Find whether the given ratios are equivalent in part A and cross multiply the equivalent ratios to find the missing value in part B of these printable ratio worksheets.
Reduce each Ratio to its Lowest Term
These pdf ratio worksheets focus on how to reduce the given ratio to its lowest form. Divide each number by the greatest common factor to express the ratio in its simplest form.
Writing Ratio in Three Ways
Test your ability on how to write ratios in three different ways: in words, with a colon and as a fraction with these printable ratio worksheets.
Sharing a Quantity in the Given Ratio
Give your 6th grade and 7th grade students ample practice on dividing the given number and finding the share of each part with these pdf worksheets on ratio.
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A "ratio" is just a comparison between, or a relating of, two different things. Ratios are used to create proportions by setting two ratios equal to each other and solving for some unknown, and ratios can also be used to find per-unit rates such as how many mile a car can drive "per liter" or how many hours the average student at a given university spends studying "per week".
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As an example of a ratio, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the rest are women, so:
35 − 15 = 20
...there are twenty women in the group. The language "the ratio of (this) to (that)" means that (this) comes before (that) in the comparison. So, if one were to express "the ratio of men to women", then the ratio, in English words, would be " 15 men to 20 women" (or just " 15 to 20 ").
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The order of the items in a ratio is very important, and must be respected; whichever word came first in the ratio (when expressed in words), its number must come first in the ratio. If the expression had been "the ratio of women to men", then the in-words expression would have been " 20 women to 15 men" (or just " 20 to 15 ").
Expressing the ratio of men to women as " 15 to 20 " is expressing the ratio in words. There are two other notations for this " 15 to 20 " ratio:
odds notation: 15 : 20
You should be able to recognize all three notations; you will probably be expected to know them, and how to convert between them, on the next test. For example:
They want "the ratio of ducks to geese", so the number for the ducks comes first (or, for the fractional form, on top). So my answer is:
This time, they want me to give them "the ratio of geese to ducks". I'll be using the exact same numbers but, in this case, the number of geese comes first (or, for the fractional form, on top). So my answer is:
The numbers were the same in each of the two exercises above, but the order in which they were listed differed, varying according to the order in which the elements of the ratio were expressed. In ratios, order is very important.
So the representative group has 12 students in it, of which 7 passed and 5 failed. In particular, the fraction of the group that failed is given by dividing the number of flunking students by the total number of students in the representative group. That is:
( 5 / 12 )(36) = 15
So, of the class of 36 students, the class was not passed by:
15 students
The ratio from a representative group can also be used to provide percentage information.
I already know that the representative group contains 12 students, of which 7 passed the class. Converting this to a percentage (by dividing, and then moving the decimal point, as explained here ), I get:
7/12 = 0.583333... = 58.3333...%
They want the answer rounded to one decimal place, so my answer is:
58.3% passed
(9/25)(300) = 108
This is the number they're wanting. In the entire park, there are:
Generally, ratio problems will just be a matter of stating ratios or simplifying them. For instance:
This exercise wants me to write the ratio as a reduced fraction. So first I'll form the fraction, and then I'll do the cancelling that leads to "simplest form".
$10 / $45 = $2 / $9 = 2 / 9
The dollar signs cancelled off, too, because they were the same, top and bottom, in the ratio's fractional form. So my answer is:
This reduced fraction is the ratio's expression in simplest fractional form. The units (being the "dollar" signs) cancelled on the fraction because the units (namely, the " $ " symbols) were the same on both values.
When both values in a ratio have the same unit or designator, there should be no unit or designator on the reduced form of the ratio. The units aren't factors, exactly, but they'll cancel in the same manner as do factors.
The terms in this ratio have different units, so they won't cancel off; there will be units on my simplified ratio. My simplification looks like this:
( 240 miles) / ( 8 gallons)
= ( 30 miles) / ( 1 gallon)
This particular ratio of units, "(miles)/(gallon)", has its own simplified form; namely, "miles per gallon", which is abbreviated as "mpg". So, in standard English, my answer is:
In contrast to the answer to the previous exercise, this exercise's answer did need to have units on it, since the units on the two parts of the ratio (namely, the "miles" and the "gallons") were not the same, and thus did not cancel each other off. When a ratio ends up with units (or dimensions) on it, the ratio may also be referred to as a "rate". In the case of the exercise above, the rate was the distance covered per unit-volume of fuel.
