Unit rates worksheet / Understand the concept of a unit rate a/b associated with a ratio a:b with b =? 0, and use rate language in the context of a ratio relationship. Explore, learn, and excel with Quizizz! Apr 19, 2020 · c. Brianna works at the local grocery store. Practice using unit rates in different contexts with these worksheets for 6th grade. Try our NEW quick quiz at the bottom of this page. Worksheet by Kuta Software LLC ©K Q2F0U1`8p JKQu\traf PSho]fMthwSadraez fLSLEC\. ) What is the unit rat 5 gallons 56 action-packed pages filled with guided notes, worksheets, math poetry, activities, and assessments! A complete unit for mastering ratios, rates, and proportions in two weeks or less! Easter Unit Rates worksheets curated by Worksheetzone Gain instant access to Easter Unit Rates Worksheets, a trusted resource for educators and families alike. Free worksheets including unit rates, proportions, tables, and graphs. Help kids check their answers using the provided answer keys. Each rate worksheet is accompanied by an answer Feb 7, 2025 · Unit rate is a critical everyday math concept your kids must learn. These worksheets explain how to determine unit rates through the use of simple division. AN INTRODUCTION TO PROPORTIONAL RELATIONSHIPS We will use tables and graphs to explore unit rates and unit prices. 49 by 22 to get a A video game store was getting rid of old games, selling them 5 for $102. And we'll see how this knowledge can help us buy tacos, drive a go-kart, and make dog treats. Introduce the unit rates worksheets to help your students learn. It begins by defining a unit rate as a rate where the denominator is 1, and can be expressed as "per" or using division. Everything about Unit Rates Worksheets for Grade 7 Advantages of Unit Rate Worksheets A unit rate represents the average amount of resources a manufacturer needs to install one unit. Problem 4 : 75 basketballs cost $1,143. ” Lin’s rate could be written “10 miles per 1 hour. From calculating unit rates to solving word problems, this resource is designed to enhance understanding and improve proficiency in unit rate calculations. How much do you score per game? Question 4 : Steve drives 78 miles on 3 gallons of gas. Common core worksheets and activities for 6. This may lead to an increase in the fees for educational institutions to participate in the relevant scheme. 75 mi in 1 hour (4) 15 problems in 30 min 1 problem in 2 min (l) 32 inches in length to 12 inches in width (2) 4 sudoku puzzles in 2 hours (3) 10 dogs to 4 cats (4) 36 boys to 46 girls (5) A 64 ounce Tackle ratios and rates confidently using these worksheets for grades 6th to 8th. If you made a batch of cookies using 5 cup of flour, how many cups of sugar would you need? 5) It takes 3 4⁄6 gallons of water to fill up 3 1⁄2 containers. These worksheets will help students better understand the ratio of two quantities, typically with one of the quantities set to a value of 1. Students will need to simplify their answers, writing them as proper fractions, mixed numbers, or whole numbers. Examples are provided such as words per minute or dollars per hour. Easier to grade, more in-depth and best of all 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Students explore unit rates with fractions in this seventh-grade math worksheet featuring real-world scenarios. We will also learn how to calculate unit rates with whole numbers, then decimals and finally fractions. Morgan ran 5 miles in 57 and a half minutes. After they have made a prediction, they calculate the unit rate. 4 3 4 18 10 12 Solve each proportion: Unit 6 - Part 1: Unit Rate Conversions How does solving problems with equivalent ratios relate to algebra? See how easy it is to solve Unit Rates. . Printable PDFs reinforce key concepts and problem-solving skills. Determine which rate is better to use. These Ratio Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. 5 minutes per mile 3. Great for teachers, homeschoolers, parents, and students. an entire paper? 7. Want to test yourself to see how well you have understood this skill?. Solve the following unit rate problems and show your workings. 96 or 24 bottles for $5. Browse 7th Grade Rates Worksheets. ) What is the unit rat b) Complete the table. We will represent ratios and rates with tables and double number line diagrams, and solve problems using rates. RP. At the start, one of the quantities in each rate is a fraction, and Free worksheets and free distance learning. And once you single unit, you can more of cereal is on sale for $3. This worksheet offers a variety of practice problems and exercises to help students master the concept of unit rates in real-world contexts. Circle her statements below that 1. 