Just like any language, math has a way to communicate ideas. An algebraic expression is a compact way of describing mathematical objects using a combination of numbers, variables (letters), and arithmetic operationsnamely addition, subtraction, multiplication, and division.
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In other words, the three main components of algebraic expressions are numbers, variables, and 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 following are easy examples that can help you get familiarized with the operations of addition, subtraction, multiplication,and division.Addition
the sum of x and 5 → x+5Subtraction
the difference of y and 3 → y-3Multiplication
the product of n and 2 → 2nDivision
the quotient of k and 7 → \Largek \over 7
Writing Algebraic Expressions Step-by-Step Examples
Let’s go over more examples.
Example 1: The sum of twice a number and 3
Answer: Let variable x be the unknown number. So twice a number means 2x. The sum (use plus symbol) of twice a number and 3 can be written as 2x+3.
Example 2: The difference of triple a number and 5
Answer:Let variable y be the unknown number. So triple a number means 3y. The difference (use minus symbol) of triple a number and 5 should be written as 3y - 5.
Example 3:The sum of the quotient of m and 2, and the product of 4 and n.
Answer:In this case, the unknown numbers are already provided as m and n. That’s one less thing to worry.
The key is to recognize that we are going to add a quotient and a product.the quotient of m and 2 is expressed as \Largem \over 2the product of 4 and n is expressed as 4n
Therefore, the sum of the quotient and product is \Largem \over 2 + 4n.
Example 4: The difference of the productof 7 and w, and the quotient of 2 and v.
Answer: In this case, the unknown numbers have been assigned with corresponding variables which are w and v.
The key is to recognize that we are going to subtract the product by the quotient of some expressions.the product of 7 and w is expressed as 7wthe quotient of 2 and 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 Words or Terms to Mean Addition, Subtraction, Multiplication, and Division
Now, let’s go over some common words or phrases that describe the four arithmetic operations. It is critical that you knowthese words or phrases to be successful in writing or interpreting any given algebraic expression.
Math Phrases into Algebraic Expressions
The key to learning is to study a LOT of examples!
|MATH PHRASES||ALGEBRAIC EXPRESSIONS|
|a number plus 9||y + 9|
|the sum of a number and 10||m + 10|
|total of a number and 5||b + 5|
|a number increased by 4||x + 4|
|h take away 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 n||25 − n|
|5 less than a number||x − 5|
|x less than the number 5||5 − x|
|the product of r and 4||4r|
|7 times a number||7p|
|double a number||2x|
|triple a number||3x|
|a number divided by 4||w / 4|
|the quotient of w and 6||w / 6|
|the quotient of 12 and m||12 / m|
|a number divided by 3||f / 3|
|t over 7||t / 7|
|5 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 less than the quotient of c and 10||( c / 10 ) − 6|
|3 minus the product of 5 and a number||3 − 5x|
|the sum of 5 and the quotient of z and 7||( z / 7 ) + 5|
|the difference of twice a number and 3||2m − 3|
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