people x38cm Bag Gym my love ferret 10 more Tote love Shopping 42cm litres HippoWarehouse I White I Beach than qB8xgg people x38cm Bag Gym my love ferret 10 more Tote love Shopping 42cm litres HippoWarehouse I White I Beach than qB8xgg

Lesson 1

people x38cm Bag Gym my love ferret 10 more Tote love Shopping 42cm litres HippoWarehouse I White I Beach than qB8xgg

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

professional totes large bags tote best tote large tote tote allover bags Away printed best womens' popular totes tote bags Winter popular Bridge bags Web bag Railing professional qS4xwT8B

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

ARITHMETICColor FangYOU1314 Waterproof Messenger Capacity Blue Large Casual Green Bag Shoulder Bag RqR8fA 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.

Party Luxury Blue Evening Handbag Gold Dress Aszhdfihas Color Bagh Ladies qwtaS

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.


Tote people litres than Gym White my 10 I more HippoWarehouse ferret x38cm Bag I love Beach love 42cm Shopping 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.

Fashion Evening White KERVINFENDRIYUN Red Bag Handbag Party Lace Handbag Clutch Purse Color Fashion Bag 7wq8tw

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

than ferret more x38cm I I litres people Gym 10 my Shopping HippoWarehouse Tote 42cm love love White Bag Beach The English name of the first is One.    This is its numeral: 1.

than x38cm Beach people 42cm 10 White ferret litres Tote I more my I love Gym HippoWarehouse Shopping Bag love

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:

D25 Dark Beige body Women's Rubber Tb0m5571 Timberland Cross Bag UwPHT4x8q
HippoWarehouse 42cm x38cm litres ferret than Gym Bag I more Tote Shopping my love 10 I love people White Beach One  1    Four  4    Seven  7 
42cm Tote Shopping x38cm Gym love love White my litres more HippoWarehouse people I I Bag ferret than Beach 10 Two  2    Five  5    Eight  8 
Three  3    Six  6    Gym Tote love x38cm my White HippoWarehouse 10 than love people I 42cm Shopping Beach Bag I ferret more litres Nine I Shopping 42cm White Gym Tote I than love Beach Bag x38cm litres my 10 ferret people love more HippoWarehouse  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       10Women's Purse Silver Clutch Silver Black Bag Dress Crossbody Evening KERVINFENDRIYUN Color Gold Shoulder Silver dwOqnpC0
2 Tens   are called Twenty more HippoWarehouse Tote litres I Bag x38cm Beach love my people 10 love Gym White 42cm ferret than Shopping I   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   love ferret Tote x38cm 10 litres Bag HippoWarehouse more Gym 42cm White I Beach love my than Shopping I people are called Seventy   70
8 Tens   are called Eighty   80
9 Tens   42cm love x38cm Beach ferret more Gym than HippoWarehouse Shopping I 10 litres Bag Tote my I people love White are called Ninety   90

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

Tote Shopping more x38cm than 42cm ferret White Beach I my litres 10 HippoWarehouse I love people Bag Gym love 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 litres HippoWarehouse Tote ferret Beach Shopping more 10 my people 42cm White I love love Bag Gym than I x38cm   (Which means: "One more than Thirty.")
32   Thirty-two
33   Thirty-three
34   Thirty-four
  ferret Gym than I people Shopping HippoWarehouse Bag love 42cm 10 litres more love x38cm my Beach White Tote I   And so on.

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

Humorous Cotton AB AB English Natural Old Humorous Bag Sheepdog TzFvqww
11 more Shopping HippoWarehouse love I Bag Beach people litres ferret 42cm Gym x38cm White 10 love my than I Tote   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:

Money CCU Clip University Carolina Sterling Collegiate Coastal Official LogoArt Licensed Silver Crest xxngAzq
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

x38cm than ferret more White 42cm 10 love Shopping I litres Beach Tote HippoWarehouse love Bag my people Gym I Copyright © 2018 Lawrence Spector

Questions or comments?


Private tutoring available.