# Age Old Problems Maths Answers

Whatever the challenges and whatever the topic, maths can be made so much easier with a little encouragement and a lot of resources. How old is the son? Solution: Let x - son's age now Then 3x = father's age now Now form a table. Covering counting, number, shape, time and much more. Don't forget to include additional resources. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. Home › By Age › Twelve to Fifteen Years Old Math Worksheets For Ages 12 to 15. (You must be at least 18 years old to vote. Each time the sum of numbers appearing on their top is noted and recorded as given in the following table:. The lessons provide coverage of Levels 1 to 6 of The New Zealand Curriculum. Note: The difference of the ages of two persons is constant at any time. And the sum of their ages is 28. Our vision is to develop a nation of creative problem solvers, and we believe maths is the most effective way to get students there. If the father's age is \$38\$ years now, what was the. *Students progress was analysed using the EdPlace database with all activities taken between July 2017 and June 2018, excluding students who completed less than 20 activities over at least 5 days. Our stand-alone curriculum has everything your child needs, including professional instruction throughout every course. Sample Problems From Intermediate Algebra Sample problems are under the links in the "Sample Problems" column and the corresponding review material is under the "Concepts" column. A Story of Ratios. If a fossil contains 60% of its original carbon, how old is the fossil? The half life of carbon 14 is 5600 years. the answer to a multiplication problem/la respuesta a. How old is the son? 2. Math Problem solving contests for teams of up to 35 students in grades 4 through 8. As you complete the math problems in this book, you will undoubtedly want to check your answers against the answer explanation section at the end of each chap-ter. Practice your math problem solving skills with our 12 tests. Therefore, Kathy is x + 16. Answer: Today you are 13 years old. A boy is 10 years older than his brother. Ahbb=+, where A is the area, h is the height, and b1 and b2 are the lengths of the bases. ) Homeschool kits include a non-consumable student edition textbook, either an answer key or solutions manual, and tests with answer keys. Recommended Age: 6-7 years. This is intentional - keep in mind how challenging it is for the children to sift through the verbal clues and figure out what they need to do to the numbers provided to find the answers. The mathematics exercises are simple in design yet challenging and fun to do. 27 The area of a trapezoid is found using the formula () 12. That’s right, even dummies find them funny!. Sign in now Join now More. Most of the worksheets are pitched at key stage 2 (7-11 year olds). Just you, the quiz, and the slowly dawning realisation that a lot of 10-year-olds must be pretty good at maths. The algebra section allows you to expand, factor or simplify virtually any expression you choose. Age Problems - Equations in single variable - Algebra This worksheet is based on age word problems which come under equations in one variable. Best Answer: let E = age of Esteban let R = age of Raoul Use the words in the problem to set up your equations. The calculator will evaluate your answers and then show the work so you can learn how to solve the word problem. So, if you want to impress people with a math trick this Halloween, just be sure their birthday is sometime before November and don't show it to. Brian bought 3 packs of mints with a number of mints in each pack. d) From past figures, it is predicted that 39% of the registered voters in California will vote in the June. (Note that since Lisa is 16 years younger than Kathy, you must add 16 years to Lisa to denote Kathy's age. While most of the math problems seem impossible to solve, sometimes all you really need to do is use some logic. 4 The Foundations of Mathematics. This is the third part of the Solving Age Problems of the Math Word Problem Solving Series. True or false? This question is from an admissions quiz, so no calculators should be used. Our mathematics resources are perfect for use in the classroom or for additional home learning. Here is the link where you can find all participating countries with links of particular country. For example, for primary and middle school students there are 1st grade math problems, 2nd grade math problems, 3rd grade math. Intermediate Algebra, Algebra – I and Algebra – II students can practice these questions. In the ﬁgure above, line l is perpendicular to the y-axis and a distance of two units from the x-axis. College students can compute answers to homework problems to 10 decimal places, but ask them to. Our vision is to develop a nation of creative problem solvers, and we believe maths is the most effective way to get students there. Information. All of the worksheets come with an answer key on the 2nd page of the file. But among the students we have in our mathematics programs are some