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.
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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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