Math Cross Numbers Solver

Math Zone combines logic and numbers with fun and challenging math games for kids online. Cross number puzzles use digits rather than words. Welcome to the fractions worksheets page at Math-Drills. Designed for algebra I. Introduction to the cross product. Home Calculators Mobile Apps Math Courses Math Games. Enter a number below. Guidelines to follow when using the proportion calculator Each table has two boxes. Math Puzzles - Numbers Level 2. "The American Mathematics Competitions are the contests that the students strive to take every year. These puzzles are designed in the same way as a traditional crossword but using numbers instead of words. Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. Home | About We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result. Cross multiplying is the other method of finding the unknown number in a proportion. Typically, A-1 is calculated as a separate exercize; otherwise, we must pause here to calculate A-1. Already have an individual account with Creative Coding?. I hope this is what you are looking for!. A fraction with a zero denominator is undefined. It is a challenging Math Cross Numbers Puzzle to improve memory, concentration and logical thinking skills. Real and imaginary components, phase angles. Enter a matrix, and this calculator will show you step-by-step how to convert that matrix into reduced row echelon form using Gauss-Jordan Elmination. Creates a series of calculations that can be printed, bookmarked, shared and modified. Instructions:: All Functions. If you are having a problem with math, Sobtell has the best math experts which can help with everything math class throws at you. Numbers Game Solver This is a perfect solver for the Numbers Game. Solve this by cross multiplication method- 2(ax- by)+ a+ 4b = 0 2(bx+ay) + b - 4a = 0 For what values of a the following pair of equation 4x+3y=3 and 8x+ay=5 will have a unique solution Without drawing graph, check whether the lines 3x + y = 10 and 6x - 2y = 20 are parallel or not. Complex Numbers and Geometry. This video shows students how to solve 2-step Algebra equations involving one addition or subtraction and one. Math Cross Number. Emily Guerin (2004-06-18; e-mail) The Equal Sign Who was the first person to use the modern equal sign? A very elongated form of the modern equality symbol (=) was introduced in print in The Whetstone of Witte (1557) by Robert Recorde (1510-1558) the man who first introduced algebra into England. They are fairly easy to solve and can become quite addictive. The calculators and solvers below do more than just calculate the answer. In many cases, just remember the connection between percents and fractions and you’re halfway home: Solve simple percent problems Some percents are easy to figure. Enter the number of cells that will be blank The more blank cells, the more difficult the puzzle. 3 Problem 8E. A perfect 10, but purely imaginary. Solve linear or quadratic inequalities with our free step-by-step algebra calculator. They lied for him, they enabled him, they subverted the law and the constitution and now they have no choice but to go down with the ship. Punchline Math is a series of books, worksheets and interactive DVDs created by Steve and Janis Marcy. Dig deeper into specific steps Our solver does what a calculator won't: breaking down key steps into smaller sub-steps to show you every part of the solution. All Operations Crossnumber Math Puzzle Worksheet About This Worksheet: There are 4 versions that test all the different operations. The ''U'' shaped graph of a quadratic is called a parabola. How do I create a matrix from a file from Learn more about matlab MATLAB. I am not sure what a cross sum is, and have been unable to find resources on it. com! Use the given numbers and operation symbols to make the target value. Introducing cross number puzzles to 5th grade students who have not had Think Math! before. On occasion, a puzzle will be generated which reveals equations that are solvable by more than one combination of numbers. BYJU'S online cross multiplication calculator tool makes calculations faster and easier. Enter simple fractions with slash (/). Math Cross Number. Learn math the fun way with our free educational games! With animation, music, and lots of fun- kids can enjoy practicing math and increase their math skills and math memory. Cross-Number Puzzle. Study each case carefully before you start looking at the worked examples below. The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. General Math. Teachers are encouraged to not only use these tasks with their students, but also to endeavor to implement them with fidelity by utilizing the. Each clue is a sum, and the result should be entered into the matching squares on the numbered grid. You have to find the numbers that make all of the equations valid. It is a useful technique. Math Crush: Is constantly updating and improving its material. Because the multiplication