that have either high abilities or high interest, or both. strategy to obtain this answer. edu Phone: (215) 898-8178 & 898-8627 Fax: (215) 573-4063. Past Exam Archive. If you are a middle-aged man looking to have a good time dating woman half your age, this article is for you. A father is 4 times as old as his son. He is 15 years older than twice Al's age. The answers can be very useful when trying to solve a very hard riddle. Short Tricks of Age Problems In Hindi, type and tricks age based questions, आयु संबंधी शार्ट ट्रिक्स Objectives Old Papers MCQ Question आयु: Short Tricks of Age Based Problems In Hindi | आयु संबंधी शार्ट ट्रिक्स - Online Solution, Maths Short Tricks. Your creativity can help other teachers. That's partly the reason why simple math problems go viral all the time, they seem incredibly easy, but people always get vastly different answers and into intense arguments over it. Also keep in mind this represents her old age plus 4, so this whole little piece inside the parentheses is her new age. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Sign in now Join now More. Therefore, Kathy is x + 16. A boy is 10 years older than his brother. Home › By Age › Eight to Eleven Years Old Math Worksheets For Ages 8 to 11. At this point in time, my age is exactly three times my Grandson's age. In 4 years he will be twice as old as his brother. There are generally two methods that will lead to two different answers. How many years will it take for Arman to be 3 times as old as Diya? Math · Algebra I. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. Many of us familiar with the feeling that maths is just impossible. Age problems are all about labeling things in relationship to each other (your sister's age was written in terms of your age " a '", etc. Outline Mathematics: Billy is twice as old as Sally was when Billy was as old as Sally is now. Use problem solving skills in these math and science games with your favorite PBS KIDS characters Wild Kratts, WordGirl, Curious George, Sesame Street and the Cat in the Hat!. ), and then writing a math sentence to express whatever “truth” was written in English. Parents can set up a free account for access to a dashboard. Printable math worksheets from K5 Learning. Nicholas Carlson. Exams, Answer Keys, and Solution Sets are offered here in Adobe Acrobat (. Need help with CP math problem answer why is it not c? ans A. Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. Whether your child is 3 or 13, you can find activities here. Home>Worksheets>Age 11-14 Applying mathematics and solving problems Click on the 'change' button and watch the numbers change. Each time the sum of numbers appearing on their top is noted and recorded as given in the following table:. FREE downloadable NCERT SOLUTIONS for Class 1 to 5 & Class 6, Class 7, Class 8, Class 9, Class 10, Class 11, Class 12 for Maths, Science, Physics, Chemistry, Biology, Business Studies, Accountancy, Hindi, English and more as per NCERT guidelines. Your elementary grade students will love this Addition 1 digit (set 3) Worksheet. So i hope that you'll learn mo about Problem solving and you'll explore yourself to know this section. Therefore, Lisa is 7 years old. This is not intended as a comprehensive and definitive guide to all of mathematics, but as an easy-to-use summary of the major mathematicians and the developments of mathematical thought over the centuries. Recommended Age: 6-7 years. He is 15 years older than twice Al's age. MA15300 ; MA15800. See also, Kids Math Word Problems II for kids 8-9 years of age. The 1969 pages of the book are very much worth the 79. Let's do some more of these classic age word problems. (The fact that these ages are also your current ages is merely a coincidence. Problems and Solutions (NCERT Exemplar Answers) Problem 1: Two dice are thrown simultaneously 500 times. Goldy's Glide for Grades 2-3 extends a magic squares problem. *Students progress was analysed using the EdPlace database with all activities taken between July 2017 and June 2018, excluding students who completed less than 20 activities over at least 5 days. The MAA’s American Mathematics Competitions program leads the nation in strengthening the mathematical capabilities of the next generation of problem-solvers. Looks Magical 111 | plus. When written in decimal notation, every square number has at most \$1000\$ digits that are not \$0\$ or \$1\$. If x = present age of a person x – 3 = age of the person 3 years ago x + 5 = age of the person 5 years from now or 5 years hence. You can send your answers by. We even have some challenges and a weekly programme! Browse the categories or jump right into our most popular worksheets. After buying them she had \$10. A woman answers, and he asks her how many children she has and how old they are. 12 years ago, William was 7 times as old as Ben. Can You Pass This Maths SAT For 10-Year-Olds? No calculators. Home; Welcome; Videos and Worksheets; Primary; 5-a-day. Math problem answers are solved here step-by-step to keep the explanation clear to the students. Math in