MATHS SYMBOLS - INVERSE OPERATIONS - ADDITION and SUBTRACTION - MULTIPLICATION and DIVISION - MODULO - EXPONENTIATION and ROOT - EXPONENTIAL and LOGARITHM - CALCULATION RESULTS

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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