and division algorithms are built on the logic of the cross number puzzles, students who are seeing them for the first time in grade 5 should be given the chance to understand the logic. Designed for algebra I. Students, teachers, parents, and everyone can find solutions to their math problems instantly. Your math book might say it is a comparison of two numbers or quantities. Solve the addition problems below. If you're just starting out, selecting "pencilmarks" and/or "validity" might make things easier, and if you get stuck you can ask for a hint, or even a full solution. Please enter a number: Prime numbers are positive, non. Yesterday afternoon I met professor Halfbrain at an art gallery. I liked them and began to construct such puzzles on my XT computer, mostly for myself to solve. For permissions beyond the scope of this license, please contact us. Each math worksheet is accompanied by an answer key, is printable, and can be customized to fit your needs. Answers provided. Polar to Rectangular Online Calculator. Square of the sum of the digits of b down. Write, read, and evaluate expressions in which letters or symbols stand for numbers. Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. To give everyone an idea, here are some examples of Common Core math problems. The sum of any real number and zero which is equal to the given real number. How to Use the Cross Multiplication Calculator?. tips and tricks to solving these puzzles. Use these free math worksheets for teaching, reinforcement, and review. Play Calculator Chaos at MathPlayground. The thick heavy line is a separator. If ever you need assistance on rational functions or even inequalities, Factoring-polynomials. Free Math Apps These apps are based on the visual models featured in Bridges in Mathematics. Get the free "3x3 Determinant calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. The number of hours and minutes between the two selected times will appear. You can't actually solve 2 equations with 3 variables to obtain the values. Step 2: Place numbers in the circles such that the product of the circles is the quadratic term. Guidelines to follow when using the proportion calculator Each table has two boxes. Daily Sudoku. 618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. If you want to solve an algebraic expression that uses fractions, then you have to cross multiply the fractions, combine like terms, and then isolate the variable. It doesn't need to be that difficult! Our math books are for all study levels. The standards call for learning mathematical content in the context of real-world situations, using mathematics to solve problems, and developing “habits of mind” that foster mastery of mathematics content as well as mathematical understanding. The cross product is the product of the numerator of one of the ratios and the denominator of the second ratio. Solve the number puzzles drawn on the pavement of Trafalgar Square in London. Cubed numbers are expressed with a little three at the top right of the number. com free math solvers! We know math is hard, and we are here to help. Most of the time they're actually pretty cool, and require you to think differently to solve them. doc, 34 KB. Based on the original concept by John Gowland. equations where the unknown variable is found in the denominator. only one ten, cross off the If there is ones I 12 - 4: 15 - tens and tens and ones ones ones tens and 14 + 5 tens and ones _ 8: ones 13+5: tens and tens and EUREKA MATH Lesson 27: Solve addition and subtraction problems decomposing and composing teen numbers as 1 ten and some. Golden Ratio, Phi, 1. Letter Worksheets : Kindergarten Printouts Compound Words With Pictures Worksheets Printable Practice Number Algebra Homework Answers Hindi For Pdf Kids Worksheet Essentials Dummies Confusing In English. Your math book might say it is a comparison of two numbers or quantities. This page will show you how to multiply polynomials together. When I had eighty puzzles saved, I printed them in pocket-book format and even sold three copies on Amazon. Wikipedia – Normalization… Captain Calculator >> Math Calculators Math Calculators >> Statistics Calculators. They will generally have two solutions; that is, two different values of x that make the equation true. Click for this puzzle's answer key. These math word problems are most appropriate for grades four and five, but many are designed to be challenging and informative to older and more advanced students as well. SolveMyMath - Your math help website. Complex Number Calculator. How do I create a matrix from a file from Learn more about matlab MATLAB. Answers For Drops In The Bucket Math Level E Number 9. Here at FreedomWorks, we often hear from parents who are fed up with the math homework that their children are bringing home. The tool displays the unknown value in a fraction of seconds. You multiply each numerator with the other number’s denominator. 