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

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.    ## Math Phrases into Algebraic Expressions

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

 MATH PHRASES ALGEBRAIC EXPRESSIONS a number add to 9 y + 9 the sum of a number and also 10 m + 10 total that a number and 5 b + 5 a number increased by 4 x + 4 h take far 2 h − 2 2 take far by a number 2 − h a number minus 11 k − 11 11 minus a number 11 − k a number reduced by 7 y − 7 the difference of n and 25 n − 25 the difference of 25 and n 25 − n 5 less than a number x − 5 x much less than the number 5 5 − x the product that r and also 4 4r 7 times a number 7p double a number 2x triple a number 3x a number separated by 4 w / 4 the quotient that w and also 6 w / 6 the quotient that 12 and m 12 / m a number divided by 3 f / 3 t end 7 t / 7 5 right into a number a / 5 a number into 5 5 / 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 y 3y + 11 6 much less than the quotient that c and 10 ( c / 10 ) − 6 3 minus the product the 5 and also a number 3 − 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 3 2m − 3

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