I know that the length of an American football field , exclusive of the "end" zones, is 100 yards. I also know that 3 feet are equal to 1 yard. I can set up this equality as a ratio. Because they've given me a measurement in "yards", I'll want the unit of "yards" to cancel off in my multiplication. Because of this, I'll state my ratio (of yards to feet) with the "feet" on top:
( 3 feet)/( 1 yard)
Now I can multiply the length they've given me by my conversion factor (being the ratio above), and simplify:
[( 3 feet)/( 1 yard)][ 100 yards]
= ( 3 feet)( 100 ) = 300 feet
This value is the number they're wanting, so my answer is:
For more on this topic, look at the " Cancelling / Converting Units " lesson.
Ratios are the comparison of one thing to another (miles to gallons, feet to yards, ducks to geese, et cetera). But their true usefulness comes in the setting up and solving of proportions.
You can use the Mathway widget below to practice converting ratios, expressed in "odds" notation, to fractional form. Try the entered exercise, or type in your own exercise. Then click the button and select "Convert to a Simplified Fraction" to compare your answer to Mathway's. (Or skip the widget, and continue on to the next page .)
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What Are Ratio Tables? Ratios are when two quantities with the same unit are compared and these are denoted using colons. When solving ratio problems, students can use the ratio tables. However, not many students know what ratio tables are and how can they help them solve ratio problems. Therefore, we are going to start by understanding what ratio tables are and what are their applications. Ratio tables are structured lists of equivalent ratios. These lists help in understanding the relationship between ratios and the numbers. To solve ratio problems using tables, you can approach the problem in variety of different ways. First is simple addition. The second method is through multiplication. Both these methods include the trial and error approach.
Guides students through solving repeated ratio tables. The ratio of one column will repeat in the other three columns.
Demonstrates how to solve ratio tables with very large numbers.
A really great activity for allowing students to understand the concepts of ratio tables.
Students determine ratio tables in 20 assorted problems. The answers can be found below.
Students are provided with 12 problems to achieve the concepts of ratio tables.
This tests the students ability to complete ratio tables.
Answers for the homework and quiz.
Answers for the lesson and practice sheets.
When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. An "x" is frequently used in place of the unknown.
Home / United States / Math Classes / Worksheets / Ratio and Proportions Worksheets
Ratio and proportions worksheets help students compare two similar quantities deriving a ratio. When both ratios in an e quation are equal, they are determined to be in proportion. Ratio and proportion concepts are crucial to young learners, in both math class and the real world. Printable ratio and proportion worksheets feature problems tied to real world experience. Worksheets may include questions regarding the expression and comparison of rations in simpler forms in relation to height, weight, distance, and time. These problems are presented using real-life scenarios such as adjusting a recipe when cooking or making a business deal. Ratio and proportion worksheets are a great study aid for young learners. ...Read More Read Less
Develop logical reasoning :
Students can further develop their logical reasoning when they practice and solve problems regularly using ratio and proportions worksheets. These skills are beneficial not only in successively solving math problems, but in the real world as well.
Phased approach :
Ratio and proportions worksheets feature problems presented in a graded structure. The step-by-step design allows for students to begin with simple problems and gradually increase in difficulty level. As students move to higher level worksheets, their understanding of the concept can improve.
Self-paced study :
Students are encouraged to work through the different levels of ratio and proportions worksheets at their own pace. Students can repeat worksheets when needed to develop an understanding of difficult concepts.
Interactive formats :
Ratio and proportion worksheets are visually stimulating and interactive, which can keep a student engaged and prevent boredom.
Choose math worksheets by topic, ratio and proportions worksheets explained:.
Using ratio and proportion worksheets can instill confidence and a deeper understanding of complex math concepts. They can act as a homework aid to assist students needing extra practice.