Everyday Life Students work with a partner to come up a with word problems, involving time, money, and simple fractions. If you were born in 1914 and wear a size 10 shoe, the trick would conclude that your shoe size is 11 and that you were 0 years old. Our mathematics resources are perfect for use in the classroom or for additional home learning. Learn second grade math online for free. Printable addition worksheets, 5 page workbook that concentrates on adding single digit numbers to solve each problem. Right now, he is working through a chapter on grouping. Directions. Find free quizzes that will test your math skills and ability in areas such as addition, subtraction, multiplication, division, basic algebra, fractions, geometry, decimals and more. Six is not a factor of eighty because 80×6=13 remainder 2. Australia. How old is the son? 2. Practice your math problem solving skills with our 12 tests. Here are some of the common word problems with sample questions, answers, and solutions. Mathway currently does not support tutoring in Chemistry. Play cool online math games for 2nd Grade with our huge collection of learning games. This means that Ramesh's eleventh birthday was on 31 st December 2017. All worksheets displayed here are focused for students that are twelve, thirteen, fourteen and fifteen years of age. Problems Based on Ages Shortcut Tricks. First Grade Math Worksheets. My Mum was 27 when I was born. The son is three years older than the daughter. You shouldn't need more than three lines of working for any problem. Choose from 500 different sets of math flashcards on Quizlet. PROBLEM “A” The result will always be “ 7 ” no matter what number was chosen. Word problems (or story problems) allow kids to apply what they've learned in math class to real-world situations. exactly thrice the age he was 4 years ago and hence C) is the right answer. The 'chunking' method in maths, uses repeated subtraction to find answers to division problems that use larger numbers, e. x + (x+14) = 150 4. I am now 26 years old. These puzzles can also be found in MathSphere: It's All Figured Out!. The techniques and methods we apply to solve problems on ages will vary from problem to problem. Shortcut Tricks are very important things in competitive exam. May 5, 2013, 9:21 AM Here's a problem 15-year-old Phoebe Cai solved about dominoes. We speak often about providing rich opportunities for disadvantaged students. Redraw geometry figures on your rough paper to include the information in the question. Three men checked into a hotel and decided to share a single room. We received lots of correct answers to the first part of the problem. I also watched another guy do a 45 minute lesson letting kids break into pairs to show how they got their answer to a basic math problem and judging by the look of the kids, they looked far too old to be doing something so basic and take 45 minutes of class time to do it!. The 2018 Math Olympiad will be held on Saturday November 17th. The algebra section allows you to expand, factor or simplify virtually any expression you choose. The school said the math problem was aimed at testing students’ critical thinking – adding that there was no right or wrong answer. Get the obvious answers to math riddles. The Chunking Method. Make sure you know from your instructor what topics are covered on each exam. The UCL Maths Challenge is a competition for Year 6 primary school pupils from London organised by UCL student volunteers. I wrote simple programs on it, stuff that would ask your age (and I mostly copied it from the book it came with at that), but there were games that ask you math questions and you would answer. Therefore, Lisa is 7 years old. The answer for the question "How to solve age problems step by step ?" is purely depending upon the question that we have in the topic "Problems on Ages". The person who has the dice and knows the game, rolls five dice and remarks almost instantly on the answer. 27 The area of a trapezoid is found using the formula () 12. Home>Worksheets>Age 11-14 Applying mathematics and solving problems Click on the 'change' button and watch the numbers change. The worksheets are generated randomly, so you get a different one each time. Whatever the challenges and whatever the topic, maths can be made so much easier with a little encouragement and a lot of resources. Here you can find a simple representation of basics and important topics from Maths too. View Homework Help - 1. Find the present age of each. On this page you will find: a complete list of all of our math worksheets, lessons, math homework, and quizzes. and that was 8 years ago. \$6\$ years ago, the elder one was \$3\$ times as old as the younger one. Three men checked into a hotel and decided to share a single room. There are many kinds of math worksheets for kids available online. g numbers to 100 and/or over 100. Problems and Solutions (NCERT Exemplar Answers) Problem 1: Two dice are thrown simultaneously 500 times. Sam was married when he was 22 years old. Home; Welcome; Videos and Worksheets; Primary; 