If I have x pencils and you have twice as many, how many pencils have you got?

Level 3-4 Algebra - Expressions

You'll have come across expressions in your KS3 Maths lessons. By now you'll know that expressions are a very important part of algebra and, for that matter, of maths in general.

Algebra is all about using symbols, usually letters, to represent a number that we don’t yet know. We call these letters variables, as their value can change, or vary, depending on the situation. A situation can be written down as a mathematical sentence, or an expression. So, in Algebra, you can think of an expression as one or a number of mathematical symbols that represent a number or quantity. Expressions can contain any number of numbers, letters and symbols. Even a single number on its own is an expression.

As with any test, take your time, read each question carefully and think about your answer. Think you've mastered expressions? Then see how well you can express yourself by playing this quiz!

Jane is c years old and her sister Katie is three years younger so how old is Katie?

c + 3

c - 3

c - 3 - 3

If she is younger then her age is less than. 3 less than is the same as minus 3

Simplify 5a + 7a.

12a

12aa

57a

57aa

Let us suppose that a = 3. (5 x 3) + (7 x 3) = 36. This is the same as saying 12 x 3 (12a) = 36

Simplify 4a + 5b + 6b + 11a

26ab

15a² + 11b²

15a + 11b

9a + 17b

Here we are adding numbers together, NOT multiplying them together

If I have x rabbits and you have twice as many, how many rabbits have you got?

2 + x

2 - x

x²

You have two times the number that I have got and 2 times x is the same as 2x

Which of the following is not a mathematical expression?

6a x 14

5a - 4b +16c x 8d

Oh my gosh!

The correct answer might well be an English expression but it is NOT a mathematical one!

What is the simplification of 3a + 4b + 6c + 3a - 6c - a - 3b?

4a + 2b - 3c

5a + b

6a - 3b

9a - 2b - c

Be careful to account for all the a's, then all the b's and then all the c's. In this case + 6c and - 6c cancel each other out and therefore they do not appear in the simplification

In an algebraic expression letters are often used to represent what?

Other letters

Only numbers greater than 1

Only numbers less than 1

Values

A letter can be used in place of any number - especially if the number has not yet been worked out

Peter has x brothers, Paul has y brothers and Graham has z brothers. Between the three boys, how many brothers have they got?

xyz

x + y + z

x + y - z

x - y + z

Don't get baffled by complicated wording - often the answer is easier than you think

Suzie is x years old and she has a sister called Rosie who is four years older. Rosie's mother was 28 when Rosie was born. How old is Rosie's mother now?

x + 28

x - 4

x + 32

If you got the answer wrong then think carefully through each aspect of the question. Rosie's mother was 28 when Rosie was born. 4 years later, Suzie was born. Suzie is now x years old so Rosie's mother's age is now
28 + 4 + x = 32 + x

10.

Which of these is a simplification of 2a x 3a?

23aa

6a²

You must multiply the numbers together AND the letters. Remember a x a = a²

Author: Frank Evans