( Lesson 3.)Īs for a hundredth, we will separate two decimal digits: Since this is money, we report the answer as $27. See Lesson 11, Question 2, and especially Example 6.Īnswer. 2 is the fifth part of what number?Įvery number is the fifth part of five times itselfĤ is the fifth part of 5 × 4, which is 20.ĩ is the fifth part of 5 × 9, which is 45.Ģ0 is the fifth part of 5 × 20, which is 100.ĭivide by the cardinal number that corresponds to the name of the part. Because 28 is made up of four sevens.Įxample 3. What number is the fourth part, or a quarter, of 28?Īnswer. Part of 4, the fifth part of 5, the hundredth part of 100. Which part is it? The part that says the number's name. Note that 1 is a part of every number (except itself) because every number is a multiple of 1. We can then explain that the number we call is the third part of 1.Īnswer. Why is the number we write as 1 over 3 - called "one-third"? Because the numerator is one third - the third part - of the denominator. It should be clear that the ordinal names of the parts belong to language itself, and are prior to the names of the proper fractions, which are the parts of 1. We will come to those symbols in Lesson 20. When answering the questions of this Lesson, the student should not write fractions. name the equal parts into which a number has been divided. We are explaining how the ordinal numbers - third, fourth, fifth, etc. It is important to understand that we are not speaking here of proper fractions - numbers that are less than 1 and that we need for measuring. But if we divide into two equal parts, then we have divided it in half. Then we have divided it into fourths (or quarters) if into five equal parts, If we divide a number into four equal parts, This use of ordinal numbers does not imply a sequence: the first part, the second, the third, and so on. So with the exception of "half," an ordinal number names into which parts a number has been divided.ġ5 has been divided into Thirds that is, into three equal parts. (We do not say the second part.) And 5 is not a part of itself there is no such thing as the first part. 5 is the fifth part of 25, the sixth part of 30 and so on. Since 20 is the fourth multiple of 5, we call 5 the fourth part of 20. We use that same ordinal number to name the part. Since 15 is the third multiple of 5, we say that 5 is the third part of 15. Equivalently, the smaller is contained in the larger an exact number of times.ĥ, then, will be a certain part of each one of its multiples. It means that the larger number is a multiple of the smaller. What does it mean to say that a smaller number is a part of a larger number? They are the numbers produced when that number is repeatedly added.ĥ is the first multiple of 5 10 is the second multiple 15, the third and so on. What do we mean by the multiples of a number?
To each cardinal number except 1, there will correspond the name of a part. With the exception of "half," an ordinal number will name which part - the third part, the fourth, the fifth, and so on. They answer the question Which one? We will see that those ordinal numbers express division into equal parts. They answer the question How many? The ordinal forms are The names of the natural numbers have two forms: cardinal and ordinal. We calculate with those symbols, and so it has become conventional to call the symbols themselves "numbers." Yet a symbol is not what it symbolizes, what it stands for, which in this case is a number of discrete units.īy a number in what follows, we will mean a natural number. To those collections we give a sequence of names and symbols.ġ, 2, 3, 4, and so on, are the familiar numerals for the natural numbers. It is a collection composed of equal indivisible units each of which we say is one. How can we calculate parts of a number?.What does it mean to say that a smaller number is parts of a larger number?.How can we calculate a part of a number?.What does it mean to say that a smaller number is a part of a larger number?.What do we mean by the multiples of a number?.In this Lesson, we will answer the following: