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.

Addition

the sum of x and also 5 → x+5

Subtraction

the difference of y and 3 → y-3

Multiplication

the product of n and 2 → 2n

Division

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.

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Math Phrases into Algebraic Expressions

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

MATH PHRASESALGEBRAIC EXPRESSIONS
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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