Counting Numbers

Index Natural Numbers Ordinal Numbers Operations and expressions Powers Properties BEDMAS

Review: Counting Numbers

Matematicas 2o E.S.O.Alberto Pardo Milanes

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1 Natural Numbers

2 Ordinal Numbers

3 Basic operations and expressions

4 Powers

5 Properties of powers

6 Order of Operations

Alberto Pardo Milanes Integers


Natural Numbers



Natural Numbers

Counting numbers

IN is the set of natural numbers:1 One2 Two3 Three4 Four5 Five6 Six7 Seven8 Eight9 Nine10 Ten

11 Eleven12 Twelve13 Thirteen14 Fourteen15 Fifteen16 Sixteen17 Seventeen18 Eighteen19 Nineteen20 Twenty

21 Twenty-one30 Thirty40 Forty50 Fifty60 Sixty70 Seventy80 Eighty90 Ninety100 A hundred200 Two hundred

We can use commas to write large numbers ...1, 000 A thousand 100, 000 A hundred thousand1, 000, 000 A million



Ordinal Numbers



Ordinal Numbers

An ordinal number describes the numerical position of an object.

1st First2nd Second3rd Third4th Fourth5th Fifth6th Sixth7th Seventh8th Eighth9th Ninth10th Tenth11th Eleventh12th Twelfth

13th Thirteenth14th Fourteenth15th Fifteenth16th Sixteenth17th Seventeenth18th Eighteenth19th Nineteenth20th Twentieth21st Twenty-first22nd Twenty-second23rd Twenty-third24th Twenty-fourth

25th Twenty-fifth30th Thirtieth31st Thirty-first41st Forty-first52nd Fifty-second63rd Sixty-third70th Seventieth80th Eightieth90th Ninetieth91st Ninety-first100th Hundredth101stHundred and 1st



Basic operations andexpressions



Basic operations and expressions

Bracket and square bracket:To make groups we can use brackets ( ) and square brackets [ ].

Sum or addition:Example: 6 + 9 = 15, six plus nine equals/is fifteen.

a+ b is a sum. In a sum you add two numbers.

Difference or subtraction:Example: 20−3 = 17, twenty minus/take-away three is seventeen.

a− b is a difference. In a difference you subtract two numbers.

Order:Example: 2 < 8: two is less than eight.12 > 5: Twelve is greater than five.



Basic operations and expressions

Multiplication or product:Example: 5 · 6 = 30, five times six equals thirty or five multipliedby six is thirty.

a · b is a multiplication. In a product you multiply two numbers.

Division:Example: 40 : 5 = 8, forty divided by five is eight.

a : b is a division. In a division you divide two numbers.Sometimes a division is not exact, so you also must write theremainder.

Example: Forty-two divided by five is eight and two left/remainsbecause42 = 5 · 8 + 2.



Powers



Powers

A power of a number is a number multiplied by itself severaltimes.A power is made of two parts: the base is the number beingmultiplied, and the index/exponent is the number of times youmultiply.

Example: 34 = 3 · 3 · 3 · 3 = 81, 3 is the base, 4 is the in-dex/exponent.Read 34 = 81 three to the fourth power is eighty-one or three tothe power four is eighty-one.

When you square a number, you multiply it by itself. When youcube a number, you multiply it by itself three times.

Example: Read 52 = 25 five squared is twenty-five or the squareof five is twenty-five. Read 53 = 125 five cubed is a hundred andtwenty-five or the cube of five is a hundred and twenty-five.



Properties of powers



Properties of powers

Any base number to the power one is the same base number.

Any base number to the power zero is one.

To multiply powers with the same base, you add the exponents.

To divide powers with the same base, you subtract the exponents.

Example:81 = 830 = 123 · 24 = 23+4 = 27

37 : 35 = = 37−5 = 32



Order of Operations



Order of Operations

1 Simplify the expressions inside grouping symbols, likebrackets, square brackets, ...

2 Find the value of all powers and roots.

3 Multiply and divide in order from left to right.

4 Add and subtract in order from left to right.

B E D M A SB - bracketsE - exponentsDM - divide or multiply (left to right)AS - add subtract (left to right)


Education

Counting Numbers