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Algebra: fun facts and quiz
The essentials in 7 ideas, with fun facts, an illustrated story and a quiz to see how much you know.
The essentials
What Algebra Is
Algebra uses letters to stand for unknown numbers, so we can reason about them. If x + 3 = 10, then x must be 7.
Key fact
“Algebra” comes from Arabic “al-jabr”, in a 9th-century book.
Balancing Equations
An equation is like a balance scale: whatever you do to one side, you do to the other. That’s how you get the unknown on its own.
Key fact
The equals sign was invented in 1557 by Robert Recorde.
Order of Operations
Maths has a set order: brackets first, then powers, then multiplication and division, then addition and subtraction. So 2 + 3 × 4 is 14, not 20.
Key fact
Many viral maths puzzles are really about this order.
Patterns & Sequences
Algebra describes patterns. In 2, 4, 6, 8…, the nth number is 2n. In the Fibonacci sequence, 1, 1, 2, 3, 5, 8…, each number is the sum of the two before.
Key fact
Fibonacci numbers show up in sunflower seed spirals.
Graphs & Lines
Equations can be drawn as graphs. y = 2x makes a straight line that climbs 2 for every 1 across; that climb is called the slope.
Key fact
René Descartes linked algebra and geometry with the coordinate grid.
Everyday Formulas
A formula is an equation you can reuse. Speed = distance ÷ time; the area of a rectangle = length × width.
Key fact
Spreadsheets are full of formulas.
Powers
Powers are repeated multiplication: 3² = 9 and 2¹⁰ = 1,024. Powers grow fast, which is why doubling adds up so quickly.
Key fact
In theory, paper folded 42 times would reach the Moon.
Fun facts
Using x for an unknown was popularised by René Descartes in 1637.
Recorde chose two parallel lines because, he wrote, “no two things can be more equal”.
Simple calculators don’t always follow the order: many basic ones work left to right, so 2 + 3 × 4 gives 20.
Divide a Fibonacci number by the one before it and you get closer and closer to the golden ratio, about 1.618.
Legend says Descartes thought up coordinates while watching a fly crawl across his ceiling.
The first spreadsheet program, VisiCalc (1979), is often credited with making personal computers useful for business.
Legend says a chess inventor asked for rice doubling on each square. The last square alone would need over 9 quintillion grains.
Story: The Quick Sum
The Quick Sum
Germany, 1780s. A teacher asks his class to add up every number from 1 to 100, hoping for a quiet hour. So the story goes.
Within moments, young Carl Friedrich Gauss hands in his slate with a single number on it: 5,050.
He had paired them up, 1 + 100, 2 + 99 and so on: fifty pairs of 101. He grew up to be one of the greatest mathematicians ever.
True or false?
Tap your answer to see if you got it, and why.
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Question 1 of 10
If x + 3 = 10, then x = 7.
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True. 7 + 3 = 10.
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Question 2 of 10
Whatever you do to one side of an equation, you do to the other.
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True. That keeps it balanced.
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Question 3 of 10
2 + 3 × 4 equals 14.
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True. Multiply first: 3 × 4 = 12, then add 2.
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Question 4 of 10
In the Fibonacci sequence, each number is the sum of the two before.
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True. 5 + 8 = 13, and so on.
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Question 5 of 10
y = 2x makes a straight line.
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True. Every step across climbs by 2.
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Question 6 of 10
Speed equals distance divided by time.
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True. 100 km in 2 hours is 50 km/h.
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Question 7 of 10
Any number to the power of 0 equals 1.
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True. By convention, so the rules stay consistent.
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Question 8 of 10
In algebra, letters can only stand for the number 1.
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False. They can stand for any number.
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Question 9 of 10
The equals sign has been used since ancient Egypt.
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False. It was invented in 1557.
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Question 10 of 10
You always work from left to right, whatever the operations.
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False. Multiplication and division come before addition.
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