Algebra

Algebra sounds grown-up, but it is really just a clever shortcut you already use. When you say "I have some sweets and Mum gives me 3 more", that "some" is an unknown number — and in algebra we give it a letter instead of leaving it blank. A letter is just a placeholder for a number we do not know yet. Once you see that, algebra becomes friendly. Let's crack the code.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to use a letter for an unknown, write and read expressions, simplify like terms, and evaluate by substitution. Here we go.

Using a letter for an unknown

In algebra we use a variable — usually a letter such as n — to stand for an unknown number. If you have n stickers and get 5 more, you now have n plus 5 stickers. The letter holds the place of the mystery number until you find out what it is.

A neat habit: when a number multiplies a letter, you write them side by side. So 3 times n is written as 3n, with no times sign needed. The number in front is how many of that letter you have.

Writing and reading expressions

An expression describes a situation using letters and numbers. Read it carefully both ways — from words to symbols and back. "Twice a number, then add 7" becomes 2n plus 7. "A number shared by 4" becomes n over 4.

Take care with order in subtraction: "5 less than a number" is n minus 5, not 5 minus n. Read slowly and match each word to its symbol.

Simplifying like terms

When an expression has like terms, you can collect them into one. Just as 2 apples plus 3 apples is 5 apples, 2n plus 3n is 5n. You add the numbers in front and keep the same letter.

But you can only combine terms with the same letter, and plain numbers stay separate from letter terms. So 4n plus 3 plus 2n simplifies to 6n plus 3 — the 6n and the 3 cannot merge because one has a letter and one does not.

Evaluating by substitution

To substitute means to replace the letter with a given number and work out the answer. If n equals 4, then 2n plus 1 becomes 2 times 4 plus 1, which is 8 plus 1, equal to 9. Always do the multiplying before the adding.

Substitution turns an expression into a plain number. It is how you check an answer or find a value once the unknown is known.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. Mei has y dollars and earns 6 more. How much does she have now?

   y plus 66y6 minus y

2. Which expression means a number multiplied by 7?

   7nn plus 7n minus 7

3. Which expression means 8 less than a number?

   n minus 88 minus n8n

4. Simplify 6n plus 3n.

   9n918n

5. Simplify 4n plus 2 plus n.

   5n plus 27n6n

6. If n equals 5, what is the value of 3n plus 4?

   191227

See my score