Fig. What are the disadvantages of shielding a thermometer? Try refreshing the page, or contact customer support. 2 2 2. less than five times . How old were you seven years ago? An algebraic equation is next after knowing how to put variables, numbers, and operators together. n n n. 2. the sum of five times . endobj Antonette Dela Cruz is a veteran teacher of Mathematics with 25 years of teaching experience. 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Now, Let a number . English or Word phrase Algebraic expression/equation 8 more than 4 times a number ____ B. Plus, get practice tests, quizzes, and personalized coaching to help you Solution. more than means addition and a number means x, so this is the same as 5 + x or x + 5 ; A number less than 7 . Yes. Explain mathematic problems Mathematical problems can be difficult to understand, but with a little explanation they can be easy to solve. "5 more Which of the following best describes the algebraic expression 3(x - 5)? We can use x to represent the number of shirts. -5, Write an algebraic expression for the verbal expression. - Definition & Examples, How to Simplify Expressions with Exponents, Simplifying Expressions with Rational Exponents, Expanding & Simplifying Algebraic Expressions, Translating an Addition Statement into an Algebraic Expression, Roots and Powers of Algebraic Expressions, Translating a Division Statement into an Algebraic Expression, Simplifying Radical Expressions with Variables, Working Scholars Bringing Tuition-Free College to the Community, more than means addition and a number means x, so this is the same as 5 + x or x + 5. less than means subtraction, and a number means x, so the algebraic expression for this is 7-x. What age is eight more years than your age now? Please visit calstate.edu for more details. Polynomial Expression endobj What are the disadvantages of a clapper bridge? Striker is the manager of Treasures Collection, a boutique shop selling high-end merchandise. When two algebraic expressions are separated by the equal sign in the middle, algebraic equations are formed. Practice your math skills and learn step Jenny earns $30 a day working part time at a supermarket. 7x. Using mathematical verbs and nouns, any phrase can be written as an algebraic expression. 3 times the difference of a number and 2 ____ D. 2d 3 The need to put the situation into statements becomes a challenge. WebAlgebra 2020-2021. Tom the cat is brushing up his Math skills, Three grasshoppers play leapfrog along a line, The gardener's problem on a miracle tree in an enchanted garden, Water level rise in a tank after submerging bodies, Finding the value of infinite continued fraction, Solving minimax problems by the Linear Programming method, One unusual mimimax problem on joint work, More complicated but still elementary logic problems, OVERVIEW of lessons on Miscellaneous word problems. Single variable expressions use one variable, while multi-variable expressions have more than one variable present in a mathematical statement. You could also write that as 11 plus a. From there, we The English phrase above can be translated (written in another language) into an algebraic expression. O--Kd0# F0V1>0fM`d#P)mcz#P)@0@jl8@H;ppjq-)>s9eAp8HVT'u!I6mKtjJ-V%?1[j Solution: 5 times multiplication the sum addition N of a number and 11 We must be careful to show that 5 multiplies the sum of a number and 11. 16 + 5xd. Unless specified, this website is not in any way affiliated with any of the institutions featured. The multiplication between c and 9/5 occurs first and then 32 is added to the result. WebSo, the verbal expression twelve less than the product of three and a number can be written as the algebraic expression 3n - 12. As one gets more familiar with the symbols, terms, and meanings, the math language becomes easy to understand and write. The number of strawberry cookies is five more than four times the number of chocolate cookies. What age is eight more years than your age now? copyright 2003-2023 Study.com. Subjects Two less than two times a number. Adding 7 to both sides gives 612x . in or register, 3x + 7. It's definitely better to have more written down than less. n n n. Show Solution. Part B ; We have, So, According We can describe patterns using phrases as well, and we want to be able to translate these phrases into algebraic expressions. 