Unit 1 integers

Bilingual Program

MATHS – 2nd CSE (Compulsory Secondary Education) Unit 1: INTEGERS AND DIVISIBILITY NATURAL NUMBERS

natural number Roman number a < b --- a is smaller than b a > b --- a is bigger than b a = b --- a is equal to b unit ten hundred unit of thousand ten of thousand hundred of thousand unit of million ten of million hundred of million addition subtraction or difference product or multiplication division The 6-times table

dividend divisor quotient remainder whole division exact division combined operations priority or hierarchy of the operations smallest to biggest biggest to smallest numerical straight line approximation by defect approximation by excess error (in an approximation) infinity/ies set decimal number system digit or figure

INTEGERS

integer positive number negative number absolute value opposite of a number

sign rule distance to zero degrees below zero symmetrical with respect to numerical value

POWERS AND ROOTS

power base index, indices square number square root exact root whole root To square a number is to multiply it by itself.

Departamento MatemĂĄticas

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Bilingual Program Reading operations: 3+5 = 8 12 – 3 = 9 8 x 4 = 32 28 : 4 = 7

three plus five equals eight twelve minus seven equals nine eight times four equals thirty-two (or eight multiplied by four equals thirty-two) twenty-eight divided by four equals seven (or twenty-eight divided into four equals seven)

25 5 2

4 73

four squared seven cubed

154 65

The squareroot of twenty five is five

fifteen (raised) to the power of four/ fifteen to the fourth power/ fifteen to the four

289

sixty five to the power of two hundredand eighty nine

Réstale X a Y

---

Escribe en una sola potencia Eleva al cuadrado esto

Subtract X from Y ---

---

i.e. Subtract 3 from 8

Write as a single power Calculate the square of this or Square this.

Tienes que sacar raiz cuadrada de … --- You have to calculate the square root of ...

Saca la raiz cúbica de…

---

Calculate the cube root of… or Take the cube root of…

DIVISIBILITY

divisibility rules divisible (by) prime number composite number (or compound number) common multiples common divisors

prime factors write a number in prime factor form prime numbers between them highest common factor (HCF) or greatest common factor (GCF) lowest common multiple (LCM) or least common multiple (LCM)

DEFINITIONS:

o

The multiples of an integer are found by multiplying the integer by another.

o

The divisors of an integer (or factors) are those numbers that divide the number without leaving a remainder.

o

A prime number is a natural number that has only two divisors, itself and one. (1 is not a prime/compound number)

o

A number is a compound number (or composite number) when it is not a prime number.

o

The lowest common multiple (LCM) of two or more numbers is the smallest of the multiples common to all of them.

The highest common factor (HCF) of two or more numbers is the largest of the divisors common to all of them.

o

Departamento Matemáticas

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Bilingual Program

The Divisibility Rules These rules let you test if one number is divisible by another, without having to do too much calculation!

A number is divisible by:

If:

Example:

2

The last digit is even (0,2,4,6,8)

128 is 129 is not

3

The sum of the digits is divisible by 3

381 (3+8+1=12, and 12รท3 = 4) Yes

4

The last 2 digits are divisible by 4

1312 is (12รท4=3) 7019 is not

5

The last digit is 0 or 5

175 is 809 is not

6

The number is divisible by both 2 and 3

114 (it is even, and 1+1+4=6 and 6รท3 = 2) Yes 308 No If you double the last digit and subtract it from the rest of the number and the answer is:

7

0, or divisible by 7

672 (Double 2 is 4, 67-4=63, and 63รท7=9) Yes 905 No

(Note: you can apply this rule to that answer again if you want) The sum of the digits is divisible by 9

9

10 11

1629 (1+6+2+9=18, and again, 1+8=9)Yes

(Note: you can apply this rule to that answer again if you 2013 (2+0+1+3=6) No want)

The number ends in 0

If you sum every second digit and then subtract all other digits and the answer is:

220 is 221 is not

1364 ((3+4) - (1+6) = 0) Yes 3729 ((7+9) - (3+2) = 11) Yes

0, or divisible by 11

Departamento Matemรกticas

25176 ((5+7) - (2+1+6) = 3) No

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