A Number P Minus 19

Writing Algebraic Expressions

Math, like any other language, has a style of communicating ideas. An algebraic expression is a curtailed way of describing mathematical objects through the utilize of numbers, variables (letters), and arithmetic operations such as addition, subtraction, multiplication, and division.

The iii principal components of algebraic expressions are numbers, variables, and arithmetic operations.

Numbers or Constants

Examples: $1$ , $6$ , $eight$ , $27$ , $32$ , etc.

Variables or Letters

Examples: $10$ , $y$ , $a$ , $h$ , $p$ , etc.

Arithmetic Operations

Examples: $+$ (addition), $-$ (subtraction) , $\times$ (multiplication) , $\div$ (sectionalisation)

The following are like shooting fish in a barrel examples that tin help you get familiar with the operations of addition, subtraction, multiplication, and division.

Addition

the sum of $x$ and $five$ → $10+5$

Subtraction

the divergence of $y$ and $3$ → $y-iii$

Multiplication

the product of $north$ and $2$ → $2n$

Sectionalization

the caliber of $k$ and $7$ → $\Large{{k \over 7}}$

Writing Algebraic Expressions Stride-past-Step Examples

Let'due south go over more examples.

Example 1: The sum of twice a number and $3$

Answer: Let variable $x$ be the unknown number. So twice a number means $2x$ . The sum (utilize plus symbol) of twice a number and $three$ can be written every bit $2x+3$ .

Example 2: The difference of triple a number and $v$

Answer: Allow variable $y$ be the unknown number. So triple a number means $3y$ . The difference (use minus symbol) of triple a number and $5$ should be written as $3y - five$ .

Example 3: The sum of the quotient of $g$ and $2$ , and the product of $4$ and $due north$ .

Answer:In this case, the unknown numbers are already provided as $m$ and $due north$ . That's ane less thing to worry most.

The cardinal is to recognize that we are going to add together a quotient and a product.

the quotient of $m$ and $two$ is expressed as $\Big{{one thousand \over 2}}$

the production of $iv$ and $n$ is expressed every bit $4n$

Therefore, the sum of the quotient and product is ${\Big{{m \over ii}}} + 4n$ .

Example 4: The divergence of the production of $7$ and $due west$ , and the caliber of $two$ and $v$ .

Reply: In this case, the unknown numbers accept been assigned with respective variables which are $west$ and $5$ .

The cardinal is to recognize that we are going to subtract the product by the quotient of some expressions.

the product of $seven$ and $w$ is expressed every bit $7w$

the quotient of $2$ and $five$ is expressed as $\Large{{two \over v}}$

Therefore, the departure of the production and quotient is $7w - {\Large{{two \over 5}}}$ .

Common Words or Terms to Mean Addition, Subtraction, Multiplication, and Division

Let'due south go over some common words or phrases that depict the four arithmetics operations. It is critical that you understand these words or phrases in gild to successfully write or interpret whatsoever given algebraic expression.

algebraic terms which imply addition are plus, more than, sum, and, total, greater than, and increased by.

algebraic terms which imply subtraction are minus, difference, take away, subtract, less than, decreased by, and less.

algebraic terms which imply multiplication are multiply, product, double, twice, triple, quadruple, and times.

algebraic terms which imply division are quotient, divided by, ratio, share, into, and over.

Math Phrases into Algebraic Expressions

The primal to learning is to study a LOT of examples!

MATH PHRASES	ALGEBRAIC EXPRESSIONS
a number plus ix	y + 9
the sum of a number and 10	m + x
total of a number and 5	b + 5
a number increased by 4	x + 4
h take away 2	h − ii
2 take away by a number	2 − h
a number minus eleven	k − 11
11 minus a number	eleven − k
a number decreased past 7	y − 7
the departure of due north and 25	n − 25
the difference of 25 and n	25 − n
five less than a number	10 − five
x less than the number 5	5 − 10
the product of r and 4	4r
seven times a number	7p
double a number	2x
triple a number	3x
a number divided by 4	w / 4
the quotient of w and 6	west / 6
the quotient of 12 and m	12 / m
a number divided past 3	f / 3
t over 7	t / 7
v into a number	a / five
a number into 5	5 / a
the sum of x and seven divided past 2	( 10 + 7 ) / 2
the departure of m and iii over five	( m − iii) / 5
11 more than than the production of three and y	3y + 11
vi less than the quotient of c and ten	( c / x ) − 6
3 minus the production of v and a number	three − 5x
the sum of five and the quotient of z and 7	( z / 7 ) + 5
the difference of twice a number and 3	2m − three