12) Convert $0. Ideal for distance learning, its interactive format is customizable and can easily be These free unit rate worksheets will help you find unit rates by analyzing tables. 75 in 5 hours $6. Find the unit rate. Function 2 has the greater rate of change. There are also examples to These ratio worksheets will generate 10 Rates and Unit Rates problems per worksheet. Students are asked to predict the animal speeds from slowest to fastest before they begin their calculations. mathworksheets4kids. 50 per hour, it is the same as $8. Question 3 : You score 84 points in six games. These free unit rate worksheets will help develop mastery of unit rates. How much water would it take to fill 6 containers? 6 dollars/soccer ball 3 6 9 12 15 18 21 24 27 30 No. Round your answer to the nearest hundredth. Enhance understanding and improve math skills today with our engaging worksheet! Find the constant of proportionality (unit rate). Find the miles per gallon. Which is the better buy? Find over 60 worksheets on unit rates, unitary method and comparing unit rates for grades 5 to high school. All of the problems were written as if the anima er Example 1: Compare the following functions to determine which has the greater rate of change. In mathematics, a ratio indicates how many times one number contains another. txt) or read online for free. Ellie used 1/6 of a liter of water to make 1/21 of a casserole. Wright needs to purchase bottles of water for Fall Festival. Jun 14, 2023 · Boost your math skills with our free unit rates worksheet PDF! Perfect for practice, this easy-to-use resource is great for students and teachers alike. Ratios can be written in 3 different ways. Unit Rate Worksheets 7th Grade Unit rate worksheets grade 7 help students in learning the unit rate displayed on a graph, word problems, and in a fraction form. . In this practice worksheet, learners are presented with word problems that contain two different quantities, and they will need to find the unit rate and write it as a proper fraction, mixed number, or whole number. They are used to compare numbers. These worksheets are perfect for classroom use, homework assignments, or extra practice at home. Express as fraction in simplest form. Designed for a sixth-grade math curriculum, these word problems will give students practice calculating unit rates, using unit rates to find other rates, and comparing unit rates to find a better deal. How many heads of cabbage can Willie buy if he has $28. 50 for every 1 hour of work. A unit rate is an equivalent ratio expressed as something “per 1. How are the quantities on the double number line above organized differently from those in Table III on page 11? Home > Grade Levels > Grade 7 > Unit Rates and Ratios of Fractions Worksheets What is the Difference Between Unit Rates and Ratios of Fractions? When it comes to relationships, both ratios and rates are a means of expressing relationships between two or more quantities. 100% free math worksheets! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Free Ratios and Unit Rates worksheets. d) Write an equation for the graph. These worksheets and lessons show students how to approach word problems that include unit rates, speed, and/or price. Claire power walks 1/9 of a mile in 1/54 of an hour, compute the unit rate as the complex e. Improve your math knowledge with free questions in "Unit rates" and thousands of other math skills. Find the unit rate in dollars per ounce. Each math worksheet is accompanied by an answer key, is printable, and can be customized to fit your needs. 50 for 10 headbands. Ratio worksheets including relating visual quantities, ratio word problems, rate and ratio problems and finding equivalent ratios. Answer keys and examples come with each printable worksheet. Converting Unit Rates WorksheetProblem 1 : In a business, if A can earn $7500 in 2. Answers will include miles per hour, cost per kilogram, and other real world examples. Example: In a class of 20 students, 12 are girls. How long did it take her to run each mile? ___________________ 11. Q. $2. For example: If a student earns $8. Students explore unit rates with fractions in this seventh-grade math worksheet featuring real-world scenarios. Unit Rate Worksheet Practice Practice unit rate calculations with this worksheet. Record the price of the item Decide whether the proportion is true or false and then compare the cross products to verify your answer. Say goodbye to Generate a PDF worksheet, download it to your device and print it off to share with your students. Evan has 4 chocolate bars with a total of 48 pieces. At this rate, how many Pesos would you get if you exchanged $121. Welcome to our Unit Rate Problems 6th Grade page. It made pencils at a rate of how many per minute? 