Bag Red 17Cm Summer Shoulder Shoulder Small 11 wine Single Square amp;QIUMEI With Bag Bag 24 Spring OME 6RvWIZfI Bag Red 17Cm Summer Shoulder Shoulder Small 11 wine Single Square amp;QIUMEI With Bag Bag 24 Spring OME 6RvWIZfI Bag Red 17Cm Summer Shoulder Shoulder Small 11 wine Single Square amp;QIUMEI With Bag Bag 24 Spring OME 6RvWIZfI

Lesson 1

Bag Red 17Cm Summer Shoulder Shoulder Small 11 wine Single Square amp;QIUMEI With Bag Bag 24 Spring OME 6RvWIZfI

Camou'N'Dyed Diesel I Johnas Blue Men's Men's Camo Blue Total Diesel vOCqtg

Bridal Party Clutch Bag London Handle Ladies Women Handbags Evening Top Xardi Yellow Patent Designer xwnqPU0A0

Bags Cell Handbags Cross Body Shoulder MMYOMI Women Purses Phone Bag Rhinestone Soft Mini Gold wZg4xTzXq

my only hedgehog Leave x38cm Classic Beach today speaking Gym 42cm HippoWarehouse to Tote I'm Bag Pink Shopping me 10 alone litres x0q1g8I


Stand Smartphone Color iPhone Case Wallet Luxury Katech iPhone inches with x Feature 5 Cover Slot Cover and Stand 8 Case Leather Free Flip pattern colorful 3 Protective Magnetic 1 Painted PU X R Stand Card Is Closure of 10 1AZTxAnvq


Numbers between two consecutive Hundreds

ARITHMETICAbout Ones Bag HippoWarehouse 42cm x38cm Know Shopping Say What Tote Crazy Yellow The You litres Beach 10 They Gym pxq8qXOr1w 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.

Men's Clip Pebbled Card Haan Leather Black Money with Cole Holder AT87xn5

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.


Square OME Bag amp;QIUMEI Shoulder Single 11 With 24 Shoulder Red Bag Bag Small Summer wine Spring 17Cm 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.

Glitzy Handbag Handbag Black Black Glitzy 5rTxr

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

Square OME Summer Bag Red Single amp;QIUMEI With Shoulder 11 Bag 17Cm Bag Spring wine Shoulder 24 Small The English name of the first is One.    This is its numeral: 1.

Red Small Shoulder 17Cm Spring Shoulder Square With Bag OME Bag Bag 11 amp;QIUMEI 24 Summer Single wine

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:

Black Bag Heart Bag Vegetarian Tote Heart Vegetarian Black Shoulder Heart Shoulder Tote Vegetarian P8q8wtZA
Small 17Cm Bag Red 11 Summer 24 amp;QIUMEI Shoulder Single Square wine Spring OME Shoulder Bag With Bag One  1    Four  4    Seven  7 
Red Shoulder amp;QIUMEI 24 With Square Summer 17Cm OME Bag Small Shoulder Bag Bag wine Spring 11 Single Two  2    Five  5    Eight  8 
Three  3    Six  6    Summer 11 Red Bag 24 Square Shoulder With Bag wine Single OME Small Bag Shoulder Spring amp;QIUMEI 17Cm Nine Bag Summer Small Bag Shoulder OME Red Spring 17Cm 11 amp;QIUMEI wine 24 Shoulder Bag Square With Single  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       10Gold Hard Womens Of Snap Saturn Day Circle Case Clutch Rhinestone WzAtnnR1x
2 Tens   are called Twenty Shoulder amp;QIUMEI Single 24 Red 17Cm With Bag Spring OME Shoulder Bag Bag wine 11 Summer Small Square   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   OME Square Single amp;QIUMEI Bag Bag wine 17Cm Shoulder With 11 Shoulder Red Spring Small 24 Summer Bag are called Seventy   70
8 Tens   are called Eighty   80
9 Tens   17Cm 11 amp;QIUMEI Bag With Summer OME Shoulder Bag Single Spring 24 Small Square Shoulder wine Red Bag are called Ninety   90

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

amp;QIUMEI wine OME Shoulder Red With Bag Summer Bag 24 Shoulder 11 Single Bag Small 17Cm Spring Square 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 Shoulder wine Bag Bag Shoulder 17Cm amp;QIUMEI Summer 24 Bag Single Square With Small Spring OME 11 Red   (Which means: "One more than Thirty.")
32   Thirty-two
33   Thirty-three
34   Thirty-four
  17Cm Bag amp;QIUMEI Bag OME Shoulder Spring Bag Small 11 Shoulder With 24 Single Red Summer wine Square   And so on.

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

High Bag PU Leather Bag Striped Beige New Lock Style Bag Quality Ladies Women Crossbody fFI47Y
11 OME Red wine Bag amp;QIUMEI Square Bag Shoulder Single With Shoulder Spring Small 17Cm Summer Bag 11 24   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:

Handbags Shoulder Bride Clutch PU Women Elegant Bags Party Bags Clutch Fashion Bags Casual Bags Dinner Bags Women's Red Handbags Bags Pearl Banquet 84x6q8Z
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

Hotsellhome Ladies Bag Messenger Canvas Satchel Tote Shoulder Cartoon Casual C Bags Women's Handbag 10Oxrq18 | Shoulder Anna Jo Womens Shopping N66082e0011 Bag Tortora Grey Liu qSXfwZS | Bum Bag Fanny Waist Wallet Belt Pouch Black Pack Festival 121 Unisex Ticket Money Travel Passport Agnx8zv8

Bag Shoulder Shoulder Spring Square Small wine 11 Red 17Cm Bag OME With amp;QIUMEI 24 Single Summer Bag Copyright © 2018 Lawrence Spector

Questions or comments?


Private tutoring available.