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 ConstantsExamples:1, 6, 8, 27, 32, etc.
Variables or LettersExamples:x, y, a, h, p, etc.
Arithmetic OperationsExamples:+ (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.
Additionthe sum of x and 5 → x+5
Subtractionthe difference of y and 3 → y-3
Multiplicationthe product the n and also 2 → 2n
Divisionthe 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 4nTherefore, 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 vTherefore, 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!
| MATH PHRASES | ALGEBRAIC EXPRESSIONS |
| a number to add 9 | y + 9 |
| the sum of a number and 10 | m + 10 |
| total the a number and 5 | b + 5 |
| a number raised by 4 | x + 4 |
| h take far 2 | h − 2 |
| 2 take away by a number | 2 − h |
| a number minus 11 | k − 11 |
| 11 minus a number | 11 − k |
| a number decreased by 7 | y − 7 |
| the difference of n and 25 | n − 25 |
| the difference of 25 and also n | 25 − n |
| 5 less than a number | x − 5 |
| x less than the number 5 | 5 − x |
| the product the r and 4 | 4r |
| 7 time a number | 7p |
| double a number | 2x |
| triple a number | 3x |
| a number split by 4 | w / 4 |
| the quotient the w and 6 | w / 6 |
| the quotient that 12 and also m | 12 / m |
| a number divided by 3 | f / 3 |
| t end 7 | t / 7 |
| 5 right into a number | a / 5 |
| a number right into 5 | 5 / 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 y | 3y + 11 |
| 6 much less than the quotient that c and also 10 | ( c / 10 ) − 6 |
| 3 minus the product the 5 and also a number | 3 − 5x |
| the sum of 5 and the quotient of z and also 7 | ( z / 7 ) + 5 |
| the difference of double a number and also 3 | 2m − 3 |
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