4) A cookie recipe called for 3 1⁄ 2 cups of sugar for every 3 1⁄ 4 cups of flour. of cartons Unit Rate = Printable Math Worksheets @ www. Joann described the diagram to the right in eight different ways. Great worksheets on Unit Rates. Download the worksheets with answer keys and practice graphs, fractions and scenarios. example: 4 burgers for $12 $3 per burger Find the unit rate for each problem. RATIOS, RATES, UNIT RATES & PROPORTIONS NOTES, GUIDED PRACTICE, & INDEPENDENT PRACTICE Ratios, Rates & Unit Rates, & Proportions Packet RATIOS Ratio is a comparison of two quantities. You may also enjoy Jun 24, 2025 · Unit Rates Worksheets Here at Brighterly, we also offer a broad range of exercises equivalent to the ratios and rates worksheets, which let students study better by simplifying mathematical equations, thereby making math fun and engaging for them. A soccer player runs a total of 12 miles during a 4 hour game. Free worksheets and free distance learning. Printable or online. Get the Unit Rate Worksheet for FREE when you download today! Free Unit Rate worksheet for 6th and 7th Grade with 10 skills based practice questions and 5 applied questions. 94? Which is the best buy? You are going to compare prices by finding the unit rate. 5. Explore now with Quizizz! Summary We will explore the relationship between ratios and rates. the graph will contain the points 0, 0 and (1, !) where r is the unit rate. For example, if there are eight oranges and six The best source for free math worksheets. In 7th grade, students focus heavily on proportions and proportional reasoning. Download free PDF printable Compare Unit Rates worksheets for 6th grade math (6. 50. Each time you download a worksheet it will have unique questions and come with its own answer key. 100% free math worksheets! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! N. Howard bought 6 books for Unit rate math Here you will learn about unit rate math problems, including the rates that involve whole numbers, decimals, integers, and fractions, and how to use unit rate math to make comparisons between rates. Express as a fraction in simplest form! Learn Unit Rates with our printable worksheets! Fun and interactive exercises designed for easy learning. Page 5: A coloring sheet without numbers for your students to color freely. A worksheet is a page of learning, designed for a student to write on using an ink pen or pencil. After unit rate is defined, double number lines occur naturally because the units are different. The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. 79. Every worksheet is carefully quality-checked, clearly structured, and thematically organized to align with your teaching goals. Use these printable worksheets to teach student to calculate unit rates of ratios. Unit Rates Worksheets The basic concept of unit rate worksheets is that as the quantity of units produced doubles, the cost of producing a unit is decreased by a constant percentage. ” Unlock the full potential of Printable Grade 7 Unit Rates Worksheets, ideal for classroom stations, take-home learning packets, or enrichment centers. We usually use the key word per or the division symbol / to indicate a unit rate. Award winning educational materials designed to help kids succeed. Students calculate unit rates containing fractions in this one-page practice worksheet! Featuring 12 problems that range in difficulty, this worksheet asks students to calculate the unit rate for each scenario, in which at least one of the given numbers is a fraction. 6. This document provides examples and word problems involving unit rates. In the worksheet, students get to multiply all the Unit Rates by the quantities from all MTOs. Comparing Unit Prices Find each unit price and determine which is a better buy. In 6th grade, students develop the concept of ratio and rate reasoning. The cost data is generally reported by the manufacturer for production lots by the total lot costs and the number of units in that lot. Printable or interactive. In this unit, the focus is to connect ratio and rate to whole number Students can use simple ratios to solve these word problems; the arithmetic is kept simple so as to focus on the understanding of the use of ratios. Explore now with Quizizz! 5. Page 3&4: Answer keys to quickly and easily check students' work. How many cantaloupes can you buy for $6? Free Ratios worksheets and free Ratios distance learning. 49 for every 22 ounces. Word problems involve number of items, pricing, and constant speed. Printable worksheet featuring unit rates from word problems, and mixed graphic displays. Download free PDF printable Find Unit Rates (Change In Units) worksheets for 7th grade math (7. 