PSLE Mathematics · Primary 5 and 6
Algebra
Algebra at PSLE level means using a letter to stand for an unknown number. In Primary 6 you write algebraic expressions in one letter, simplify them, find their value by substitution, and solve simple linear equations with whole number coefficients. These are the first steps towards the algebra you will meet in secondary school, and they also give you a neat way to set out word problems that you might otherwise solve with a model. This guide explains the notation, the rules and the common traps.
What the syllabus expects
- Use a letter to represent an unknown number, and write expressions such as 3n, n + 5 and n/4
- Interpret and write simple algebraic expressions from word descriptions
- Simplify linear expressions in one letter, without brackets, by collecting like terms
- Evaluate an expression by substituting a whole number for the letter
- Solve simple linear equations involving whole number coefficients
- Form an expression or equation from a word problem and use it to find the answer
Using a letter for an unknown
A letter such as n stands for a number you do not know yet. Some notation rules make expressions shorter. 3 × n is written 3n, with the number in front. n ÷ 4 is written n/4. n + n + n = 3n, and 1n is written simply as n. Writing expressions from words needs care with order. '5 more than n' is n + 5. '4 less than n' is n − 4, not 4 − n. 'Twice n' is 2n, and '4 less than twice n' is 2n − 4. If a pen costs y cents, 6 pens cost 6y cents. If 3 friends share k sweets equally, each gets k/3 sweets. Always include the unit when the expression stands for money, length or another measure.
Simplifying expressions
To simplify, collect like terms: add or subtract the terms with the letter, and separately add or subtract the plain numbers. For example, 4k + 7 − k + 3 = 3k + 10, because 4k − k = 3k and 7 + 3 = 10. Similarly, 5p − 2 + 2p − 6 = 7p − 8. Each sign belongs to the term just after it, so in 10 − y + 3y the minus belongs to y, and the expression simplifies to 2y + 10. An expression such as 3k + 10 cannot be simplified any further, because 3k and 10 are unlike terms. Writing 13k would be wrong. At PSLE level, expressions do not contain brackets, so you will not need to expand anything.
Evaluating by substitution
To evaluate an expression, replace the letter with its value and work out the result, multiplying and dividing before adding and subtracting. If m = 6, then 4m − 5 = 4 × 6 − 5 = 24 − 5 = 19, and m/3 + 7 = 6 ÷ 3 + 7 = 2 + 7 = 9. Write the multiplication sign when you substitute, because 4m with m = 6 means 4 × 6 = 24, not the two-digit number 46. Substitution is also the way to check an answer to an equation. If you think n = 7 solves 3n + 5 = 26, substitute it back: 3 × 7 + 5 = 21 + 5 = 26, so the answer is correct.
Solving simple equations
An equation says that two expressions are equal, like a balance with equal masses on each side. Whatever you do to one side, you must do to the other. To solve 3x + 5 = 26, subtract 5 from both sides to get 3x = 21, then divide both sides by 3 to get x = 7. To solve 4y − 9 = 15, add 9 to both sides to get 4y = 24, so y = 6. This matches model drawing: in 3x + 5 = 26, the bar has 3 equal units and an extra 5, so 3 units = 21 and 1 unit = 7. Write each step on a new line with the equals signs lined up, and finish by substituting your answer back into the original equation.
Worked example
Jia Hui is w years old. Her father is 4 times as old as she is. Her brother is 5 years older than she is. (a) Express the sum of their three ages in terms of w. (b) The sum of their ages is 59 years. Find Jia Hui's age and her father's age.
- Jia Hui is w years old, her father is 4w years old and her brother is w + 5 years old.
- Sum of ages = w + 4w + w + 5 = 6w + 5 years, by collecting the w terms (1 + 4 + 1 = 6).
- Form the equation 6w + 5 = 59.
- Subtract 5 from both sides: 6w = 54.
- Divide both sides by 6: w = 9, so Jia Hui is 9 years old.
- Her father is 4 × 9 = 36 years old, and her brother is 9 + 5 = 14 years old.
- Check: 9 + 36 + 14 = 59.
Answer: (a) (6w + 5) years (b) Jia Hui is 9 years old and her father is 36 years old.
Common mistakes
- Reversing a subtraction. '4 less than n' is n − 4. Writing 4 − n means n less than 4, which is a different number.
- Reading 3n as a two-digit number. If n = 5, then 3n = 3 × 5 = 15, not 35. Put in the × sign when you substitute.
- Combining unlike terms, such as writing 2k + 5 as 7k. A letter term and a plain number cannot be added together.
- Forgetting that n means 1n. n + 3n = 4n, not 3n, so count the hidden 1 when collecting like terms.
- Doing an operation to only one side of an equation. If you subtract 5 on the left, subtract 5 on the right as well, or the balance is broken.
- Not checking the solution. Substituting back into the original equation takes seconds and catches arithmetic slips.
Exam tips
- Underline phrases such as 'more than', 'less than' and 'times' and translate them one at a time, paying attention to the order of subtraction.
- Line up the equals signs when solving an equation and write what you did to both sides, so each step can be checked.
- Answer the question that is asked. In the worked example, finding w alone is not enough if the question also asks for the father's age.
Practice questions
1. Easy: Simplify 7a + 4 − 2a + 9.
Show answer
5a + 13. Working: 7a − 2a = 5a and 4 + 9 = 13.
2. Medium: Find the value of 3p − 4 + p/2 when p = 8.
Show answer
24. Working: 3 × 8 − 4 + 8 ÷ 2 = 24 − 4 + 4 = 24.
3. Harder: A cup costs $m. A plate costs $3 more than a cup. Mr Ong buys 4 cups and 2 plates for $42. Find the value of m and the cost of one plate.
Show answer
m = 6, and a plate costs $9. Working: one plate costs $(m + 3), so 2 plates cost $(2m + 6). Total cost = 4m + 2m + 6 = 6m + 6 = 42. Then 6m = 36 and m = 6. A plate costs 6 + 3 = $9. Check: 4 × $6 + 2 × $9 = $24 + $18 = $42.
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