The document outlines various mathematical operations including addition, subtraction, multiplication, division, exponentiation, and logarithm. It discusses direct and inverse calculations, as well as special cases involving division by zero and modulo operations. Additionally, it provides examples of each operation and includes a sitography for further reference.

1. ENZO EXPOSYTO
MATHS
SYMBOLS
2 - OPERATIONS
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2. 2+3 5-3 2x3 6:3
OPERATIONS
23 ∛8 2x log2(2x)
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3.
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4. 1 - Calculation Results 5
2 - Inverse Operations 6
3 - Direct and Inverse - Addiction and Subtraction 10
4 - Direct and Inverse - Multiplication and Division 12
5 - Division 0/n, Division n/0, Division 0/0 18
6 - Modulo (mod) 25
7 - Direct and Inverse - Exponentiation and Root 27
8 - Direct and Inverse - Exponential and Logarithm 31
9 - SitoGraphy 35
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5. Enzo Exposyto 5

6. INVERSE
OPERATIONS
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7. Enzo Exposyto 7

8. EXPONENTIATION
and
ROOT
ARE
INVERSE
OPERATIONS
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9. EXPONENTIAL
and
LOGARITHM
ARE
INVERSE
OPERATIONS
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10. DIRECT
and
INVERSE
CALCULATIONS
Addition
and
Subtraction
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11. Addition and Subtraction
+ plus sign;
4 + 6 means the addition of 4 and 6; 4 + 6 = 10.
4 is a summand (or the augend),
6 is a summand (or the addend),
the result is 10 (sum):
we start from 4 (beginning),
we add 6 and we get 10
- minus sign;
10 − 6 means the subtraction of 6 from 10; 10 − 6 = 4.
10 is the minuend,
6 is the subtrahend,
the result is 4 (difference):
we restart from 10, we subtract 6
and we come back to 4 (beginning)
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12. DIRECT
and
INVERSE
CALCULATIONS
Multiplication
and
Division
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13. Multiplication
× multiplication sign;
3 × 4 means the multiplication of 3 by 4; 3 × 4 = 12
... times ...;
... multiplied by ...;
a x b is "a times b";
a multiplied by b
• multiplication dot, multiplication sign;
a b is equivalent to a × b or "a times b”
* multiplication sign (Computer Science);
a*b is equivalent to a × b or "a times b
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14. Division
÷ division sign;
12 ÷ 4 means the division of 12 by 4; 12 ÷ 4 = 3.
12 divided by 4 is 3;
12 is the dividend, 4 is the divisor;
the result of the division (3) is the quotient;
7 divided by 3 is 2, the remainder is 1
: division sign
/ slash, solidus, virgule, division sign
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15. Multiplication and Division
2 × 3 2 × 3 means the multiplication of 2 by 3; 2 × 3 = 6.
2 is a factor (or the multiplicand),
3 is a factor (or the multiplier),
the result is 6 (product):
we start from 2 (beginning),
we multiply by 3 and we get 6
6 ÷ 3 6 ÷ 3 means the division of 6 by 3; 6 ÷ 3 = 2.
6 is the dividend,
3 is the divisor,
the result is 2 (quotient):
we restart from 6, we divide by 3
and we come back to 2 (beginning)
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16. Fraction
2 fraction two-tenths;
10 2 over ten;
2 is the numerator and 10 is the denominator;
in a fraction,
the numerator is the number that is above the line
and that is divided by the number below the line
(denominator);
the fraction 2 is equal to the decimal .2:
10
2 = .2
10
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17. y divisible or not divisible
| vertical line
x|y if the remainder, when dividing y by x, is 0 then we say:
"x divides y and y is divisible by x";
y divided by x means the same as y ÷ x or y
x
x ∤ y x does not divide y
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18. Division 0
n
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19. Divisions 0
n
0 0 divided by n;
n n ≠ 0, n is not equal to 0;
the result is 0
0 = 0
1
0 = 0
2
0 = 0
3
…
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20. Division n
0
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21. n division by zero (n ≠ 0)
0 1) A first way of looking at division by zero is
that division can always be checked
using multiplication.
Considering the 10 example,
0
setting x = 10 ,
0
if x equals ten divided by zero,
then x times zero equals ten,
but there is no x that,
when multiplied by zero,
gives ten
(or any other number than zero):