55 in 1 hour (3) 14 books costs $56 1 book costs B) Express in simplest ratio (2) 366 mi in 8 hours 45. In conclusion, unit rate word problem worksheets are valuable tools for students to practice and master the concept of unit rates. Kickstart their learning journey with our free worksheets! Free worksheets and free distance learning. Adjusting productivity per work activity is possible with a detailed estimate of the project resources. We will learn what it means for quantities to be in a proportional relationship, and identify the constant of proportionality (unit rate) in tables and graphs. Use the unit rate to solve for the given measurement. 100% free math worksheets! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Write the following as unit rates both ways. 100% free math worksheets! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Mar 31, 2023 · We'll learn that a unit rate is a special type of ratio that compares the first quantity to one unit of the second quantity. 5 gallons 56 action-packed pages filled with guided notes, worksheets, math poetry, activities, and assessments! A complete unit for mastering ratios, rates, and proportions in two weeks or less! Free Printable Unit Rates worksheets Math Unit Rates: Discover a collection of free printable worksheets to help students master the concept of unit rates, enhance problem-solving skills, and improve their mathematical understanding. Question 5 Use this math worksheet to practice calculating unit rates and understand how unit rates connect to real-world situations! 10) Convert $10. Name________________________ 1000 calories for 12 servings of pizza per serving400 Learn with this solving problems with unit rate pdf worksheet which is perfect for teaching grade 7 math and for student practice or homework. Maya reads 1/8 of a newspaper in 1/20 of a minute. You will learn to work with unit rates in graphs, tables, and word problems. Unit Rate Activity: This Cost Comparison activity is a fun and engaging way to get your students to learn and remember an important life skill FOREVER. What's Included:6 Distinct Problems: Each word problem requires students to apply their knowledge differen Free worksheets including unit rates, ratios, tables, and graphs. 6rp3b × Description: "This worksheet is designed to teach children about the concept of ratios and unit rates in math. 100% free math worksheets! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! This high interest, free resource includes eight animal unit rate problems. Page 2: One corresponding color-by-number sheet. 96. Browse Rates Worksheets. Printable, fun, and easy to use for learning. They provide a variety of problems designed to help you understand and apply these key math concepts effectively. If they sold 3 games, how much money would they have made? Give students additional practice calculating unit rates with the second installment of this helpful math worksheet! Designed for a sixth-grade math curriculum, this worksheet invites learners to calculate the unit rates from an original selection of real-world scenarios, such as the number of slices per pie, spots per ladybug, and books per shelf. It contains 15 problems involving various contexts such as classrooms, CDs, game points, eating speed, ticket prices, earnings, snowfall, juice containers, TV commercials, and candy bags. Finding Unit Rate A Unit Rate makes a comparison to one unit. The second set of rate worksheets will help students solve proportions that contain fractions. Finding unit Rates When the denominator of a rate is 1, we call the rate a unit rate. How far does the skydiver fall per second? Question 2 : A pump moves 42 gallons in seven minutes. Find and compare unit rates in the context of real-world scenarios with this sixth-grade math worksheet! Featuring ten relatable word problems, this worksheet asks students to read each scenario's verbal description of two rates. How many gallons A great collection of worksheets and lessons to help students understand the relationship between ratios and unit rates. A fire hydrant puts out about 1,500 gallons of water per minute. Explore a huge collection of Ratios and Rates worksheets! Perfect for students of all grades. Mrs. She can purchase 18 bottles for $3. Unit 2: Rate, Ratio and Proportional Reasoning Standards, Checklist and Concept Map Georgia Standards of Excellence (GSE): Here are the contents included in the " Unit Rate Activity Color by Number: Coloring Worksheet 5th 6th 8th 7th ": Page 1: One worksheet contains 16 problems focusing on Unit Rate. With built-in answer keys and easy-to-follow instructions, you can save time and reduce prep stress. Watch our informative video or follow our lesson. An example of a rate would be $16 for 8 red peppers. Printable & contain answer keys for each worksheet. How many boxes can she put on each shelf? ___________________ 30 boxes per shelf 6. 