BUKU AJAR BAB 1 Tika

NUMBER CONCEPT AND BASIC OPERATION BAB 1 BAB I Number Concept And Basic Operation A. Pendahuluan Pada Bab I ini, mahasiswa diharapkan dapat menguasai konsep dan menerjemahkan istilah-istilah matematika dalam bahasa ingris. Istilah-istilah ini adalah beberapa hal yang wajib diketahui sebagai konsep dasar untuk melakukan riview pada jurnal internasional matematika maupun menerjemahkan buku atau bahan ajar matematika berbasis bahasa inggris. Adapun materi yang dipelajari pada Bab Number Concept and Basic Operation diantaranya adalah Definition of Numbers, Cardinal and Ordinal Numbers, Types of Number, Symbols and Meaning, Basic Operation, Fraction than Decimal. B. Number Concept And Basic Operation 1. Definition of Number, Numeral and Digit A number is a count or measurement that is really an idea in our minds. We write or talk about numbers using numerals such as \"5\" or \"five\". We could also hold up 5 fingers, or tap the table 5 times. And than, there are also special numbers (like) that can't be written exactly, but are still numbers because we know the idea behind them. These are all different ways of referring to the same number. A numeral is a symbol or name that stands for a number. For example : 12, 8, 1987, thirty three, etc, are all numerals. So, the number is an idea and the numeral is how we write it. A digit is a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numerals. For example: a. 1987 is made up of 4 digits (\"1” “9” “8” “7”) b. 12 is made up of 2 digits (“1” “2”) c. 8 is made up of 1 digit (“8”) A single digit can also be a numeral. So digits make up numerals, and numerals stand for an idea of a number. Look at to this illustration about digit, numeral and number. Tika Septia, S.Si., M . P d Page 1

NUMBER CONCEPT AND BASIC OPERATION BAB 1 Illustration 1. 1987  1987  Digit Digit Digit Digit Numeral Number Often people say \"Number\" when they really should say \"Numeral\" . It doesn't really matter if you do that, because other people understand you. And we must try to use \"digit\" only when talking about the single symbols that make up numerals. 2. Cardinal, Ordinal and Nominal Number 2.1 Cardinal Numbers A Cardinal Number says how many of something. Such as one, two, three, four, five, etc. It does not have fractions or decimals, it is only used for counting. In other words Cardinal is Counting, for example: a. Felicia has three books for mathematics subject. b. There are five coints in the pocket. Some examples shows in this table: Cardinal Number How to write or spell it 1 One 4 Four 8 Eight 11 Eleven 100 One hundred 123 One hundred and twenty-three 222 Two hundred and twenty-two 745 Seven hundred and forty-five 1,000 One thousand 1,037 One thousand and thirty-seven 2.2 Ordinal Numbers An Ordinal Number is a number that tells the position of something in a list. 1st, 2nd, 3rd, 4th, 5th and so on. Ordinal says what Order things are in. For example: Tika Septia, S.Si., M . P d Page 2

NUMBER CONCEPT AND BASIC OPERATION BAB 1 a. I am the second child in my family b. Valentino Rossi get the fourth place in Misano World Circuit Marco Simoncelli champion Most ordinal numbers end in \"th\" except for:  one ⇒ first (1st)  two ⇒ second (2nd)  three ⇒ third (3rd) Some examples shows in this table: Ordinal Number How to write and spell it 1st First 2nd Second 3rd Third 4th Fourth 5th Fifth 7th Seventh 18th Eighteenth 19th Nineteenth 20th Twentieth 21st Twenty first 22nd Twenty second 23rd Twenty third 24th Twenty fourth 25th Twenty fifth 2.3 Nominal Numbers A Nominal Number is a number used only as a name, or to identify something (not as an actual value or position). Nominal is a Name, for example: a. The number on the back of Valentino Rossi is \"46\" b. A zip code : \"91210\" Tika Septia, S.Si., M . P d Page 3

