Just like any language, math has actually a means to communicate ideas. One algebraic expression is a compact means of describing mathematical objects using a combination the numbers, variables (letters), and arithmetic operationsnamely addition, subtraction, multiplication, and division.

You are watching: The product of 5 and x

In other words, the three main components of algebraic expressions room numbers, variables, and also arithmetic operations.

Numbers or Constants

Examples:1, 6, 8, 27, 32, etc.

Variables or Letters

Examples:x, y, a, h, p, etc.

Arithmetic Operations

Examples:+ (addition), - (subtraction) , \times (multiplication) , ÷ (division)

The complying with are easy instances that can help you get familiarized v the operations of addition, subtraction, multiplication,and division.


the sum of x and 5 → x+5


the difference of y and 3 → y-3


the product the n and also 2 → 2n


the quotient the k and 7 → \Largek \over 7

Writing Algebraic expression Step-by-Step examples

Let’s walk over more examples.

Example 1: The amount of double a number and 3

Answer: Let variable x it is in the unknown number. So twice a number means 2x. The amount (use to add symbol) of twice a number and 3 can be created as 2x+3.

Example 2: The distinction of triple a number and 5

Answer:Let change y it is in the unknown number. So triple a number means 3y. The difference (use minus symbol) of triple a number and also 5 need to be written as 3y - 5.

Example 3:The amount of the quotient that m and 2, and also the product the 4 and also n.

Answer:In this case, the unknown numbers space already noted as m and also n. That’s one much less thing come worry.

The key is to recognize that we room going come add a quotient and a product.

the quotient of m and also 2 is expressed together \Largem \over 2the product the 4 and n is expressed together 4n

Therefore, the sum of the quotient and product is \Largem \over 2 + 4n.

Example 4: The difference of the productof 7 and w, and also the quotient the 2 and v.

Answer: In this case, the unknown numbers have actually been assigned with equivalent variables which room w and also v.

The vital is to identify that we space going to subtract the product by the quotient of some expressions.

the product the 7 and w is expressed as 7wthe quotient of 2 and v is expressed as \Large2 \over v

Therefore, the difference of the product and quotient is 7w - \Large2 \over v.

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Common native or terms to typical Addition, Subtraction, Multiplication, and also Division

Now, let’s walk over some common words or phrases that define the 4 arithmetic operations. That is vital that you knowthese words or phrases come be successful in composing or interpreting any type of given algebraic expression.


Math Phrases into Algebraic Expressions

The vital to finding out is to examine a lot of examples!

a number to add 9y + 9
the sum of a number and 10m + 10
total the a number and 5b + 5
a number raised by 4x + 4
h take far 2h − 2
2 take away by a number2 − h
a number minus 11k − 11
11 minus a number11 − k
a number decreased by 7y − 7
the difference of n and 25n − 25
the difference of 25 and also n25 − n
5 less than a numberx − 5
x less than the number 55 − x
the product the r and 44r
7 time a number7p
double a number2x
triple a number3x
a number split by 4w / 4
the quotient the w and 6w / 6
the quotient that 12 and also m12 / m
a number divided by 3f / 3
t end 7t / 7
5 right into a numbera / 5
a number right into 55 / a
the sum of x and 7 separated by 2( x + 7 ) / 2
the difference of m and also 3 over 5( m − 3) / 5
11 more than the product the 3 and y3y + 11
6 much less than the quotient that c and also 10( c / 10 ) − 6
3 minus the product the 5 and also a number3 − 5x
the sum of 5 and the quotient of z and also 7( z / 7 ) + 5
the difference of double a number and also 32m − 3

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