Writing Algebraic Expressions Examples

Translate the following phrase into an algebraic expression:

3 times 4 more than x.

The first phrase is "3 times," so we write 3 with a set of parentheses to hold whatever we're multiplying 3 by.

3( )

The last phrase is "4 more than x," which means x + 4 (or 4 + x is also correct, since addition is commutative). We put this inside the parentheses and bam, we're done.

3(x + 4)

Translate the following phrase into an algebraic expression:

8 less than 2 times x.

We know that 8 is going to be less than something, which means it's going to be subtracted from something. We can bust out an empty set of parentheses for whatever it's being subtracted from, and then toss in a minus sign and 8.

( ) – 8

Reading on, we see that 8 is being subtracted from "2 times x." We can write 2 multiplied by the variable x by squishing them next to each other. This is what 8 is being subtracted from, so we put it in the parentheses and we're done.

(2x) – 8

Translate the following phrase into an algebraic expression:

The quotient of 5 and a number.

The word "quotient" means we'll be dividing. We can show this in two ways: with a fraction, or with a division symbol. Let's use a fraction.

The first value given is the dividend, or the number on top that's being divided into itty-bitty pieces. We write 5 as the numerator in a fraction and an empty set of parentheses waiting to hold whatever 5 is being divided by.

The next phrase says "a number," some random unknown number which we represent with a variable. Let's use x. Plop it into the parentheses and we can simplify our expression to or just .

Translate the following phrase into an algebraic expression:

Five less than the quotient of twice a number and 11.

The first part reads "five less than," which means we'll be subtracting 5 from something. Don't worry, "something"; we left a set of parentheses for you.

( ) – 5

What is 5 less than? It's less than a quotient. This time we'll represent the quotient with a division symbol, which goes inside the parentheses.

(__ ÷ __) – 5

The first value, or dividend, in the quotient is "twice a number," which means some number doubled, or some number multiplied by 2. We write this as 2x.

(2x ÷ __) – 5

The second value, or divisor, in the quotient is 11. We plug that in and pat ourselves on the back for a job well done.

(2x ÷ 11) – 5