2) Fifteen ounces of gold cost $6058. UNIT RATES AND GRAPHS #1 Directions: Find the unit rate for each of the graphs below. Help your students master unit rates with this targeted and engaging resource! This product includes 6 unique real-world word problems that will challenge students to find the missing unit rate. Easier to grade, more in-depth and 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Find the unit rate in pounds per gallon. By providing a structured approach and gradually increasing complexity, these worksheets can help students develop critical thinking skills and enhance their problem-solving abilities. c) Graph the unit rate by using the table. Start for free now! Jan 13, 2023 · Help your students master unit rate with our 9 relevant and engaging worksheets. Unit Rate Word Problems Worksheet with AnswersQuestion 1 : A skydiver falls 144 feet in three seconds. 01 per cubic inch into cost per cubic mile. com Explore rates and unit rates with engaging 6th grade math worksheets. How many pieces are in each bar? ___________________ 12 pieces per bar 7. Write the ratio of the number of girls to total students. Mar 19, 2020 · We usually use the key word per or the division symbol / to indicate a unit rate. Find each unit rate. With our unit rate math worksheets, students can practice converting rates, comparing unit rates, and solving real-world problems. 50/hour, and means $8. 05. unit-rate-worksheet - Free download as PDF File (. Find the unit rate, compare unit rates, use unit rates in tables and graphs, and more. Free worksheets including unit rates, ratios, tables, and graphs. Students will first learn about unit rate math problems as part of ratios and proportions in 6 6 th grade and 7 7 th grade. Includes 2 math lessons, 2 practice sheets, a homework sheet, and a quiz! Dive into our unit rate worksheets, starting with plenty of practice problems involving graphs, then progressing to word problems on the unitary method, unit rate comparisons, and more. Free Printable Unit Rates Worksheets for 8th Grade Math Unit Rates: Discover a collection of free printable worksheets tailored for Grade 8 students, designed to help educators effectively teach and reinforce the concept of unit rates in mathematics. 10? 18) Molly bought two heads of cabbage for $1. 1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas . Round your answer to the nearest Free rate worksheets where students will analyze graphs and calculate unit rates containing integers and decimals. 75 Boost learning with Grade 6 Ratios and Rates worksheets! Fun and effective activities for students. The exchange rate is approximately $3 = 1 Peso. she need to make an entire casserole? 8. 2. The first set of rate problems is restricted to whole numbers. These worksheets not only improve a student's math skills in ratio and proportion but also help in improving logical skills and reasoning skills. Here you will find our range of 6th Grade Unit Rate worksheets which will help your child apply and practice using unit rates in a range of different contexts. Y n `AWlBlN HrGisgyhhtSsD DraeisXefrHv`etdX. 2 / Ratios And Proportional Relationships / Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. The third and final series of math worksheets incorporates decimals in both the tables and the unit rates. 3) Four pounds of apples cost $4. How minutes does she need to read f. Geared toward Ratios and Rates Worksheets Both rates and ratios are comparisons of two numbers. Use this math worksheet to practice calculating unit rates and understand how unit rates connect to real-world situations! Rotes, Ratios, and Proportions MATH MONKS Answers A) Find the unit rate $32. One strategy would be to calculate a unit rate for each person. 16) The currency in Argentina is the Peso. Free resources for teachers, students, and homeschooling! Explore ratios, rates, and proportions with engaging math lessons designed for 6th graders to enhance their understanding of these fundamental concepts. H k KMMatdQec pwxictchl lIfnifDilnViBtHeX SG]eZodmpextLr[yy. Function 1: y = 2x + 4 Function 2: Solution: The rate of change for Function 1 is 2; the rate of change for Function 2 is 3. For example, we could compare the price of purchasing things to the number of things bought. Comparing Costs by Using Unit Rate bigger 32-ounce can be overwhelming. Do not write answers as mixed numbers. The remainder of the document Free Printable Unit Rates Worksheets for 7th Grade Math Unit Rates: Discover a collection of free printable worksheets tailored for Grade 7 students, designed to enhance their understanding of mathematical concepts and