Just like any language, math has actually a way to connect ideas. One algebraic expression is a compact method of explicate mathematical objects using a combination that numbers, variables (letters), and arithmetic operationsnamely addition, subtraction, multiplication, and also division.

You are watching: Five less than the product of a number and 3 is 14

In various other words, the 3 main contents of algebraic expressions space 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 examples that can assist you obtain familiarized through the operations of addition, subtraction, multiplication,and division.


the sum of x and also 5 → x+5


the difference of y and 3 → y-3


the product of n and 2 → 2n


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

Writing Algebraic expressions Step-by-Step examples

Let’s walk over an ext examples.

Example 1: The sum of twice a number and 3

Answer: Let change x be the unknown number. So twice a number way 2x. The amount (use to add symbol) of double a number and also 3 deserve to be composed as 2x+3.

Example 2: The difference of triple a number and 5

Answer:Let change y be the unknown number. Therefore triple a number method 3y. The difference (use minus symbol) of triple a number and also 5 need to be composed as 3y - 5.

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

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

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

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

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

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

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

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

the product that 7 and also w is expressed as 7wthe quotient the 2 and also 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 indigenous or state to typical Addition, Subtraction, Multiplication, and Division

Now, let’s walk over some common words or unit volume that define the 4 arithmetic operations. It is an important that girlfriend knowthese native or phrases to be effective in composing or interpreting any kind of given algebraic expression.


Math Phrases into Algebraic Expressions

The an essential to finding out is to study a lot of examples!

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

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