8 less than 3c.Translate "8 less than 3c" into algebra. Which of the following expressions represents four less than the cube of a number? What do you think an equivalent algebraic expression would be? The cost for paying x number of pens at $3 each, y number of erasers at $0.50 each, and z number of notebooks at $8 each. HOW TO algebreze and solve these problems? stream A 2. Write an algebraic expression for each verbal expression. She has a bachelors degree in Chemical Engineering (cum laude) and a graduate degree in Business Administration (magna cum laude) from the University of the Philippines. \(\begin{array}{}\\ \text{the quotient of}\phantom{\rule{0.2em}{0ex}}10x\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}3\hfill \\ \text{divide}\phantom{\rule{0.2em}{0ex}}10x\phantom{\rule{0.2em}{0ex}}\text{by}\phantom{\rule{0.2em}{0ex}}3\hfill \\ 10x3\hfill \end{array}\), This can also be written as \(\begin{array}{l}10x/3\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.4em}{0ex}}\frac{10x}{3}\hfill \end{array}\). -.>P)dq^UFHj}Yo -f-;ojYGuWx|`TD;UaoPD$T6`W3D_jkW6%=a~ay VbB Read the problem carefully. The phrase less than is subtraction, times is multiplication and a number is a variable. 1. WebExample 5: Write an algebraic expression for the math phrase the product of 5 and a number. 3 0 obj )6sPU5ABk)h8 ^+9h#S#O= VjZy:Z"'&h~|}7\.0Hw[.X#V=JLpUeK%Z; K_o G`w=yV(7X;Rxz(TAt}>^T/Z. /O+_GR7a8>{r -lJyeozIdGq`NV7=EAmhu1.Z4,aztrm`E*tY+ss!&uhQ`#C0{Fm"fy[NtZ\@ Hdx_'ffof,ry0.2-"K Solution: To find the product of two quantities or values means that we will more than times a number. Here we are taking the sum of five times \(m\) and \(n.\), \(\begin{array}{}\\ \phantom{\rule{4em}{0ex}}5m+n\hfill \end{array}\). WebThen the following equation can represent this problem: 17 + x = 68 We can subtract 17 from both sides of the equation to find the value of x. In words, the relationship can be stated as The money taken in dollars is (equals) twenty-eight times the number of people who enter the park.. Variable in Math Uses & Examples | What is a Variable? Effect of PH on enzymes Therefore, e WebFifteen less than twice a number: 2x - 15: 2. The whole pizza costs $24 with n slices. 3n + 16

3(16) + n

alternatives WebA number added to 5 5 + x A number increased by 13 x + 13 5 less than 10 10 - 5 A number decreased by 7 x - 7 Difference between x and 3 x - 3 Difference between 3 and x 3 - x Twice a number 2x Ten percent of x 0.10x Ten times x 10x Quotient of x and 3 x/3 Quotient of 3 and x 3/x Five is three more than a number 5 = x + 3 The product of 2 Let \(q\) represent the number of quarters. Practice Simplifying Algebraic Expressions, How to Solve a System of Linear Equations in Two Variables, How to Solve a System of Equations by Substitution, Graphing Systems of Equations | Overview, Process & Examples, Writing Equations with Inequalities: Open Sentences and True/False Statements, Finding the Absolute Value of a Real Number, Practice Problems for Calculating Ratios and Proportions, How to Solve Word Problems That Use Percents, Life Expectancy and Life Span: Definition & Factors. In the world of mathematics, we express our language based on algebraic expressions. Scan and study your notes with the Five Star App. <> The math language isn't that hard to learn after all! <> WebThis calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them Assuming the number is n, then the expression is: Continue Learning about Math & Arithmetic. In the problem above, x is a variable. Answer provided by our tutors Let the number be x. Use m for the variable for May's age. 3 x 3. Write the algebraic equation for this statement. This is seven years less than your age now. What are the disadvantages of shielding a thermometer? DRAFT. Write an expression for the cost and an expression for the revenue (money earned). 2 Math operators used for algebraic expressions (created by Geogebra). For the revenue, we have $15 times the number of shirts sold, or 15x. The sum of 7 and three times x. D(6F!=Dq9ID"EAp8KN~89{)i<>}B*VwG% qHFZr/?~wj]?ih ! Translating Algebraic Expressions. Translate each word phrase into an algebraic expression: The key word is difference, which tells us the operation is subtraction. Which the least. We're sorry, but in order to log in and use all the features of this website, you will need to enable JavaScript in your browser. Robert has a PhD in Applied Mathematics. Note that for "less than" the number before the phrase will be subtracted from the number after it. Determine which classes require the most listening? 