3i · 4i = 12i 2 = 12(−1) = −12. The cross-number puzzle replaces the words in a crossword with numeric digits, and math equations replace the the word hints. Get Gina Wilson All Things Algebra 2016 Answers PDF Download and save both time and money by visit our website, available in formats PDF, Kindle, ePub, iTunes and Mobi also. It can factor an expressions with polynomials involving any number of variables as well as more complex function. Cross-multiplication is a shortcut, an easily understandable procedure that can be taught to students. Please be courteous. Need the word cross answers for all levels. Learn Numbers at PrimaryGames This is a number learning game for preschoolers. For instance, the fraction 4/5 would look like this: Later on, the system was used by the Arabs while trading with the Indians. They either determine the missing values or find the number that does not belong in a group. To get started, add some formulas, fill in any input variables and press "Solve. Can solve Sudokus, but also many other number puzzles. What better way to learn. This algebra math solver section involves all calculators related to algebraic. A:The answer 1 is a positive number. For instance, the fraction 4/5 would look like this: Later on, the system was used by the Arabs while trading with the Indians. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. So we can find information about the number of real zeroes of a polynomial by looking at the graph and, conversely, we can tell how many times the graph is going to touch or cross the x-axis by looking at the zeroes of the polynomial (or at the factored form of. Annie and Ben are playing. Logical Puzzles Questions and Answers. Follow the right path with this number puzzle game. Plots & Geometry. The complex number i is purely algebraic. Returns the remainder left over after you've divided the left number into a number of integer portions equal to the right number. The Cross Multiplication Calculator is a free online tool that displays the unknown value in the given fraction. You can't actually solve 2 equations with 3 variables to obtain the values. Three ways to solve proportions Finding the missing value in a proportion is much like finding the missing value for two equal fractions. See below the step-by-step solution on how to find equivalent fractions. com is certainly the ideal place to check out!. BrainPOP's math movies cover all sorts of calculations and computations: Tim and Moby talk you through algebra, probability, geometry, and even data analysis!. This is the updated version. This online publication cross disciplinary skills answers integrating mathematics can be one of the options to accompany you subsequent to having other time. That is, we call it a "number" because it will obey all the rules we normally associate with a number. What is the number? 18) How many quarters are there in 25% of 2? 19) Jules, Nadia and Steff saved $50 altogether. one more than a number questions answers "Slow" - Write algebraic Expressions 49 problems in writing simple algebraic expressions. Plus each one comes with an answer key. Mathematics Instructional Plan – Grade 7 Solve Problems Involving Operations with Rational Numbers Strand: Computation and Estimation Topic: Solve practical problems involving operations with rational numbers. This video shows students how to solve 2-step Algebra equations involving one addition or subtraction and one. Cross multiplying is the other method of finding the unknown number in a proportion. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. It was first Introduced in. Balanced Magic Square If weights of the same amount are substituted for the numbers of each square, the balance point will be at the exact center of each square. The first abstraction, which is shared by many animals, was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members. Use of Cross Product Calculator. It was the Arabs who drew a line to distinguish the top number from the lower number in the fraction. Online math calculators and solvers to help calculate and solve problems are included in this site. Trigonometry. Teachers can also incorporate fractions into the math puzzles. The sum of digits of a across. All Functions Operators +. Just a little side note. All apps are available in two or more versions: a web app for all modern browsers, and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad). Not as complete as the previous book, but enough for most students. A History of God's Number. Learn more about the EM curriculum and how to assist your child. Interesting Worksheets For Kindergarten. Basic puzzles use the mathematical operations subtraction, addition, multiplication, and division. With a huge collection of educational maths, visit Funbrain here. Download free on iTunes. In this video the tutor shows how to solve the missing ratios or proportions. More infomation. Three of the professors in the department have recently been named fellows of prestigious mathematical