NUMBER CONCEPT AND BASIC OPERATION BAB 1 Illustration 2. In this photo there are 6 cars. Car Number \"99\" (with the yellow roof) is in 1st position: 6 is a Cardinal Number (it tells how many), 1st is an Ordinal Number (it tells position) and \"99\" is a Nominal Number (it is basically just a name for the car) 3. Types Of Numbers In mathematics, a number is an arithmetic value which is used to represent the quantity of an object. We are using numbers in our day-to-day life, such as counting money, time, things, and so on. We have different types of numbers in the number system. And now we are going to discuss the types of numbers in Maths. The different types of numbers are as follows: Type of Number Definition Example Natural Numbers Natural numbers are also called “counting N = {1, 2, 3, 4, 5, …} numbers” which contains the set of positive integers from 1 to infinity. The set of natural numbers is represented by the letter “N” Whole numbers Whole numbers are also known as natural W = {0,1, 2, 3, 4, 5, …} numbers with zero. The set consists of non- negative integers where it does not contain any decimal or fractional part. The whole number set is represented by the letter “W” Integers Integers are defined as the set of all whole Z = {…,-3, -2, -1, 0, 1, 2, numbers with a negative set of natural 3,…} numbers. The integer set is represented by the symbol “Z” Faction A fraction represents parts of a whole piece. It 3/7, 99/101, 7/3, etc Tika Septia, S.Si., M . P d Page 4

NUMBER CONCEPT AND BASIC OPERATION BAB 1 Prime Numbers can be written in the form a/b, where both a Odd Numbers and b are whole numbers and b can never be Even Numbers equal to 0. All fractions are rational numbers, Real Numbers but not all rational numbers are fractions. Prime numbers are the type of integers which 2, 3, 5, 7, etc Rational Numbers have no factors other than itself and 1. Any integer that cannot be divided exactly by −3, 1, 7 and 35 Irrational Numbers 2 Any integer that can be divided exactly by 2. −24, 0, 6 and 38 Complex Numbers Any number such as positive integers, ¾, 0.333, √2, 0, -10, 20, Imaginary Numbers negative integers, fractional numbers or etc decimal numbers without imaginary numbers are called the real numbers. It is represented by the letter “R”. Any number that can be written in the form 7/1, 10/2, 1/1, 0/1, etc of p/q, , a ratio of one number over another number is known as rational numbers. A rational number can be represented by the letter “Q”. The number that cannot be expressed in the √2, π, etc form of p/q. It means a number that cannot be written as the ratio of one over another is known as irrational numbers. It is represented by the letter ”P”. A number that is in the form of a+bi is called 4 + 4i, -2 + 3i, 1 +√2i, etc complex numbers, where “a and b” should be a real number and “i” is an imaginary number. The imaginary numbers are categorized under √2, i2, 3i, etc. complex numbers. It is the product of real numbers with the imaginary unit “i”. The imaginary part of the complex numbers is defined by Im (Z). Tika Septia, S.Si., M . P d Page 5

NUMBER CONCEPT AND BASIC OPERATION BAB 1 4. Symbols and Meaning No matter where you are in the world - unlike the many languages and dialects that exist from country to country - mathematics remains the same, from North America to Africa, Asia to Europe and everywhere in between. For simplicity's sake, we've broken it down into five groups from basic math symbols to more complex ones: 1. Basic math symbols 2. Algebra symbols 3. Geometry symbols 4. Set theory symbols 5. Calculus & analysis symbols Symbols save time and space when writing. Here are the most common mathematical symbols: Symbol Meaning Example + add/ plus 3+7 = 10 − subtract/ minus 5−2 = 3 × multiply 4×3 = 12 ÷ divide 20÷5 = 4 / divide 20/5 = 4 ( ) grouping symbols 2(a−3) [ ] grouping symbols 2[ a−3(b+c) ] { } set symbols {1, 2, 3} π pi A = πr2 = Equals/ equal to 1+1 = 2 ≠ Not equals/ not equal to π≠2 < less than 2<3 ≤ less than or equal to 2≤3 > greater than 5>1 Tika Septia, S.Si., M . P d Page 6

