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- The language of algebra
The language of algebra
Algebra is a short way of writing rules about numbers. At GCSE you need to read it, write it and undo it quickly.
How algebra is written
Leave out the × sign: 3 × a × b = 3ab.
Numbers go first: y × 4 = 4y.
Repeated letters use powers: a × a = a2.
Division is written as a fraction: x ÷ 4 = x4.
Numbers go first: y × 4 = 4y.
Repeated letters use powers: a × a = a2.
Division is written as a fraction: x ÷ 4 = x4.
From words to algebra
Read the instructions in order.
"Take 5 from n, then double" is 2(n − 5).
"Double n, then take 5" is 2n − 5.
The order changes the answer, and brackets show what happens first.
"Take 5 from n, then double" is 2(n − 5).
"Double n, then take 5" is 2n − 5.
The order changes the answer, and brackets show what happens first.
Solving with inverse operations
Undo each step in reverse order using the opposite operation.
3x + 7 = 22
Subtract 7: 3x = 15
Divide by 3: x = 5
Check: 3 × 5 + 7 = 22
3x + 7 = 22
Subtract 7: 3x = 15
Divide by 3: x = 5
Check: 3 × 5 + 7 = 22
I think of a number, multiply it by 5 and subtract 8. The answer is 27. What was my number?
- Write an equation: 5n − 8 = 27
- Add 8: 5n = 35
- Divide by 5: n = 7
Answer: 7
Write 3ab, not 3 × a × b. Follow word instructions in order and use brackets when an operation happens to a whole expression. Solve by undoing each step in reverse, then check.
Check you have got it
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