organizations. speed/distance or cost/amount problems). Solve for an unknown value x with this fractions calculator. Algebra Four: Students play a generalized version of connect four, gaining the chance to place a piece on the board by solving an algebraic equation. The cross product is the product of the numerator of one of the ratios and the denominator of the second ratio. Download free on Amazon. College Math Multiple Choice Questions and Answers pdf is a revision guide with a collection of trivia questions to fun quiz questions and answers pdf on topics: Application of basic identities, double angle identities, functions and limits, fundamentals of trigonometry, matrices and determinants, number system, partial fractions, permutations. Whenever possible, these calculator illustrate the steps and explain how certain math formulas, unit conversions and calculations are performed whether you are trying to reduce a square root to its simplest radical form, find the prime factorization of a number , use the quadratic formula or are interested in unit. Forgot Password Log in with Clever. Enter a number below. The speed of the train for the first part of the journey was 40 miles per hour while the speed for the second part of the journey was 50 miles per h. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. QuickMath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices. How many different answers can you get? Now take one number from the other. Practice math the fun way, on your mobile phone or tablet like iPad, iPhone, or Android. They have specific rules, but they do not usually involve competition between two or more players. These math word problems are most appropriate for grades four and five, but many are designed to be challenging and informative to older and more advanced students as well. boise, idaho 83702. Solve the following proportions and then check the solution in the original statement. Oh no! The calculator is broken. Therefore, each table represents a ratio. The tool displays the unknown value in a fraction of seconds. Using the Proportion Method to Solve Percent Problems There are a variety of ways to solve percent problems, many of which can be VERY confusing. Thanks to its literal computing capabilities, the calculator can easily simplify this fraction. Enjoy these free printable sheets focusing on the complex and imaginary numbers, typically covered unit in Algebra 2. Simplify complex numbers. Each worksheet has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. Snap a pic of your math problem With our mobile app, you can take a photo of your equation and get started, stat. Math allows us to isolate one or a few features such as the number, shape or direction of some kind of object. One source with over 100 articles and latest findings. This lesson plan has a number of fun worksheets for a pre-algebra or beginning algebra class. Translate and Solve Basic Percent Equations. How to Use the Calculator. 194 This work is derived from Eureka Math ™ and licensed by Great Minds. Anthony Fauci answers. Three of the professors in the department have recently been named fellows of prestigious mathematical organizations. This can be frustrating at times. However, they did not place a line in between it. You can use them to create complex numbers such as 2i+5. Explore the connections between mathematics and music in the videos, podcasts, and articles below. What is the number? 18) How many quarters are there in 25% of 2? 19) Jules, Nadia and Steff saved $50 altogether. To factor integer numbers please use number factorizer. Given two equivalent ratios, you can solve for the missing value using cross multiplication to convert the proportion into a equation and then solve for the variable. Draggable Multiplication Solve multiplication problems using this interactive work mat. Enter simple fractions with slash (/). Typically, A-1 is calculated as a separate exercize; otherwise, we must pause here to calculate A-1. Learn more about the EM curriculum and how to assist your child. If you're behind a web filter, please make sure that the domains *. Explore the Science of Everyday Life. Skip to main content. Steps for Using the Substitution Method in order to Solve Systems of Equations. To show x on the number line, you need to show every number whose absolute value is greater than 2. Snap a pic of your math problem With our mobile app, you can take a photo of your equation and get started, stat. If you're behind a web filter, please make sure that the domains *. Math Antics has a brand new look!. Because the multiplication and division algorithms are built on the logic of the cross number puzzles, students who are seeing them for the first time in grade 5 should be given the chance to understand the logic. 