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# Writing Algebraic Expressions And Equations

Ms. Lizzy likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.

In this case, start assuming stuff, like ‘g’ for the number of groups in Lizzy’s class. Because there are 2 groups, you’ll have something like ‘2g’. The algebraic expression where the letters you allocate like ‘g’ and such like are called variables.

Take a look at these ridiculously easy expressions:

Sum of five and two = 5 + 2

Sum of five and a number = 5 + x [‘x’ is the variable representing ‘a number’]

nine increased by a number x = 9 + x

fourteen decreased by a number p = 14 – p

seven less than a number t = t – 7

the product of 9 and a number n = 9 * n

thirty-two divided by a number y = 32 ÷ y

five more than twice a number = 2n + 5

the product of a number and 6 = 6n

seven divided by twice a number = 7 ÷ 2n

three times a number decreased by 11 = 3n – 11

If you’re someone who likes to dabble in definitions, here’s what you need to know…

A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change.
An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.

With these simple Algebraic Expressions, you can better understand the next section, that of writing Algebraic Equations.

Stacy has $17 in her piggy bank. How much money does she need to buy a game that costs$68?

If this is your query to convert into algebraic equation form, here’s how you do it…

‘x’ represents the amount of money Stacy needs. Then, 17 + x = 68 as the question provides.

To figure out ‘x’, isolate it and send its numerical partner to the other side along with the math symbol it’s associated with. Remember that when these math symbols shift sides this way, they change their natures and become the opposite of who they are.

You now have 68 – 17

So, x= 51 and Stacy needs \$51 to buy the game.

‘x’ is the variable, and 17 + x = 68 is the algebraic equation. Isn’t it easy?

Here are some more Algebraic Equations that are certain to prove to you just how easy it is to write them:

A number increased by nine is fifteen: y + 9 = 15

Twice a number is eighteen: 2n = 18

Four less than a number is twenty: x – 4 = 20

A number divided by six is eight: (k / 6) = 8

Twice a number, decreased by twenty-nine, is seven: 2t – 29 = 7

Thirty-two is twice a number increased by eight: 32 = 2a + 8

The quotient of fifty and five more than a number is ten: 50 / (n + 5) = 10

Twelve is sixteen less than four times a number: 12 = 4x – 16

That’s all there is to the basics of writing Algebraic Expressions and Algebraic Equations.