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An algebraic expression is a mathematical phrase that may contain numbers, variables, and operators. Numbers have fixed values. Variables are symbols with unknown values and are usually represented by the letters of the alphabet. Operators are the things that we do with numbers such as addition, subtraction, multiplication, and division.

Example 1: Twice a number

We can think of it as doubling a number or two times a number. Since we don't know the exact value of the number, we'll call it "n". Therefore, for this, we have \(2n\).


Example 2: A number decreased by 5

The phrase "decreased by" is the same as subtracted by. That means whatever the number is, we subtract it by \(5\). Therefore, \(n-5\).


Example 3: One-half of a number

One-half implies dividing by \(2\). Here, we divide the unknown number by \(2\) which gives us \(\large{n \over 2}\).


Example 4: The sum of a number and \(7\)

Sum is addition. Since we have an unknown number "n" being added to \(7\), this gives us \(n+7\).


Example 5: \(4\) less than a number

We need to be a bit careful here. "\(4\) less than" means we are taking \(4\) from the number, and not the other way around. Thus, we have \(n-4\).


Example 6: The difference of a number and \(10\)

When we use "difference of", the order matters. We are subtracting the number by \(10\) which means we have \(n-10\). It is wrong to write it as \(10-n\) because \(10-n\) means the difference of \(10\) and a number which is different.


Example 7: The quotient of a number and \(3\)

The word quotient means to divide. We divide a number by \(3\). Therefore, we get \(\large{n \over 3}\).


Example 8: The sum of twice a number and \(9\)

Two things are going on here. First, a number is multiplied by \(2\). Then \(9\) is added to whatever is the product. Therefore, we have \(2n+9\).