mathematics as
a language
Group 1
Have you ever wondered why
mathematics is understood
universally, no matter what
country or culture you are
from?
MATH & LANGUAGE
LANGUAGE
Language is a system of communication
that allows people to express thoughts,
ideas, and emotions. It consists of
words, symbols, sounds, and grammar
rules that help in understanding and
sharing information.
MATH & LANGUAGE
MATH
Mathematics is the study of numbers, shapes, patterns, and
logical relationships. It involves operations like addition,
subtraction, multiplication, and division, as well as
advanced concepts like algebra, geometry, and calculus.
Math provides a universal way of understanding and solving
problems through precise and structured reasoning.
MATHEMATICAL LANGUAGE
mathematical language is the system used to communicate
mathematical ideas.
This language consists of some natural language using
technical terms (mathematical terms) and grammatical
conventions that are not common to mathematical
discourse, supplemented by notation for mathematical
formulas.
CHARACTERISTICS
Precise
Concise
Powerful
mathematical
symbols and
language
MATHEMATICAL LANGUAGE
is an extension of natural language (like
English) used in mathematics and science to
express results, theorems, proofs, and logical
deductions with clarity and precision.
MATHEMATICAL SYMBOLS
are characters or figures that represent mathematical
objects, actions on objects, relations between objects,
or structure formulas.
MATHEMATICAL SYMBOL AND
LANGUAGE
are a system used to express mathematical ideas, concepts, and
theories concisely and precisely, using symbols and notation to
represent mathematical objects, operations, and relationships.
MATHEMATICAL EXPRESSION
is a combination of numbers, variables, operators, and
sometimes parentheses, that represent a value.
SYMBOLS
are concise marks, signs, or notations that represent
mathematical operations, quantities, relations, and functions,
enabling the precise and efficient communication of mathematical
concepts.
THE SYMBOLS USE IN
MATHEMATICS
1. The ten digits symbol - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
2. The symbols in arithmetic operations
ADDITION/PLUS +
SUBTRACTION/MINUS -
MULTIPLICATION/MULTIPLY × OR •
DIVISION/DIVIDE ÷ OR /
Special Symbols Word Symbols mathematical expression
√ the square root of 4 is 2 √4=2
= x is equal to 10 x = 10
< 10 is less than 15 10 < 15
> 15 is more than 10 15>10
≤ a is equal or less than 5 a ≤ 5
≥ b is equal or more than 5 b ≥ 5
π the area of a circle is πr² A = πr²
Σ the summation of all natural numbers ΣN
translation of word
expressions to
mathematical symbols
MATHEMATICAL LANGUAGE
Three is added to five is eight
Five less four is one
Forty is subtracted from ninety is fifty
The product of three and five added to six
is 21
Eighty divided by four is twenty
THE SYMBOLS FOR SETS
EXPRESSIONS
Intersection
Union and Universal
Belongs to an element of
subset
Proper subset
FOR EXAMPLE
A B, this means set A intersection set B
A B, this means set A union set B
4 A, this means 4 is an element of the set of A
B ⊂ A, this means B is a subset of A
C ⊆ A, this means is a proper subset of A
SET NOTATIONS
Set A,B,X,Y,N,Q,R,C,O,E,Z
N = Natural numbers Q = Rational Numbers
E = Even Numbers O = Odd Numbers
Z = Integers Z- = Negative Integers
Z+ = Positive Integers R = Real Integers
C = Counting Numbers
FOR EXAMPLE
The symbols for sets
N = [1, 2, 3, 4, 5]
Z = [- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4]
E = [2, 4, 6, 8]
R = [2, 3/2, √5, 1 1/2, - 4]
the set of natural numbers less than 6
the set of integers greater than -5 but less than 5
the set of even numbers less than 9
the set of real numbers
VARIABLES
These are symbols used to represent quantities that vary or take different
values.
1. If a man walks a distance of 5 kilometers in 60 minutes, what is his speed?
Solution: if d represents distance, t represents time, and s for speed. Then, the
statement can be stated this way, "If a man walks at a d (kilometres) in t
(seconds), what is his s (km/s)?
2. Juan is twice the age of Maria.
Solution: In this statement, we can let x be the unknown which is the age of
Maria. We state this as "Juan's age is 2x. In here, the variable x represent the
age of Maria.
OTHER SYMBOLS
plus, add, more, increase, positive
minus, subtract, deduct, less, decrease, negative
multiply
divide
equals
approximately equals to
not equal to
less than, lesser than
more than, greater than
less than or equal to
OTHER SYMBOLS
square root
cube root
summation
percent
factorial
parenthesis (grouping symbol, can be used as multiplication)
brackets ( grouping symbol, can be used as multiplication)
braces ( grouping symbol, can be used as multiplication)
pi
translation of
mathematical sentence
to english sentence and
vice versa
Mathematical Sentences are statements that make up of
symbols and expressions, whether it be numbers or
variables or both, that states a complete thought and
can be defined as true or false.
symbols used as a language = jeje typings
ex. 2log , aqou3h, bk8 som4sakH3t oLo mU3 nd3h k4h
b4h n4ki$$
Let's Read: 7-3<30-20
translation: the difference of 7 and 3 is less than the difference of 30
and 20 is it true or false?
ny=5
translation: the product of n and y is equal to 5 with n being 5 and y
being 2, is this statement true or false?
a² + b² = c²
is this statement true or false?
Determine if the statement is true or false
3x+5=20
x being 5
2y - 5 = 11
y equals 10, determine if
it's true or false
4y - 8 = 16
y equals 6, determine
if it's true or false
3x + 7 = 22
x equals 7, determine if
it's true or false
4^x = 38
x being 7, determine
if its true or false
36 ÷ 9 = 5
determine if it's true
or false
Difficulties in the
mathematical language
Common difficulty in
mathematics
1. Understanding Basic Concepts
A weak foundation in basic arithmetic (addition,
subtraction, multiplication, division) makes it
difficult to progress to more advanced topics like
algebra, geometry, and calculus.
2. Lack of Practice
Math requires regular practice, and gaps in learning
make it harder over time. Without consistent
learning, concepts are easily forgotten.
3. Different Vocabularies Used in Mathematical
Language vs. English
Some mathematical terms have different meanings in
everyday English, leading to confusion.
Like the word "and" means differently in mathematics
from english in use. The mathematics "And" is
equivalent to any operations depending to contexts.
Examples
1. Julian has 5 candies, AND his friend gives him 3
more. How many does he have in total?
2. Each student gets 3 pencils, and there are 5
students. How many do you have?
3. You had 15 candies, and you gave away 5. How many
are left?
FUNCTIONS/CLASSIFICATIONS
OF NUMBERS
Nominal Numbers
attribute of subjects that is used for naming,
labelling and categorizing without using numerical
value or order
Ordinal Numbers
characteristic of subjects that is used for
ranking or ordering.
Cardinal Numbers
used for referring to quantity, measurement
or number of pieces.
Conventions in the
Mathematical Language
A Mathematical Convention
It is a fact, name, notation, or usage
which generally agreed upon by
mathematicians.
PEMDAS
1. Parenthesis: Solve any expressions inside parentheses (or
brackets) first.
2. Exponents: Next, deal with any exponents or roots.
3. Multiplication and
4. Division: Perform multiplication and division from left
to right.
5. Addition and Subtraction: Finally, do addition and
subtraction from left to right.
Bodmas
1. Brackets: Solve any calculations within brackets first.
Orders: Next, deal with any roots
2. Division and Multiplication: Perform these operations
from left to right.
3. Addition and Subtraction: Finally, perform these
operations from left to right.
WELL DONE
Thank You!
