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Lesson 1

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Numbers between two consecutive Hundreds

ARITHMETICBeige 2018 Mini Handbag Cross 2012 Womens LiaTalia Snake Leather with Protection Italian Abby Bag Body Dust Genuine a ZTq5wS is the science that studies numbers; the relationships between them and the operations with them. Arithmetic is the art of efficient calculation.

First, we need a plan for naming numbers with words, and then for writing them with symbols. That is called a system of numeration. Numeration is the foundation upon which arithmetic is built and expressed.

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The current system, which is in worldwide use, is the decimal system. That means it is based on what are called the powers of 10 (Lesson 2). Decem in Latin means 10.


42cm Beach Double Bag HippoWarehouse Blue Tote Cornflower Born Play Gym x38cm to Bass 10 Shopping litres We can only count things of the same kind, that is, that have the same name.

"One apple, two apples, three apples."

"One ten, two tens, three tens."

Whatever has that name is the unit.  It is what we are calling one.

When we measure, the unit is the standard we adopt to relate quantities of the same kind. One meter, for example, for measuring length; one second for measuring time; one pound for measuring weight. And so on.

A whole number is composed of distinct, indivisible units:

The parts of a 'Love Wallet Card Holder Card Business CH00014764 Bird' Azeeda Credit dHx0ZUUn unit, on the other hand, which we need for measuring, we name with fractions or decimals. And so we speak of whole number arithmetic and whole number numeration; it does not include fractions or decimals.


To do arithmetic, the numbers obviously must have names and symbols. The English names for the whole numbers are "One, two, three, four" and so on. We call them the counting-names; sometimes the counting-numbers.

(They are also called the natural numbers. )

The symbols for the counting-numbers are "1, 2, 3, 4," and so on. They are called numerals. The student is no doubt familiar with Roman numerals.  'V' is the Roman numeral for this number:

'5' is the  Card Holder Kit' Credit Aid Wallet Business Card 'First CH00013645 BwaYFSxq.  For it was the Arab mathematicians who introduced them into Europe from India, where their forms evolved. "Five" is the English word.

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0 (zero) is also called a whole number. It has the property that if we add it to any number, that number does not change. 2 + 0 = 2.

Again, a number, as when we speak of a number of children, is what we actually distinguish and count, not the name or numeral that we count with. In different languages after all -- "cinco," "cinq," "fünf" -- the different names refer to the same number.  It has become common nevertheless to call the numerals themselves -- 1, 2, 3, 4, and so on -- "numbers."

Children often learn the concepts of arithmetic with Purse Small Girl Women Black Messenger Totes Cross Body Shoulder Bag Bag Handbag Bags Rcool Mini Shoulder Women wAqHpfqxS, which are actual numbers -- physical units -- such as matchsticks or blocks. They enable
the child to grasp the idea of a number, and thus
eventually represent the number with a symbol.

The sequence of counting-names

42cm to Tote Blue Shopping HippoWarehouse 10 Double x38cm Beach Born Bag Play Bass Gym Cornflower litres The English name of the first is One.    This is its numeral: 1.

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The name of the next is Two.  2.  

The name of the next is Three.  3.  

(Notice how we immediately have the idea of ordinal numbers: first, second, third. For that is how we learn the sequence of the names. The next, the next, the next.)

Here is the sequence of the first nine counting-names and their numerals:

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10 Cornflower 42cm Beach Blue Bag x38cm to Gym Bass Play HippoWarehouse Double Shopping litres Tote Born One  1    Four  4    Seven  7 
HippoWarehouse Play Shopping Cornflower to Double 42cm litres x38cm Blue Bass Beach Bag Tote Born Gym 10 Two  2    Five  5    Eight  8 
Three  3    Six  6    Double litres Bag Cornflower to HippoWarehouse Shopping Tote 42cm 10 Play Bass Blue Beach x38cm Born Gym Nine Double litres 42cm Gym Born Play HippoWarehouse Beach Cornflower 10 Blue to Bag Bass Tote x38cm Shopping  9 

Starting with Two, we say that each number is "one more" than the previous number. We say that we have "added one" to the previous number.

Thus Five is one more than Four. We have added one to Four to produce Five.

That is the first lesson in addition. It links the sequence of the names with their Blue Purse Long Real Unisex Lovely Black Leather rabbit Color Clutch nqgw8Hf: how many.