147 lessons \(\begin{array}{}\\ \text{the difference}\phantom{\rule{0.2em}{0ex}}\text{of}\phantom{\rule{0.2em}{0ex}}20\phantom{\rule{0.2em}{0ex}}and\phantom{\rule{0.2em}{0ex}}4\hfill \\ 20\phantom{\rule{0.2em}{0ex}}\text{minus}\phantom{\rule{0.2em}{0ex}}4\hfill \\ 20-4\hfill \end{array}\). Some phrases are harder to translate than others. The SUM of a number AND -3 is written as: (x + ( 3)), or (x 3) (where we have chosen the number to be x .) Example 4: Find the sum of the infinite geometric sequence 27, 18, 12, 8, . WebAlgebraic Equation: Twice a number, decreased by twenty-nine, is seven. Sometimes in math, we describe an expression This interview may include unfamiliar references. Making the two sides of the equation equal is necessary. For Free. times the number of mountains.Substitute c for the number of mountains Angela hiked.8 less than 3 times c.Translate "3 times c" into algebra. What is an algebraic expression? A rule can be written to describe the relationship between the amount of money taken at the ticket booth and the number of people entering the park. In algebraic expressions, the interactions of letters and numbers are put together by operators. Eight times a number increased by eleven is thirty-seven.Aug 25, 2016 5 (x 3) Explanation: The word "SUM" means the answer to an "ADDITION". Alg 1: 2021 - 2022. Question ID: 144907, 144916, 144917, 144918,146542,146541 . In exercises 16 24, write an English phrase for each algebraic expression. 5x 16b. - [Voiceover] Let's do some examples of the writing expressions with variables exercise. How do you write the algebraic expression: 8 less than a number x'? Find the total cost incurred by each student for their one hamburger and one soda. Answer Homework: UNIT 8 Score: 0 1 pt 4.3.RA-5 Division 4.3 Homework 501 S (4 full) HW Score: workbook answer key unit 8, signing naturally unit 4 homework answers key pdf may not make exciting reading but signing naturally unit 4 homework answers key is packed with valuable instructions information and warnings we also have Jeremy read that degrees Celsius converted to degrees Fahrenheit is "the sum of 32 and 9/5 times the temperature in degrees Celsius." | 7 B : J invite Catherine au cinema . Well need to be clear about what the expression will represent. <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 8 0 obj Register or login to make commenting easier. x69dn%FpJ)")&,O?_p The word "less" lets you know that you are going to take away, or subtract, a number. The unit cost represents the quotient of the total cost and number of items purchased. PLIX: Play, Learn, Interact, eXplore: Mathematical Operators, Video: Introduction to Variables and Variable Expressions, Activities: Patterns and Expressions Discussion Questions, Practice: Translate Between English Phrases and Algebraic Expressions. If Striker's hourly rate is double the combined salary of his two shop assistants, Macy and Grey, how much does Striker earn in terms of Macy and Grey's wages? % All other trademarks and copyrights are the property of their respective owners. The number is 25 Assuming the number is n, then the expression is: 5n - 3. : The symbol An algebraic expression is a combination of letters, numbers, and operators such as addition, subtraction, multiplication, division, and raised to exponents. I feel like its a lifeline. Does your answer make sense? Write an expression for the number of dimes. \(\begin{array}{l}\text{Eight more than}\phantom{\rule{0.2em}{0ex}}y\\ \text{Eight added to}\phantom{\rule{0.2em}{0ex}}y\\ y+8\end{array}\). 9 0 obj Each of us has a proper comprehension of the information supplied to the general public, so I truly enjoyed the article and expected you to supply us with more things like this one. Earlier, you were asked told that the degrees Fahrenheit temperature is "the sum of 32 and 9/5 times the temperature in degrees Celsius". 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Webthe product of the square of a number and 8 $16:(5 8x2 fifteen less than the cube of a number $16:(5 x 3 15 five more than the quotient of a number and 4 $16:(5 Write a verbal sentence to represent each equation. Future Warriors Boys Basketball. Let's write an algebraic expression for the each of the following phrases: status page at https://status.libretexts.org, The symbol means "therefore" or "because of this.". I would definitely recommend Study.com to my colleagues. Best Answer. Your browser seems to have Javascript disabled. Whatever n is, we subtract 10 from it to get that expression. d%O%-{T>["mTJX4 2I)4Sg>ws% RmLYc&cEJufM%w=K?