NUMBER CONCEPT AND BASIC OPERATION BAB 1 ≥ greater than or equal to 5≥1 ° degrees 20° For example: a. 2 < 3 : Two is less than three b. 5 ≠ 6 : Five is not equal to six/ five is not equals six c. 4 ≥ 1 : Four is greater than one Etc 5. Basic Operation In basic mathematics there are many ways of saying the same thing: a. Addition uses symbol + (plus) If we add one quantity to another then we use symbol + (plus). The name of this operation is addition. The result of this operation is called the sum Example : Twenty-three plus seventeen equals forty. The sum of twenty-three and seventeen is forty. b. Substraction uses symbol – (minus) If we subtract one quantity from another then we use the symbol – (minus) The name of this operation is subtraction The result of this operation is called the difference Example : Fifty minus fifteen equals thirty-five. The difference of fifty and fifteen is thirty-five. c. Multiplication used symbol x (multiplied by or times) If we multiply one quantity by another then we use the symbol × (multiplied by or times) The name of this operation is multiplication The result of this operation is called the product Example : Twelve times five equals sixty. The product of twelve and five is sixty. d. Division used symbol ÷ (divided by) If we divide one quantity by another then we use the symbol ÷ (divided by) The name of this operation is division The result of this operation is called the quotient Tika Septia, S.Si., M . P d Page 7

NUMBER CONCEPT AND BASIC OPERATION BAB 1 Example : Seventy-eight is divided by thirteen equals six. 6. Fraction The quotient of seventy-eight and thirteen is six. 6.1 Numerator and Denominator A Fraction consist of Numerator and Denominator. For example: 2  2 is numerator and 3 is denominator. 3 The top number is the Numerator, it is the number of parts you have. The bottom number is the Denominator, it is the number of parts the whole is divided into. Other example: ¾ means We have 3 parts. Each part is a quarter (1/4) of a whole. 6.2 Equivalent Fraction Some fractions may look different, but are really the same, for example: Equivalent Fractions have the same value, even though they may look different. These fractions are really the same: Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value. The rule to remember is: \"Change the bottom using multiply or divide, and the same to the top must be applied\". If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible). It is usually best to show an answer using the simplest fraction , or simplest form ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction. Tika Septia, S.Si., M . P d Page 8

NUMBER CONCEPT AND BASIC OPERATION BAB 1 6.3 Types of Fractions There are three types of fraction: a. Proper Fractions A proper fraction is just a fraction where the numerator (the top number) is less than the denominator (the bottom number). Here are some examples of proper fractions. Example:  1 , 3, 2 3 47 b. Improper Fractions An improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator). Example:  4, 11, 7 347 c. Mixed Fractions Mixed Fraction is a whole number and proper fraction together. Example:  1 2, 2 1, 16 4 34 7 6.4 Saying Fraction Number How to read a half 1 ������ ������������������������������ / ������������������ ������������������������������ / ������������������ ������������������������ ������������������������������ 2 ������ ������������������������������������������ / ������������������ ������������������������������������������ / ������������������ ������������������������ ������������������������ 1 ������������������������ ������������������������������������ / ������������������������ ������������������������ ������������������ 3 ������������������������������ ������������������ ������������������ ������������������������ ������������������������������ 1 ������������������������������������������������ ������������������ ������������������������������ ������������������������������������������������ 4 ������������������������������������ − ������������������ ������������������������ ������ ������������������ ������������������������ ������ 5 6 1 3 3 3 13 4 (22 + ������) ������ Tika Septia, S.Si., M . P d Page 9

NUMBER CONCEPT AND BASIC OPERATION BAB 1 7. Decimal A Decimal Fraction is a fraction where the denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words a power of ten). So, 23  2,3 1325  13,25 10 1000 To write a decimal fraction we use a decimal point. Example :  If we convert 1 1 into decimal fraction, the result is 1.5 (one point five) 2  If we convert 2 into decimal fraction, the result is 0.6 (zero point six) 3 Saying Decimal Number How to read 0.4 ������������������������ ������������������������������ ������������������������ / ������������������������������������ ������������������������������ ������������������������ / ������ ������������������������������ ������������������������ 3.056 ������������������������������ ������������������������������ ������������������������ ������������������������ ������������������/ three point o five six 273.856 ������������������ ������������������������������������������ ������������������ ������������������������������������������ ������������������������������ ������������������������������ ������������������������������ ������������������������ ������������������ Tika Septia, S.Si., M . P d Page 10