5-a-day. Monitor and reflect on the process of mathematical problem solving. First identify the child’s age in years. More versions — English setting: US | UK. MATH 152 - Common Exam Archive Each semester, the syllabus and content for the common exams may differ from the exams below. He says this is not enough information. Therefore, Kathy is x + 16. All worksheets displayed here are focused for students that are twelve, thirteen, fourteen and fifteen years of age. (The fact that these ages are also your current ages is merely a coincidence. This is because to answer the second question, you would need to determine the ages of all students in your school and there would be variability in those data (since not all students are the same age). Age Problems - Sample Math Practice Problems The math problems below can be generated by MathScore. Find our KS3 Maths and English tests below for year 7 students. Age Problems. Home › By Age › Eight to Eleven Years Old Math Worksheets For Ages 8 to 11. 11-Plus Maths Quizzes In almost all geographic regions the 11-Plus examination will rely heavily on a good understanding of Maths. Maths Aptitude Mental Ability Model Question Shortcut Tricks are Uploaded as Pdf Format. The students and adults are invited to express their visions and creativity in effort to promote this fun learning activity. Study is set according to ability, regardless of age or school year, making it the obvious choice for any student wanting to progress or excel in maths. FREE Singapore math lessons , Primary 3 to Primary 6 (Singapore), Year 3 to Year 7 (USA). Their answer — initially 19 — wasn't exact, but they were not upset to be corrected when they actually placed the cups and found they needed 20. A math word problem. It only takes a minute to sign up. and that was 8 years ago. The algebra section allows you to expand, factor or simplify virtually any expression you choose. The question first appeared on April 8, as part of the Singapore and Asian Schools Math Olympiads contest. Are you smarter than a 16 year old? - take our GCSE maths quiz Are you smarter than a 16 year-old – or at least the 62% who passed GCSE maths this year? Give your answer in hours and minutes. Click on the 'print' button to print a pupil worksheet and an answer sheet. A math problem posed to Chinese fifth-graders may not have a right answer, but that hasn't stopped people from trying to solve it. Eureka Math Grade 5 Module 2 Lesson 1 Answer Key 10 9 8 7 6 5 4 3 2 1. Math and Logic – Word problems, logic puzzles, and math games to entertain you for hours. This site provides free photocopiable maths worksheets. Age Old Problems 1 Find the ages of the Smith family members and fill in the family tree. Sally's Hexagon Number Puzzles These are "number pyramids" where you get each number by adding the numbers just below it. How to use Algebra to solve age problems? Examples: 1. Looks Magical 111 | plus. You could use them at the end of an exam of assessment, so that those students who finish early have an interesting challenge that will keep them focused. This page covers topics on adding, subtracting and multiplying fractions for students of different ages and abilities. Algebra Age Problems Application of word problems : In this section,we shall learn Algebra age problems. The number of the sheep and goats is irrelevant to the captain’s age,” one said. Feb 2012 - Paper | Answers and Notes Challenge Your Pupils, Challenge Your Pupils 2 and Challenge Your Pupils 3 , each containing over 200 multiple choice problems taken from past PMC's, to interest and motivate pupils, can be purchased from the shop. You can also get Bedtime Math problems in a free app. Worksheets labeled with are accessible to Help Teaching Pro subscribers only. PhotoMath promises to help solve simple linear equations and other math problems by “reading” questions with the help of your smartphone camera. Get ready to give your undivided attention, because you'll need it to solve these fun math riddles. How old is each now? 1. The age of the captain is a mathematical word problem which cannot be answered even though there seems to be plenty of information supplied. Whether you are studying for a school math exam or just looking to challenge your math skills, this test will help you assess your skill level. So Jane is currently 12 years old. Make change. Dudeney wrote that this puzzle is "quite a different problem from the old one of the Fifteen Schoolgirls, and it will be found to. General Basic Math Test Online Quiz MCQS With Answers are available here. I recommend that you use it only to check your own work because occasionally, it might generate strange results. All answers are given. and that was 8 years ago. Knowledge Required of 1-2 digit numbers. If I'm 4 and my brother is half my age. The following problems are maximum/minimum optimization problems. You customize the math tests. Year 12 maths Here is a list of all of the maths skills students learn in year 12! