Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.
Here's the short answer to "what is algebra?" Algebra is the part of math that uses letters, like x, to stand for numbers. The letter can be a number you don't know yet, or a number that changes. Algebra lets you find missing numbers and write rules that work for every number at once.
That definition will make more sense after you try something. Do the trick below first.
Your number
Any number, written as xhidden until the end
Press Next step and follow along.
Change your number and run it again. You'll get 5 every time. Arithmetic can only check one number at a time. Algebra checked every number in four lines. The x was there at the start and disappeared when you subtracted it, so only the 5 was left. That's what algebra is for: reasoning about numbers you don't know.
Start with 100. Double it, add 10, halve it, then subtract 100. What do you get?
5. 100 × 2 = 200, 200 + 10 = 210, 210 ÷ 2 = 105, and 105 − 100 = 5. In algebra: x + 5 − x = 5 for every number.
You already did algebra in early school when you filled in the missing number. What goes in the box?
In algebra we replace the box with a letter: x + 7 = 12, so x = 5. A letter is easier to write and say than "the empty box," and if a problem has two missing numbers you can call them x and y.
A letter that stands for a number is called a variable.
Any letter works. Mathematicians started using x, y and z for unknowns after René Descartes did so in 1637.
What number goes in the box: □ − 3 = 9?
12. 12 − 3 = 9. Written with a letter, x − 3 = 9, so x = 12.
A pizza costs $8, plus $2 for each topping. Move the slider. The arithmetic changes every time. The algebra never does.
Arithmetic
8 + 2 × 3 = 14
Good for this one pizza
Algebra
cost = 8 + 2t
Works for every pizza, where t is the number of toppings
A rule written with letters is called a formula.
You've probably seen others: distance = speed × time, or the area of a rectangle, A = l × w. Phone plans, recipes, sales discounts and spreadsheets all run on formulas like these.
Use cost = 8 + 2t. How much is a pizza with 6 toppings?
$20. Replace t with 6: 8 + 2 × 6 = 8 + 12 = 20.
Words like "a number" turn into a letter. Pick the algebra that matches each phrase.
Notice the difference between the first four and the last one. x + 5 is an expression: a phrase with no equals sign. 4x − 3 = 21 is an equation: a full sentence that says two things are equal. Solving an equation means finding the number that makes it true. Here it's x = 6.
Answer: x = 6
Writing "a number decreased by 4" as 4 − x. Start with the number, then take 4 away: x − 4. The same goes for "4 less than a number". Order matters with subtraction: if x = 10, then x − 4 = 6, but 4 − x = −6.
The word comes from a book written in Baghdad around 820 by the mathematician Muhammad ibn Musa al-Khwārizmī. Its title includes al-jabr, Arabic for "restoring" or "putting broken parts back together." He wrote every problem in words. Switch between his style and ours.
"Square" meant the unknown number times itself, and "root" meant the unknown number. The answer is 3, since 9 + 30 = 39.
In al-Khwārizmī's problem, what did the word "root" mean?
The unknown number. Today we write it as x, and "a square" is x2.
Algebra is math with letters. A letter such as x stands for a number, and you use the rules of arithmetic to work out what that number is or to describe how numbers are related.
Arithmetic calculates with known numbers, like 8 + 2 × 3 = 14. Algebra uses letters for numbers that are unknown or that change, like cost = 8 + 2t, so one rule covers every case.
A variable is a letter or symbol that stands for a number. In x + 7 = 12, the variable is x, and its value is 5.
Any letter works. Using x, y and z for unknown numbers became the habit after René Descartes did it in his 1637 book La Géométrie.
No single person invented it. Babylonians and Egyptians solved equation-style problems thousands of years ago. The Persian mathematician al-Khwārizmī, working in Baghdad around 820, wrote the first book that treated algebra as its own subject, and its title gave algebra its name.
Most people find it strange at first because of the letters. Once you see that a letter is just a stand-in for a number, algebra uses the same adding, subtracting, multiplying and dividing you already know.
Now check what you learned. Every answer is explained, and each time you play you get new questions.
Quiz Complete!
Keep learning
Share this page