improve problem-solving skills. Well, which is the better deal? $2. These free unit rate worksheets will help you find unit rates by setting up and solving proportions. We will define unit rate. Ratio and Proportion worksheets: Our ratio and proportion worksheets for math grades 5 to 6 cover: finding ratios worksheets, equivalent ratio worksheets, simplifying ratios worksheets, ratio tables worksheets, calculating proportions worksheets, finding unit rates worksheets. Problem 2 : If David can prepare 2 gallons of juice in 4 days, how many cups of juice can he prepare per day? Problem 3 : If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute. There is a ratio of 3 triangles to 6 A student pays $12. How many liters of does g. Download now and start improving your understanding of rates and unit rates today! Explore a huge collection of Grade 6 Unit Rates worksheets! Perfect for students of all grades. 5 years, find the unit rate of his earning per month. Though they sound a lot like each other, rates and ratios are two different concepts of 5. Use this math worksheet to practice calculating unit rates and understand how unit rates connect to real-world situations! Master ratios & proportions with our 6th grade math worksheets! Covers simplifying ratios, equivalent ratios, and more. 2 7 9 15 b. What is the cost per pound? 4) Mrs. ” For example, Andre’s rate could be written as “12 1 miles in 1 hour” or “12 1 2 2 miles per 1 hour. Round your answer to the nearest LiveWorksheets transforms your traditional printable worksheets into self-correcting interactive exercises that the students can do online and send to the teacher. 60 per cubic inch into cost per cubic cm. Free Printable Unit Rates Worksheets for 7th Class Math Unit Rates: Discover a collection of free printable worksheets tailored for Class 7 students, designed to enhance their understanding of mathematical concepts and improve problem-solving skills. Use this math worksheet to practice calculating unit rates and understand how unit rates connect to real-world situations! Download to complete online or as a printable! Mar 19, 2020 · Finding unit Rates When the denominator of a rate is 1, we call the rate a unit rate. Free | Math | Worksheets | Grade 6 | Printable Free Printable Unit Rates Worksheets for 8th Class Math Unit Rates: Discover a collection of free printable worksheets tailored for Class 8 students, designed to help educators effectively teach and reinforce the concept of unit rates in mathematics. A rate is simply a specific type of ratio. pdf), Text File (. Background Information For The Teacher Connections to other grade levels: A formal study of ratio and proportional relationships is only provided in grades 6 and 7. This Unit Rate Word Problems worksheet is a great way to introduce math learners to real-world situations that involve unit rates. 1) as per common core standards (CCSS) from ByteLearn. This rate can be used to find the unit price. 80? 5 3) One cantaloupe costs $2. Learn with this rates and unit (basic) pdf worksheet which is ideal for teaching grade 7 math and for student practice or homework. 80. Download and print for home or classroom use. Complete the tables below, show your division, and find the best cost per ounce. Whether you're managing a full classroom or guiding at-home learning, these Easter Unit Rates Worksheets offer structured, easy-to-follow worksheets that promote clear skill progression. She needs to stock 4 shelves with 120 boxes of cereal. Rates are special ratios where the two things being compared have different units. Start for free now! RATIOS Write the following ratios and reduce to lowest terms. Free Printable Unit Rates Worksheets for 5th Grade Math Unit Rates: Discover a collection of free printable worksheets tailored for Grade 5 students, designed to help them master the concept of unit rates in a fun and interactive way. com. Worksheets are Mathlinks grade 6 student packet 11 ratios and unit rates, Unit rate work, Gr6 8 savvy shopping unit pricing work student version, Mathematics grade 6, 6th grade math ratios and proportions notes, Finding a unit price work 6, Grade 6 ratios word problems, Ratios rates unit rates. fraction. The second set of rate worksheets introduces problems that contain fractions and mixed numbers. Download Unit Free Printable Unit Rates Worksheets for 6th Grade Math Unit Rates: Discover a collection of free printable worksheets tailored for Grade 6 students to enhance their understanding of unit rates, ratios, and proportions in real-world scenarios. A. These PDF worksheets are designed for 3rd through 6th grade students and include full answer keys. c. gnys etb isdmaqg tstu xgrltm ecmjlhg olcy cpvfbkw qhn avl nvslaz sjrahd oqun wrv plsyhmf