Primary 6 Algebra
A letter stands for a number. Name what the letter means, translate the words carefully, then use familiar arithmetic to simplify or solve.
Introduction to algebra
A letter such as n can stand for a number that we do not know yet. Expressions use the letter to describe what happens to that number. Read n + 3 and 3n differently:
Three more than n: add 3 to one n.
Three times n: multiply n by 3.
Try together
If n = 6, find n + 3 and 3n.
Reveal the answers
n + 3 = 9; 3n = 18.
Using a letter to represent the unknown
In a story, first say exactly what the letter stands for. Then use the actions in the story to write an equation.
Name the unknown in a story
A jar had some marbles. Five more marbles were added. It now has 12 marbles. Let m represent the number of marbles at first. Write an equation.
- Name: m is the number of marbles at first.
- Translate: adding 5 gives the new total.
- Write the equation: the new total is 12.
Answer: m + 5 = 12
Try together
A box had p pencils. Four were taken out, leaving 9. Write an equation using p.
Reveal the answer
p − 4 = 9
Simplifying simple linear expressions
For these examples, there are no brackets. Add or subtract terms with the same letter, and work out the plain numbers separately. Keep unlike terms apart.
Collect like terms
Simplify 3x + 2x + 4 − 1.
- Letter terms: 3x + 2x = 5x.
- Number terms: 4 − 1 = 3.
- Write the expression: keep the x term and the number term.
Answer: 5x + 3
Try together
Simplify 4a + 3a + 6 − 2.
Reveal the answer
7a + 4
Evaluating simple linear expressions by substitution
When the letter's value is given, replace the letter with that number. Multiply before adding or subtracting.
Put the number in place of the letter
Evaluate 3n + 4 when n = 5.
- Substitute: replace n with 5.
- Multiply: 3 × 5 = 15.
- Add: add 4 to 15.
Answer: 19
Try together
Evaluate 2p + 7 when p = 4.
Reveal the answer
15
Solving simple linear equations
In these equations, the number multiplying the letter (the coefficient) is a whole number. Undo addition or subtraction first, then undo multiplication. Keep both sides equal.
Find the unknown number
Solve 3x + 4 = 19.
- Subtract 4: subtract 4 from both sides.
- Simplify: 3x = 15.
- Divide by 3: divide both sides by the coefficient 3.
- Write the value: x = 5.
- Check: put x = 5 into the original equation.
Answer: x = 5
Try together
Solve 2y + 5 = 17.
Reveal the answer
y = 6