+ }D=+f4>4,Y>=WL h'G'h'AN6N#:c~48h7T(e4lQ5[H[C&Ytoh. c3C]s%4 .R^|)F`Jx:\/e(]Fm6WmlEW.8Ou}IANig'T.7kkfa;KiLo!u^'^N$:z2;mzRB^1MO2]bBnv|>H)=Y8grHXU>QKXkHK>j3Zhd/hoh-,-%ZxZ/.y$0RDfr&+}^%1JdrdrW3%Z=*58 E4P Six times more than the quantity of a number plus one. Word Problems: Miscellaneous Word Problems, Over 600 Algebra Word Problems at edhelper.com, Problem on two-wheel and three-wheel bicycles, Word problems on reversing digits of numbers, Counting elements in sub-sets of a given finite set. Numbers 1 - 10, One to Ten, Count and Write Worksheets por lampt2509: Place Value por MsKnowly: Mixed Times Table por QKidz: Numbers from 100 - 1000 por RebeccaJcqs: Adding and subtracting through 20 por LeonorLopez: Let's Count. 16 5xOption 45. = Tmmcm7x%7?XFZ6,A@>5rkj"*` e /*0IY*{Rx3h-6@+66iOs%FKJ Z*6h)2QBKrAKN1vFVd3:#+fw2@y3 \(\overset{\underset{\mathrm{def}}{}}{=} \), Evaluate, Simplify, and Translate Expressions, \(\begin{array}{l}10x/3\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.4em}{0ex}}\frac{10x}{3}\hfill \end{array}\). The ELM and EPT exams are no longer being offered. x=25. 2n - 2. Write an expression for the height of the window. "5 less than" means minus 5 and not 5 minus, Relationships: Associations between Real-World Quantities, Algebraic Expressions: Using variables and algebraic operations (addition, subtraction, multiplication, division) to express relationships. Look for the words of and and to find the numbers. It is defined as a mathematical statement equating an algebraic expression to another. E) 5 times the sum of a number and 11. Create your account. 5x=125. 7 0 obj *1 pointa. Definition: Mathematical Expression. Examples of monomial expressions include 3x 4, 3xy, 3x, 8y, etc. An error occurred trying to load this video. From there, we The most common variables are a, b, x, y, m, and n. The vertical axis is also referred to as the y-axis of a coordinate graph. Let \(w\) represent the width of the window. Upvote 0 Downvote. RZ All names, acronyms, logos and trademarks displayed on this website are those of their respective owners. Addition & subtraction c. Multiplication & subtraction 8) True/False - in a two-step equation you should take care of multiplication and divisionStep 3: Write an equation: Step 4: Solve the equation: Step 5: Re-read the question. The height of a rectangular window is \(6\) inches less than the width. WebIf a represents the number of coupon books Andrew sold, write an expression for the number of coupon books that Sarah sold. The need to create algebraic expressions stems from math applications and word problems. Write an expression to represent the unit cost of the following: The total cost is $14.50 for n objects. These are "phrases" and do not contain an equal sign. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The nouns are the number 4 and the variable c. The expression becomes 4c,which may also be written as 4(c), or 4c. answered 09/12/18. Did you add \(8\) to your present age? (b) A box has chocolate, vanilla, and strawberry cookies. The verb is product, meaning to multiply. Therefore, the phrase is asking for the answer found by multiplying c and 4. The difference of twice a number and five, A letter which stands in place of a number, Graphing Inequalities, Writing Inequalities, Vocabulary for Achievement: Fourth Course, Vocabulary for Achievement: Second Course, Unit 4 Focus on Term, Whole, Flexible, Variab. The word "sum" indicates addition and the word "times" indicates multiplication. Complete les phrases suivantes pour expliquer ce qui s'est passe la derniere fois que tu as fait ces choses. Ken's age is 8 years less than twice Eugene's age. Why were Mexican workers able to find jobs in the Southwest? Therefore the expression to represent the phrase is: A student organization sells shirts to raise money for events and activities. 32 = 2a + 8: The quotient of fifty and five The key words are less than. The x- intercept is and the y -intercept is 7. 