NUMBER CONCEPT AND BASIC OPERATION BAB 1 C. SUMMARY  A number is a count or measurement that is really an idea in our minds.  A numeral is a symbol or name that stands for a number.  A digit is a single symbol used to make numerals.  Cardinal is Counting.  Ordinal says what Order things are in.  Nominal is a Name.  There are several types of numbers, like natural numbers, whole numbers, integers, prime numbers, fraction, etc  The most common mathematical symbols are basic math operation  Here are the most common mathematical symbols: Symbol How to read = is equal to ≠ is not equal to > is greater than ≥ is greater than or equal to < is less than ≤ is less than or equal to  In basic mathematics there are many ways of saying the same thing: a. Addition uses symbol + (plus) b. Substraction uses symbol – (minus) c. Multiplication used symbol x (multiplied by or times) d. Division used symbol ÷ (divided by)  A Fraction consist of Numerator and Denominator.  Equivalent Fractions have the same value, even though they may look different  There are three types of fraction: Proper Fraction, Improper Fraction and Mixed Fraction  A Decimal Fraction is a fraction where the denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words a power of ten) Tika Septia, S.Si., M . P d Page 11

NUMBER CONCEPT AND BASIC OPERATION BAB 1 D. PRACTICE A. Write out the seplling of this numbers 1. 7 11. 2 2. 11 3. 15 13 12. 57 9 13. 51.733 4. 50 14. 2,567.9 5. 100 15. 10,235.78 6. 443 7. 2,222 8. 12,123 9. 870,650 10. 1,000,000 B. Choose the sentence below is it true or false 1. Fifteen is less than twelve 2. One plus sixteen is equal to twenty 3. Fifty is greater than fifteen 4. Ninety is divided by fifteen equals seven 5. The sum of eighty and eighteen is eighty-eight 6. The difference of fifty and thirty is twenty 7. The quotient of seventy-five and fifteen is fifty 8. One hundred and ten plus one hundred and twenty is equal to one hundred and thirty 9. Twelve times four equals forty 10. One hundred and twenty two is greater than one hundred and thirty three C. Fiil in the blank and write out the sentences of the operation 1. 7 + 2 = 9 11. 1 + 2 = … 2. 56 – 12 = 44 3. 117 x 2 = 234 23 4. 228 : 3 = 76 12. 1 - 1 = … 23 13. 31 : 2 7 = … 4 10 14. 6.9 x 2.2 = … 5. 12 > 11 15. 655 : 3 = … 6. -1 < 0 7. 30 ≥ 13 8. 15 ≤ 50 9. 100 ≠ 1000 10. 1111 = 1111 Tika Septia, S.Si., M . P d Page 12

NUMBER CONCEPT AND BASIC OPERATION BAB 1 E. Use Single word, fill in the blank spaces in the following sentences. 1. The of three and four is twelve. 2. The operation which uses the symbol ÷ is called . 3. Fourty-eight thirty-six equals twelve. 4. The result of a division problem is called . 5. A whole number is also known as an . 6. Any number consists of combination of _. 7. Eighteen subtracted _ twenty equals . 8. Three multiplied _ five equals . 9. When we _ two quantities, for example seven plus twelve, the answer (ninteen) is called _ . 10. The product is the result when one quantity is _- another. D. Answer this question on your answer sheet 1. How many numerals are there altogether in the picture? And why? 2. How many numerals are there altogether in the picture? Tell the reason! 3. How many digits does the numeral 20,592 have? 4. During the race, right before the finish line, I passed the runner who won the third place. What place did I win? 5. If you add two even numbers together, the answer is: even numbers, odd numbers or sometimes even sometimes odd? Proof it! 6. If you add two odd numbers together, the answer is: even numbers, odd numbers or sometimes even sometimes odd? Proof it! 7. If you add an even number and an odd number, the answer is: odd numbers or sometimes even sometimes odd? Proof it! Tika Septia, S.Si., M . P d Page 13

NUMBER CONCEPT AND BASIC OPERATION BAB 1 E. REFERENCE Brown, Michael J. 2008. Kamus Matematika Remaja. Grasindo. Jakarta. Kerami, Djati, dkk. 2003. Kamus Matematika. Balai Pustaka. Jakarta. Math is Fun. “Number”. 2020. https://www.mathsisfun.com/. Roza, Yenita. 2006. English for Basic Mathematics. FKIP UNRI. Tika Septia, S.Si., M . P d Page 14