2 The student will solve practical problems involving operations with rational numbers. Cross number puzzles use digits rather than words. The second digit is the number of ones in the number, etc. Producing a single matrix by multiplying pair of matrices (may be 2D / 3D) is called as matrix multiplication which is the binary operation in mathematics. You interrogate, ask related questions, cross-check the answers,” Vidick said. Exponents. Murder by Numbers blends police procedural and Picross puzzling, a unique combination that will keep you solving crimes far longer than intended. The puzzle can be missing three equations (considered normal difficulty), fewer than three, or more. We may add it, subtract it, multiply it, and so on. com ; how to plug in the forumla of line equation ; linear algebra and its applications solutions lay ; READBLUECOLEDGE ; google math solver ; Glencoe Algebra 1 Answers Key ; find equation of the line ; 7 ; college algebra cliff notes ; myalgerbrasolver. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. Algebraic Fractions. com is an online resource used every day by thousands of teachers, students and parents. Learn math the fun way with our free educational games! With animation, music, and lots of fun- kids can enjoy practicing math and increase their math skills and math memory. But there's a catch — the middle pentagon is missing a number in the bottom right corner. Enter mixed numbers with space. com is certainly the ideal place to check out!. This Equivalent Fractions Calculator will show you, step-by-step, equivalent fractions to any fraction you input. Mathematics Help. A simplified and updated version of the classic Schaum's Outline. Author: Created by mrvman. WorksheetWorks. the calculator home page. The cross product occurs in many formulas in physics. Be sure to enter something in each input box before clicking solve. Explore the connections between mathematics and music in the videos, podcasts, and articles below. Enter the size of your number block Your number block can be as small as 3 x 3 or as large as 10 x 10. All Operations Crossnumber Math Puzzle Worksheet About This Worksheet: There are 4 versions that test all the different operations. " Roots, Exponents and Logarithms. It took fifteen years after the introduction of the Cube to find the first position that provably requires twenty moves to solve; it is appropriate that fifteen years after that, we prove that twenty moves suffice for all positions. Clock Math Calculator. The Lucas numbers are formed in the same way as the Fibonacci numbers - by adding the latest two to get the next, but instead of starting at 0 and 1 [Fibonacci numbers] the Lucas number series starts with 2 and 1. It was the Arabs who drew a line to distinguish the top number from the lower number in the fraction. The more you do, the better your math skills become. We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. Type your algebra problem into the text box. Make sense of problems and persevere in solving them. Most of the questions were chosen with enthusiastic, bright early teenagers in mind. The books introduce self-correcting puzzles to students, who must figure out how to solve the. 12 Number Grid Puzzles. Our CrossMath puzzles come in 2 grid sizes and 3 difficulty levels. Every Sudoku has a unique solution that can be reached logically. Solve your tough Mathematical equations, problems with this simple tool not only for the sake of doing your Maths homework but also to cross check your. Because the multiplication and division algorithms are built on the logic of the cross number puzzles, students who are seeing them for the first time in grade 5 should be given the chance to understand the logic. eureka math. Enter the size of your number block Your number block can be as small as 3 x 3 or as large as 10 x 10. An improper fraction is a fraction where the numerator (top number is greater than or equal to the denominator (bottom number). equations where the unknown variable is found in the denominator. The complex number i turns out to be extremely useful in mathematics and physics. Cool Math has free online cool math lessons, cool math games and fun math activities. When performing an operation on three or more numbers, the result is unchanged by the way the numbers are grouped. Substitution - Evaluate the expressions by substituting numbers for letters. Jules saved ¾ as much as Nadia. The complex number i is purely algebraic. Read CSV with row in quotes (string and numbers). When complete click the Answer to see if all is correct. Step 2: Place numbers in the circles such that the product of the circles is the quadratic term. Multiplication Step-by-Step Exercise. boise, idaho 83702. This article is intended for those who have trouble solving math-related word problems. BrainPOP's math movies cover all sorts of calculations and computations: Tim and Moby talk you through algebra, probability, geometry, and even data analysis!. Dig deeper into specific steps Our solver does what a calculator won’t: breaking down key steps into smaller sub-steps to show you every part of the solution. These puzzles are designed