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.

Addition

the sum of x and 5 → x+5

Subtraction

the difference of y and 3 → y-3

Multiplication

the product the n and also 2 → 2n

Division

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.

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Math Phrases into Algebraic Expressions

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

MATH PHRASESALGEBRAIC EXPRESSIONS
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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