so division by zero is impossible
and the result does not exist (DNE).
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22. n division by zero (n ≠ 0)
0 2) Another way of looking at division by zero:
considering again 10
0
(for example, 10 cookies over 0),
it is obvious that there is
no way to evenly distribute 10 cookies to nobody;
so 10,
0
at least in elementary Arithmetic,
is said to be
either meaningless
or impossible.
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23. Division 0
0
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24. Divisions 0
0
0 If, instead of x = 10,
0 0
we have x = 0,
0
then every x satisfies the question
"what number x, multiplied by zero, gives zero?"
Since any number multiplied by zero is zero,
the expression 0 has no defined value
0
and is called an indeterminate form.
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25. Modulo
(mod)
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26. Modulo (mod)
mod modulo;
7 divided by 3 is 2, the remainder is 1
and we write:
7 mod 3 = 1
7 is the dividend,
3 is the divisor,
1 is the remainder
dividend mod divisor = remainder
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27. DIRECT
and
INVERSE
CALCULATIONS
Exponentiation
and
Root
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28. Exponentiation
xn exponentiation;
(x^n) x (raised) to the power of n;
ab means a raised to the power of b:
32 = 3 × 3 = 9
We write 2 times the base 3 and, then, we multiply.
Here, the base x changes and the exponent is a constant
32 3 to the power of 2;
3 raised to the power of 2;
3 is raised to the 2nd power;
3 is the base and 2 is the exponent (the power);
the exponent 2 (or 2nd power) is the square of 3;
3 squared;
3 to the 2nd power is 9;
the power is the product (result) itself: 9 is a power of 3
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29. Root
√ square root;
the (principal) square root of ...;
√ x means the nonnegative number whose square is x
∛ cube root;
the cube root of 8 is 2,
because 2 cubed is 8;
3 (the cube) is the degree (or index),
8 is the radicand
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30. Exponentiation and Root
23 we place the base 2 under the exponent; 23 = 2 x 2 x 2 = 8
We write 3 times the base 2 and, then, we multiply;
therefore, 23 means the cube of 2: 23 = 8.
2 is the base (it changes),
3 is the exponent (it’s a constant when we cube),
the result is 8 (power):
we start from 2 (beginning), we raise it to 3 and we get 8
∛8 ∛8 means the cube root of 8; ∛8 = 2 because 23 = 8
8 is the radicand,
3 is the index (or degree),
the result is 2 (root):
we restart from 8, we ‘do’ the cube root
and we come back to 2 (beginning)
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31. DIRECT
and
INVERSE
CALCULATIONS
Exponential
and
Logarithm (log)
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32. Exponential
2x exponential;
(2^x) 2 is the base
x is the exponent
Here, the base 2 is a constant
and the exponent x changes
e the exponential constant;
e is approximately equal to 2.718281828;
ex
say: “e to the x or the exponential function"
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33. Logarithm (log)
logb(x) logarithm;
say: log (to the) base b of x;
say: log subscript b of x;
b is the base of the logarithm,
x is the antilogarithm;
log2 8 = 3 because 23 = 8
ln(x) natural logarithm;
ln(x) = loge(x)
say: lin of x;
say: "L N" of x;
say: the natural log of x;
ln is defined as logarithm (to the) base e;
ln(e) = 1 because e1 = e
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34. Exponential and Logarithm (log)
23 we place the exponent 3 on the base 2; 23 = 2 x 2 x 2 = 8
We write 3 times the base 2 and, then, we multiply;
therefore, 23 means the cube of 2: 23 = 8.
3 is the exponent (it changes),
2 is the base (a constant if we calculate the log base 2),
the result is 8:
we start from 3 (beginning), we place it on 2 and we get 8
log2(8) log2(8) means the logarithm base 2 of 8;
log2(8) = 2 because 23 = 8
8 is the antilogarithm,
2 is the base,
the result is 3 (logarithm):
we restart from 8, we ‘do’ the log base 2
and we come back to 3 (beginning)
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35. SitoGraphy
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36. http://en.m.wikipedia.org/wiki/Subtraction
http://www.gh-mathspeak.com/examples/grammar-rules/?rule=scripts
http://www.rapidtables.com/math/number/exponent.htm
http://www.rapidtables.com/math/symbols/Algebra_Symbols.htm
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