in the same way as a traditional crossword but using numbers instead of words. Snap a pic of your math problem With our mobile app, you can take a photo of your equation and get started, stat. Students enrolled in ONLINE SECTIONS of Math 1310, 1313, 1314, 1330, 1431, 1432, 2311, 2331, 2433, 3321 and 3339 can access course information here. BYJU'S online cross multiplication calculator tool makes calculations faster and easier. The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. This free area calculator determines the area of a number of common shapes using both metric units and US customary units of length, including rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Poem about algebra, solve factoring calculator, pictograph, factorise equation worksheet, 5th grade math problems with bloom's taxonomy, mathematics trivia. Learn all the major algebraic properties and find plenty of example problems. Lesson NYS COMMON CORE MATHEMATICS CURRICULUM 20 K Lesson 20: Solve take from with result unknown expressions and equations using the minus sign with no unknown. com is the ideal site to pay a visit to!. You can't actually solve 2 equations with 3 variables to obtain the values. ) to find a missing number in a proportion. Cross-products can also be used to solve proportions when one of the numbers is unknown: 5 n ---- = ---- What is n? 20 48 We know from what we have learned above that 5 x 48 must equal 20 x n: 20 x n = 5 x 48 20 x n = 240 If you don't know how to solve for n yet, you can think: what number multiplied by 20 gives me 240?. Multiplying fractions calculator. IXL offers hundreds of Algebra 2 skills to explore and learn!. It was the Arabs who drew a line to distinguish the top number from the lower number in the fraction. Maths Puzzles Collection of Best Maths Puzzles. How to Solve an Algebraic Expression. Centre Number Candidate Number Surname Other Names Candidate Signature GCSE Mathematics (Non-calculator Paper) 10 Practice Paper Style Questions – Topic: Algebra (Foundation Tier) For this paper you must have: black pen HB pencil ruler (with cm & mm) rubber protractor compass pencil sharpener. On occasion, a puzzle will be generated which reveals equations that are solvable by more than one combination of numbers. Also, you might find a math tutor online, or through local. The tool displays the unknown value in a fraction of seconds. However, they did not place a line in between it. Use logic to solve visual, interactive mathematical puzzles. Math Riddles. The Find a Pattern strategy can be used to solve many math problems and can be used in combination with many other strategies, including make a table, make a list, or simplify the problem. Introduction to the cross product. SOLVING LOGARITHMIC EQUATIONS. Cross Number Puzzles: Arithmetic to algebra. The number of successes in the sample is 7 (since there are 7 black cards in the sample that we select). Designed for algebra I. You can use them to create complex numbers such as 2i+5. Enter one digit per square. Also, explore the surface area or volume calculators, as well as hundreds of other math, finance, fitness, and health calculators. Basic Math. The number of hours and minutes between the two selected times will appear. Mathematics Help. Interactive solvers for algebra word problems. If a word is not familiar to you, look it up in a dictionary. Complex Numbers and Geometry. When you graph on the number line, an open dot indicates that the number is not part of the graph. Home | About We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result. Math Triangles add 3 single-digit numbers with totals 9, 10, 11 and 12. Ratios often look like fractions, but they are read differently. Click any of the examples below to see the algebra solver in action. only one ten, cross off the If there is ones I 12 - 4: 15 - tens and tens and ones ones ones tens and 14 + 5 tens and ones _ 8: ones 13+5: tens and tens and EUREKA MATH Lesson 27: Solve addition and subtraction problems decomposing and composing teen numbers as 1 ten and some. This Decimals Worksheet may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. The complex number i turns out to be extremely useful in mathematics and physics. The next time you hear or play classical, rock, folk, religious, ceremonial, jazz, opera, pop, or contemporary types of music, think of what mathematics and music have in common and how mathematics is used to create the music you enjoy. No need to even type your math problem. This is a perfect solver for the Numbers Game. Left to Right. Mathematics is the study of order, structure, and relation that evolved from measuring, counting and describing the shapes of objects. The first abstraction, which is shared by many animals, was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members. com is the ideal site to pay a visit to!. 2020 Distinguished Lecture Series - March 3 & 5, 2020 Fri Feb 14. Mixed Numbers Calculator (also referred to as Mixed Fractions):.