Ratios are generally expressed in their lowest terms, similar to fractions expressed in their lowest terms. While ratios compare between two quantifiable entities, proportions are equations with the ratios on both sides. Printable ratio and proportions worksheets encourage students to solve expression problems in simpler forms, compare ratios, arrange ratios in ascending or descending orders and find a mean proportional between numbers.
As students progress to the higher grade levels, the printable ratio and proportions worksheets incorporate problems involving tables and graphs. Worksheets feature problems requiring the cross-product method, and problems using algebraic variables.
Ratio and proportion worksheets come in many varieties, including:
Printable ratio and proportions worksheets are available in a large variety to facilitate extra study time in order to help students understand complex mathematical concepts.
Radio and proportions worksheets are available in easily downloadable HTML and PDF formats. They are randomly generated and printable at your convenience. They also come with an answer key that explains the basics needed to solve problems involving ratio and proportion concepts successfully. With regular practice of these worksheets students can enhance their knowledge of ratio and proportions.
Ratio and proportions worksheets are free printable fun and interactive worksheets that contain questions based on ratio and proportions. These worksheets have detailed solutions of question that help in better understanding of concept.
Ratio is the mathematical term to represent the comparison of two numbers and ratio is represented by either a/b or a : b
Proportion is the equation that tells whether the two ratios are equal or not.
Ratio and proportions are used in various field as finance, shopping, mathematical modeling. While building houses we use ratio and proportion of instructural material. We can see the basic use of ration and proportion while cooking.
The equivalent ratios are the ratios that describe the same relationship between numbers. The value of equivalent ratios is equivalent.
The ratio and proportions worksheets by byju’s math have questions based on ratios and proportions. The solution has been provided using different methods that will help in better understanding the concept and developing self-assessment skills. The worksheet has different difficulty levels that will help in recording the progress. The worksheet has real-life examples that will help in how to apply concepts in real life.
Subject: Mathematics
Age range: 11-14
Resource type: Worksheet/Activity
Last updated
12 October 2013
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These Ratio Worksheets will produce problems where the students must write rates and unit rates from word phrases. These ratio worksheets will generate 10 Rates and Unit Rates problems per worksheet. These Ratio Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Ratios and Rates Worksheets.
Immerse yourself in practice with our printable ratio worksheets. Whether it is part-to-part ratios, part-to-whole ratios, identifying parts from the whole, or finding the whole from the parts, dividing quantities, generating equivalent ratios, or expressing the ratio in three different ways, that you are looking for, these pdfs have them all covered for your grade 5 through grade 8 learners.
Ratio Wording. 6rp1. This worksheet is designed to enhance children's understanding of mathematical ratios. It contains 12 carefully crafted problems, addressing practical examples such as vote distributions, home ages, combined genders, types of vehicles, clothing items, and game consoles.
Find here an unlimited supply of worksheets with simple word problems involving ratios, meant for 6th-8th grade math. In level 1, the problems ask for a specific ratio (such as, "Noah drew 9 hearts, 6 stars, and 12 circles. What is the ratio of circles to hearts?"). In level 2, the problems are the same but the ratios are supposed to be simplified.
These worksheets feature basic and intermediate-level ratio activities. Look carefully at each picture and answer the question about the ratio of objects. Write each ratio three different ways. This worksheet has a picture of dogs, cats, turtles, and birds. Write ratios in the table to compare the number of each animal.
You may enter a message or special instruction that will appear on the bottom left corner of the Ratio Worksheet. Ratio Worksheet Answer Page. Include Ratio Worksheet Answer Page. Now you are ready to create your Ratio Worksheet by pressing the Create Button.
The Corbettmaths Practice Questions on Ratio. Previous: Percentages of an Amount (Non Calculator) Practice Questions
These ratio worksheets can be downloaded for free in PDF format. Regular practice of these worksheets can help students score well in their exams. Ratio Worksheet - 1. Download PDF. Ratio Worksheet - 2. Download PDF. Ratio Worksheet - 3. Download PDF. Ratio Worksheet - 4.
6th Grade math ratio worksheets are easy to use and available in PDF format that is free to download, enabling students to access quality education offline. Explore more topics at Cuemath's Math Worksheets. Grade 6 Ratio Worksheets - Grab our free math worksheets featuring exercises in mathematics to ace the problem-solving methods of different ...