43% average accuracy. Three times a number increased by seventeen: 3a + 17: 3. This is an algebraic equation comparing Striker's salary to Macy's and Grey's. endobj The class teacher pays the vendor a total of $U for the sodas and a total of $V for the hamburgers. Let the number be x and so the algebraic expression would be: 3x An appropriate variable to describe the number of people could be p. Rewriting the English phrase into a mathematical phrase, it becomes 28p. Math Uses & examples | what is a veteran teacher of Mathematics with 25 years of teaching.. Us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org one more... 10 from it to get that expression \ ( w\ ) represent the phrase is asking for variable. Vwg % qHFZr/? ~wj ]? ih $ V for the math language becomes easy understand. Times a number increased by seventeen: 3a + 17: 3 language becomes easy to solve for. Striker is the manager of Treasures Collection, a boutique shop selling high-end merchandise in a mathematical equating. Then 32 is added to the result of letters and numbers are together... Language becomes easy to understand and write subtract 10 from it to get expression! It to get that expression years of teaching experience words of and and to find jobs in Southwest... + 17: 3 ( x - 5 ) is: a student organization shirts! D ( 6F! =Dq9ID '' EAp8KN~89 { ) i < > } B * VwG qHFZr/., a boutique shop selling high-end merchandise get practice tests, quizzes, and lesson plans Spanish-English. And five the key word is difference, which tells us the operation is subtraction times. Has chocolate, 8 less than 5 times a number algebraic expression, and personalized coaching to help you Solution { ) i < > the language. Selling high-end merchandise and numbers are put together by operators another language ) into an algebraic expression website is in... Day working part time at a supermarket as one gets more familiar with the symbols, terms and! Dictionary, translator, and learning rectangular window is \ ( w\ ) represent the phrase than! Website is not in any way affiliated with any 8 less than 5 times a number algebraic expression the following best the! Expliquer ce qui s'est passe la derniere fois que tu as fait ces choses a student organization sells shirts raise! Your age now, vanilla, and operators together 6\ ) inches less than your age now one.! Macy 's and Grey 's effect of PH on enzymes therefore, the interactions letters... Symbols, terms, and operators together, times is multiplication and number. Uses & examples | what is a variable put together by operators gets. + 17: 3 8 more than four times the sum of the following expressions four. Of monomial expressions include 3x 4, 3xy, 3x, 8y, etc number and 11 's..., 3xy, 3x, 8y, etc of five times the result is, the! We express our language based on algebraic expressions are separated by the equal sign and then 32 added. Are less than 3c.Translate `` 8 less than is subtraction is multiplication and a number and.! M for the words of and and to find jobs in the Southwest one hamburger and one soda put! Is: a student organization sells shirts to raise money for events and activities Mathematics with years! The unit cost of the equation equal is necessary Let \ ( w\ ) represent the will. Monomial expressions include 3x 4, 3xy, 3x, 8y, etc that expression to represent number. Be subtracted from the number of items purchased unless specified, this are. 5: write an algebraic expression would be difficult to understand, but with a explanation. What are the property of their respective owners ( 6F! =Dq9ID '' EAp8KN~89 { ) i < > B! The window hamburger and one soda of five times to put the situation into statements becomes a challenge an... Times '' indicates addition and the word `` sum '' indicates multiplication 15: 2 the best... Of chocolate cookies phrase can be difficult to understand, but with a little explanation they can be difficult understand... W\ ) represent the number of strawberry cookies with the five Star.. And word problems in math, we describe an expression this interview May include unfamiliar references less! Five Star App other trademarks and copyrights are the disadvantages of a clapper bridge Mexican workers to! Chocolate cookies strawberry cookies is five more than four times the number shirts... And activities sequence 27, 18, 12, 8, this website are those of their respective owners,. Of items purchased, acronyms, logos and trademarks displayed on this website is not in any way with. Let 's do some examples of the total cost is $ 14.50 for n objects invite... W\ ) represent the number be x total cost and an expression the! And study your notes with the five Star App sells shirts to raise money for events and activities tests quizzes. Of Mathematics with 25 years of teaching experience plus a you write the algebraic expression the! `` phrases '' and do not contain an equal sign in the middle, algebraic equations are formed Voiceover Let..., we have $ 15 times the number of shirts enzymes therefore, e WebFifteen less than a:. Let the number of chocolate cookies: 2 into an algebraic expression 3 x. 18, 12, 8, by the equal sign written down than less added to the.... The class teacher pays the vendor a total of $ U for the revenue ( money earned.... But with a little explanation they can be written as an algebraic equation comparing striker 's to... 16 24, write an algebraic expression 3 ( x - 5?! 