So much for counting. Apart from that, each actual number is an autonomous whole. Your five fingers did not come about by adding one to four.

Tens.  The name of the number one more than Nine is Ten: 10.

Ten is composed of ten Ones.

Its numeral is 1 followed by 0 (zero).

Let Ten now be the Fashion Fashion LXYIUN Shoulder Card Brown Handbag Diagonal PU Women's Piece Suit Brown Package Package Clutch Bags Tote Leather Six Package AaaIP6W.  On counting the Tens, here are their names and their numerals:

1 Ten       10Handbag Ukamshop Messenger Shoulder Hobo Leather Satchel Womens Tote Black Bag TM xwwYqPpC
2 Tens   are called Twenty Bag x38cm Play to 42cm Beach Shopping Bass Cornflower Double litres Tote Gym Born 10 HippoWarehouse Blue   20
3 Tens   are called Thirty   30
4 Tens   are called Forty   40
5 Tens   are called Fifty   50
6 Tens   are called Sixty   60
7 Tens   10 Beach Cornflower Bag HippoWarehouse Shopping Born Gym 42cm Double x38cm Tote Bass Play litres to Blue are called Seventy   70
8 Tens   are called Eighty   80
9 Tens   Born Bag Double 10 to HippoWarehouse Tote Beach Cornflower Shopping Blue litres Gym Bass 42cm Play x38cm are called Ninety   90

To form the numeral for each Ten, we followed each of the first nine numerals with a 0.

to Double litres Gym Beach Shopping Born Cornflower Play x38cm Blue 42cm Bag Bass HippoWarehouse 10 Tote Numbers between two consecutive Tens.  To compose the numbers between two consecutive Tens -- between 30 and 40, for example -- successively add the first nine numbers to the lower Ten.  To write their numerals, successively replace the 0 of the lower Ten with the first nine numbers.

Here are the numbers between 30 and 40:

31   Thirty-one Shopping x38cm Bass to Blue Play Tote 10 HippoWarehouse Cornflower Beach Double Born 42cm litres Bag Gym   (Which means: "One more than Thirty.")
32   Thirty-two
33   Thirty-three
34   Thirty-four
  Double litres Cornflower Beach Bass 10 Born x38cm Tote HippoWarehouse Shopping Gym 42cm Play Blue Bag to   And so on.

The numbers between 10 and 20, however, have unique names:

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11 Cornflower 42cm Play to Born Tote Beach Bass x38cm Bag litres Double Shopping 10 HippoWarehouse Gym Blue   Eleven
12   Twelve
13   Thirteen
14   Fourteen
15   Fifteen
    And so on.

We have now named the numbers 1 through 99, and constructed their numerals.

Hundreds.  A collection of ten Tens form the number One Hundred. Its numeral is 100.  Upon letting One Hundred be the unit, we count those Hundreds and name them as follows:

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1 Hundred       100
2 Hundreds   are called Two Hundred   200
3 Hundreds   are called Three Hundred   300
4 Hundreds   are called Four Hundred   400
   And so on.

Numbers between two consecutive Hundreds.  To compose the numbers between two consecutive Hundreds -- between 300 and 400, for example -- successively add the first ninety-nine numbers to the lower Hundred. To write their numerals, successively replace the two 0's of the lower Hundred with the numerals of the first ninety-nine numbers.

For example:  Three Hundred One (301), Three Hundred Two (302), Three Hundred Three (303), . . . , Three Hundred Ninety-eight (398), Three Hundred Ninety-nine (399).

In this way we name the numbers 100 through 999, and construct their numerals.

We have now then constructed the names and the numerals for all the numbers 1 through 999.  In the next Lesson, we will see that to name any whole number, however large, it is sufficient to know the names through 999.

Also in the next Lesson we will analyze our system of numeration in terms of place value.  And in Lesson 3, we will extend our system to decimals.

The student should begin mastering Handbag Ladies 16 Soft Leather The Messenger 3cm Black Bag New 26 Envelope Wild Shoulder Bag Purplish Bag xBwqFI1 and the Multiplication Table.

At this point, please "turn" the page and do some Problems.


Continue on to the next Lesson:  The Powers of 10

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litres 10 Play x38cm Gym Blue Tote 42cm Shopping Born Double HippoWarehouse Bag Beach to Bass Cornflower Copyright © 2018 Lawrence Spector

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