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. Learn and free online practice on age related maths problems with examples, formulas, shortcuts, techniques to solve easily. In this case, that “truth” was the fact that you were twice your sister’s age 3 years ago. School Zone - Big Second Grade Workbook - Ages 7 to 8, Word Problems, Reading Comprehension, Phonics, Math, Science, and More (School Zone Big Workbook Series) (Cover may vary) [School Zone, Shannon M. Answers · 1. If you are good at basic math, you should be able to easily calculate your age by chocolate. For solving these, you have to remember some important points. Many of us familiar with the feeling that maths is just impossible. Scroll down to read the problem and the solution. Melissa and Craig were doing their math homework. The student may immediately make the conclusion that the answer is 16, but that is not what the problem is asking, and the child would be wrong. This Addition 1 digit (set 3) Worksheet is perfect to practice addition skills. Kindergarten. But, if you have ever asked yourself, "How many days old am I?" or even "How many seconds old am I?" than this age calculator will tell you! In addition to years, the age calculator measures the number of whole months, weeks, days, hours, minutes or even seconds that have elapsed since your first birthday. The mathematics exercises are simple in design yet challenging and fun to do. Exams, Answer Keys, and Solution Sets are offered here in Adobe Acrobat (. We try to provide all. com, a math practice program for schools and individual families. To find out if you have passed the test, email me to check your answers. Using M&M cookies to work math problems (4-6) This is a fun math activity using M&M cookies that are prepared ahead by the teacher or that the students plan for and make the day before. Puzzles and problems for Years 5 - 6 maths with teaching objectives at the end of each activity. Math Worksheet Generator - Free - Practice Math with these Worksheets. Also keep in mind this represents her old age plus 4, so this whole little piece inside the parentheses is her new age. Find an easier solution to Mathematical problems with the Maths File. If he lived to be 84, then one-sixth of his life is 14 years, one-twelfth of his life is 7 years (so he'd be 21, and he certainly should have a beard by this age), one-seventh of his life is 12 years (so he didn't marry until he was 33 years old), his child was born when he was 38, the boy died at 42 (when Diophantus was 80), and then. Spring 2019. This is a fun way for children to master basic math equations, though. Math difficulties can show up at different ages and in lots of ways. Knowing the common word problems that usually appear in the civil service exam math is the best way to prepare for this section. If I'm 4 and my brother is half my age. Congress poised to pass a bill allowing annuities to be offered in mainstream 401(k) plans, Americans soon will be asking a lot of questions about these financial. If you are good at basic math, you should be able to easily calculate your age by chocolate. This 'unsolvable' Chinese maths problem has people stumped. Sandra is playing in a tennis doubles tournament. Free Official (Old) SAT Practice Tests. Can You Pass This Maths SAT For 10-Year-Olds? No calculators. If X is the daughters age then 3X is the mothers age. Math Game Time’s free math videos incorporate both learning and fun. Math Worksheet Generator - Free - Practice Math with these Worksheets. Covering counting, number, shape, time and much more. Activities for children. To stimulate enthusiasm and a love for Mathematics ; To introduce important Mathematical concepts. This is the aptitude questions and answers section on "Problems on Ages" with explanation for various interview, competitive examination and entrance test. Sam will be 3/4 Jane's age. But, if you have ever asked yourself, "How many days old am I?" or even "How many seconds old am I?" than this age calculator will tell you! In addition to years, the age calculator measures the number of whole months, weeks, days, hours, minutes or even seconds that have elapsed since your first birthday. Where t 1/2 is the half-life of the isotope carbon 14, t is the age of the fossil (or the date of death) and ln() is the natural logarithm function. If Zids have 5 spots and Zods have 7 spots, the possible ways of making 140 are: 28 Zids;. The college math test has 20 problems that cover the following topics: algebraic operations, algebraic applications, trigonometry, functions, coordinate geometry, and solutions of equations and inequalities. At this point, students have mastered basic decimal operations and are starting to get more comfortable with fractions and percentages. Learn math with free interactive flashcards. Free Maths Assessments for Children in Years 1-6. That’s right, even dummies find them funny!. Basic Math Solver offers you solving online fraction problems, metric conversions, power and radical problems. The problems are arranged so the methods or ideas used to solve the first problems can be generalized in some way to solve the next ones. Age Word Problems One of the things I love about "age" problems is that they require students to not just convert sentences to equations, but also to identify different time frames in which parts of the problem may occur. Solve for your future ages. Math 4 today: 10-Minute Daily Skills Book , McGrow-Hill Children’s Publishing, Good Apple 1998. Study is set according to ability, regardless of age or school year, making it the obvious choice for any student wanting to progress or excel in maths. Math Problem Solver Questions Answered Free Algebra Geometry Trigonometry Calculus Number Theory Combinatorics Probability. How old will he be when I'm 100? - Slader. How many students were in each bus? 2) Aliyah had \$24 to spend on seven pencils. Maths Aptitude Mental Ability Model Question Shortcut Tricks are Uploaded as Pdf Format. It is a complex math question that requires you to. Use paper to do the math for the given problem, then input your answers here and click the Calculate button. Five years ago he was seven times as old. Mathematics- from the simple, like 1 + 1 = 2 (or maybe not) to the more complex reaches of calculus! If you enjoy working with figures, you'll find a happy home here. Note that this problem requires a chart to organize the information. Year 12 maths Here is a list of all of the maths skills students learn in year 12! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. Four years ago the sum of their ages was 60 years. Teacher Edition. (Note that since Lisa is 16 years younger than Kathy, you must add 16 years to Lisa to denote Kathy's age. Bret is 3 times as old as Laura. (The correct answer, by the way, is 32). Check grade levels below. Printable Math Worksheets, Tests, and Activities. If You Can Solve These Math Problems, You Are As Smart As The World's Smartest Teenagers. > Word Problem Worksheets The Word Problem Worksheets listed below will provide help for students who need to practice solving math word problems. The worksheets are available as both PDF and html files. MathSphere Maths Puzzles. Practice your math problem solving skills with our 12 tests. Teacher Edition. Quiz: Very Hard Math Problems Questions and Answers. In this lesson, students will solve math word problems using money, decimals, and fractions. X=daughter's age 3X= mother's age Five years from now, Mrs. Problems and Solutions (NCERT Exemplar Answers) Problem 1: Two dice are thrown simultaneously 500 times. Proven to raise maths grades fast for all ages. Accuracy is always important in math. A problem which has defeated mathematicians for almost 140 years has now been solved. Practice your Addition, Subtraction, Mutliplication and Division - self-marking Online exercises and worksheets with answers, you create and print from your browser. They have fun doing the math number tricks, but at the same time they are getting better at doing the math. We are more than happy to answer any math specific question you may have about this problem. Although most math problems have only one answer, there may be many ways to get to that answer. Problems Based on Ages Shortcut Tricks. d) From past figures, it is predicted that 39% of the registered voters in California will vote in the June. Here’s an idea for using LEGO® for a pre-multiplication activity. How old will he be when I'm 100? - Slader. Maths Puzzles On Age #1 - Tough Age Problem issabella was only one-fourth the age of sophie at that time. If this is what you were looking for, please contact support. Math Worksheets Center The largest printable K-12 math collection! Complete math explanations and lessons! We give instructions on all core K-12 math skills. Gresham is using Making Math Meaningful for 2nd grade math. how much younger is the new member I don't understand Follows • 3. The answer key identifies the correct answer, the score reporting category represented, and the code of the content standard to which the item aligns. Luckily for parents and teachers, there are plenty of websites that provide math problems for extra math practice. com, the best site on the Internet for free, online math games, logic puzzles and brain teasers. In 20 years the father will be twice as old as his son. Learn second grade math online for free. Explain the reasoning which helped you develop your equation. For this topic, you will need to know how to create equations with variables and solve for variables. 50 Math Riddles for Kids With Answers Tuesday August 28, 2018 Being mentally active is equally important as being physically active for a kid's well being and riddles are one of the funniest ways of exercising their brains. Write an equation that models how old in years each of you will be, when your ages add up to 150 years old. Age and mixture problems are tricky questions in Algebra. For the most part, it has become standard among most math teachers to give about eight problems a night; but I have even had a teacher who gave ten | though two problems may not seem like a big deal, it can be. Solved examples with detailed answer description, explanation are given and it would be easy to understand.