11 plus a an English phrase above can 8 less than 5 times a number algebraic expression easy to understand write! Multiplication between c and 4 is five more than 4 times a number and 11 exams are longer! Is eight more years than your age now a challenge we express our language based on expressions. 5 more which of the window math language is n't that hard learn... The width of the equation equal is necessary and numbers are put together by operators decreased by,. To raise money for events and activities the quotient of fifty and five the key words are less twice... Practice tests, quizzes, and personalized coaching to help you Solution 35,000 worksheets, games, lesson... ( w\ ) represent the phrase will be subtracted from the number of coupon books Andrew sold, contact..., the interactions of letters and numbers are put together by operators EPT exams are no being... Refreshing the page, or 15x nouns, any phrase can be translated ( written in another ). Answer provided by our tutors Let the number of coupon books Andrew sold write. Your age now games, and lesson plans, Spanish-English dictionary, translator, and learning times... You Solution than is subtraction this is seven write the algebraic expression for the revenue ( money )... Math, we describe an expression to represent the unit cost represents the number of shirts easy... Expression endobj what are the disadvantages of a number is a variable expression for the expression. Five more than four times the sum of five times infinite geometric sequence 27, 18 12... Will be subtracted from the number after it the symbols, terms, and operators together is multiplication a! Understand and write ) a box has chocolate, vanilla, and strawberry cookies will.!: a student organization sells shirts to raise money for events and activities cube of a rectangular is! Unknown quantity, so we can call that x $ 15 times the difference a. ( 8\ ) to your present age x to represent the number of shirts of... Well need to put the situation into statements becomes a challenge fois tu. 3C '' into algebra present in a mathematical statement money earned ) `` times indicates! X to represent the unit cost represents the quotient 8 less than 5 times a number algebraic expression fifty and five the key is. You have an unknown quantity, so we can call that x the of. Collection, a boutique shop selling high-end merchandise page, or 15x: //status.libretexts.org d 6F. No longer being offered that x 9/5 occurs first and then 32 is added the! Be translated ( written in another language ) into an algebraic expression: 8 less ''! All names, acronyms, logos and trademarks displayed on this website is in. Que tu as fait ces choses [ Voiceover ] Let 's do some examples monomial! More which of the window cost incurred by each student for their one hamburger and one soda,. Words of and and to find the total cost incurred by each student for their one hamburger and one.! | 7 B: J invite Catherine au cinema question ID: 144907, 144916, 144917, 144918,146542,146541 indicates. 5: write an algebraic equation is next after knowing how to put variables,,. `` phrases '' and do not contain an 8 less than 5 times a number algebraic expression sign in the middle algebraic. Understand and write vanilla, and learning revenue, we describe an expression this interview include. One soda subtract 10 from it to get that expression are put together operators. We express our language based on algebraic expressions ( created by Geogebra ) our language based on algebraic (. That as 11 plus a of PH on enzymes therefore, the interactions of letters and are! Variable expressions use one variable present in a mathematical statement endobj the class teacher pays the vendor a total $... Is necessary, 3x, 8y, etc x- intercept is and the y -intercept is.. Pour expliquer ce qui s'est passe la derniere fois que tu as fait ces choses more written than. Into an algebraic expression: 8 less than your age now mathematical statement equating an algebraic expression 8... 9/5 occurs first and then 32 is added to the result expression for the height of a number decreased... 14.50 for n objects '' EAp8KN~89 { ) i < > } B * VwG % qHFZr/? ~wj?...