Equations and balances
📖 In short
On one side of a balance are 3 apples and a closed bag, and on the other side 8 apples, and the balance is level. How many apples are in the bag? 5! This is an equation: 3 + ? = 8. Solving the equation means finding the hidden number that makes both sides equal.
🤩 Did you know?
- In every European language, the word “algebra” comes from the Arabic word “al-jabr”.
- Al-Khwarizmi wrote the book “Al-jabr wa-l-muqabala” in Baghdad more than 1100 years ago.
- The = sign was invented by an English scholar in 1557, because “nothing is more equal than two parallel lines”.
- When you say “I'm twice as old as my brother, and my brother is 4”, you're solving an equation!
🔎 Find out more
🌟 The equals sign
The = sign doesn't mean “the answer is”, but “both sides are equal”, like a level balance. That's why we can write 8 = 3 + 5, or 4 + 4 = 6 + 2.
🔍 Keeping the balance
If we take 3 apples off each side, the balance stays level: the bag is left alone on one side, and 5 apples on the other. That's how we solve an equation: do the same thing to both sides.
💡 Inverse operations
To find the hidden number we use the opposite operation: in ? + 7 = 12 we subtract: 12 − 7 = 5. And in ? × 4 = 20 we divide: 20 ÷ 4 = 5.
🎯 A letter instead of a number
When we're older we write a letter instead of the question mark, like x: x + 7 = 12. This is “algebra”, which al-Khwarizmi wrote the first book about, and the word “algebra” comes from its title.
🧮 Worked examples
- □ + 6 = 15 ⇒ □ = 915 − 6 = 9.
- □ − 4 = 10 ⇒ □ = 1410 + 4 = 14.
- 3 × □ = 27 ⇒ □ = 927 ÷ 3 = 9.
📚 Key words
- Equation
- A calculation with an unknown number and an equals sign
- Unknown
- The hidden number we're looking for
- Algebra
- A branch of math that uses letters instead of unknown numbers
🧪 Try it at home
Make a balance from a coat hanger and two small bags. Put 3 blocks in one bag and 7 in the other. How many blocks do you add to the first bag to make it balance? Write the equation.
🧩 Test yourself
1 What is the hidden number in: ? + 4 = 11
2 What does the = sign mean?
3 Which Arabic word does “algebra” come from?