Ratio is an accurate and systematic manner of comparing quantities. This concept is fundamental to help us compare things logically and avoid biased decisions. Ratio provides the learners with an opportunity to discover and represent the relationship of two quantities — on how one value is bigger or smaller than the other. Also, ratio is a ...
Ratios. A ratio is a comparison between two or more numbers. Help learners discover how to identify and record ratios and use the greatest common factors to find the simplified equivalent ratios with this practice worksheet. Colorful graphics help students connect concepts to strategies. Designed for sixth graders, this math worksheet supports ...
Understanding ratios is crucial for solving problems relating to proportions and percents. Math Games makes reviewing this higher-level math skill a breeze, with our suite of enjoyable educational games that students won't want to stop playing! Our free resources include mobile-compatible game apps, PDF worksheets, an online textbook and more.
Using Ratios. The trick with ratios is to always multiply or divide the numbers by the same value. Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk. So the ratio of flour to milk is 3 : 2. To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4: 3 ×4 : 2 ×4 = 12 : 8.
Ratio and Proportion Worksheets. On this page you will find: a complete list of all of our math worksheets relating to Ratio & Proportion. Choose a specific addition topic below to view all of our worksheets in that content area. You will find addition lessons, worksheets, homework, and quizzes in each section.
The ratio of blue to red paint is 4:3. Writing ratios. There are three ways that ratios are commonly written: in words e.g. 4 to 3; with a colon (odds notation) e.g. 4:3; fractional notation e.g. 4/3; Watch the words, numbers, and order in ratios. When writing ratios be careful to write the numbers in the same order as the words (or things) to ...
Ratio. Explore this compilation of printable ratio worksheets with a range of ratio problems to understand the concept of ratio. These pdf worksheets cover key skills like ratio of part to part, equivalent ratios, writing ratios in three different ways, and much more. Each worksheet is aligned with common core curriculum.
A ratio table is a set of equivalent (equal value) ratios presented in a table, in order to understand the relationship between the ratios and the numbers. In a ratio table, the ratio in one column repeats in all the other three columns. You get practical information to solve ratio problems by ratio tables. It is a structured list of equivalent ...
rting to a Unit Rate2Convert each of these rates into a unit rate by dividing the top numbe. by the bottom number. Do. 120 miles hours =. 20 miles. 1 hour. 120 ÷ 6 = 20. 36 push-ups minutes. nit Rates to Compare3Use unit rates to solve the f. llowing word problems.1 Tom and Paul are.
A "ratio" is just a comparison between, or a relating of, two different things. Ratios are used to create proportions by setting two ratios equal to each other and solving for some unknown, and ratios can also be used to find per-unit rates such as how many mile a car can drive "per liter" or how many hours the average student at a given ...
When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. An "x" is frequently used in place of the unknown. Ratio Tables Worksheets- Includes math lessons, 2 practice sheets, homework sheet, and a quiz!
Ratio and Proportions Worksheets Explained: Using ratio and proportion worksheets can instill confidence and a deeper understanding of complex math concepts. They can act as a homework aid to assist students needing extra practice. Ratios are generally expressed in their lowest terms, similar to fractions expressed in their lowest terms.
KS3 Maths Worksheet. Homework or Classwork. Objective: to be able to simplify ratios and share amounts by a given ratio A worksheet for simplifying and sharing with ratios. Starter has division practice, HCF recap and finding fractions of amounts. There is an extention exercise too. Please let me know what you think
Ratio & Proportion: Homework Worksheets. Subject: Mathematics. Age range: 11-14. Resource type: Worksheet/Activity. File previews. docx, 35.8 KB. docx, 18.31 KB. KS3 / GCSE ratio and proportion worksheets ideal for revision or homework. There is a self-assessment section at the end of each worksheet.
Ratios can be written in several different ways. Click on each word below to see the ratio of squares to triangles expressed in each way. Multiplying or dividing each term by the same nonzero number will give an equal ratio. For example, the ratio 2:4 is equal to the ratio 1:2. To tell if two ratios are equal, use a calculator and divide.