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On a chess board there are eight squares across and eight squares down.

Level 5-6 Algebra - Expressions

Learn how algebraic expressions work. Combine like terms, use coefficients correctly, and simplify or substitute values to make expressions neat and useful.

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Fascinating Fact:

If a cinema ticket costs £6 and popcorn costs £2, the total for x friends is 6x plus 2x, which simplifies to 8x.

In KS3 Maths, expressions are numbers, operations, and letters written without an equals sign. You will simplify by collecting like terms, substitute values for variables, and sometimes expand brackets to tidy results.

Key Terms

Expression: A mix of numbers, letters, and operations (no equals sign), for example 3x + 5.
Like terms: Terms with the same variable and power that can be combined, e.g., 4x + 3x = 7x.
Coefficient: The number multiplying a variable, such as 6 in 6x.

Frequently Asked Questions (Click to see answers)

How do I simplify an expression like 5x + 3 + 2x + 7?

Collect like terms. Combine 5x and 2x to get 7x, and 3 + 7 to get 10. The simplified result is 7x + 10.

What does 3(x + 4) mean in algebra?

It means multiply the bracket by 3. Expanding gives 3x + 12 using the distributive law (3 × x and 3 × 4).

How do I substitute values into an expression?

Replace the variable with the given number and calculate. For 2x + 5 when x = 4, work out 2 × 4 + 5 = 13.

Try These Related Quizzes

1 .

There are x number of chess boards at the school chess club. What is the total number of squares on all the boards?

64x

64 - x

64 + x

It is impossible to say

The correct answer means 64 times x. If we were then told that there were four boards at the club we could work out that the total number of squares was 256 (64 x 4)

2 .

In the first three football matches of the season James scored x goals. In the fourth match James scored two goals and in the fifth match he scored one goal. How would you write the total number of goals that James scored?

12x

2x + 1

x + 2 + 1

x + x + x

Don't get baffled with complicated questions. Sort out just the information that is required

3 .

On a chess board there are eight squares across and eight squares down. Which of these would be the best way of writing the number of squares?

8 + 8 + 8 + 8 + 8 + 8 + 8

8 x 8 x 8 x 8

8²

8 lots of 8 is the same as 8 x 8 or 8²

4 .

There are y number of students in a class. If seven of the students are away ill, how would you write the number of students still attending class?

7 - y

y - 7

y + 7

In algebra the letters 'a' and 'x' are often used to represent unknown numbers but any letter can be used

5 .

Peter has a number of brothers (let's call the number 'x') and John has two brothers more than Peter. How would you write the number of brothers that John has?

-2x

x - 2

x + 2

If John has two brothers more than Peter (x) then he must have x + 2 brothers

6 .

Solution a boils at x degrees centigrade. Solution b has a boiling point five degrees higher than solution a. Solution c has a boiling point 25 degrees higher than solution b. How would you express the boiling point of solution c?

x + 5 + 25

x + b + c

x + y + z

xyz

Don't get baffled! Write it down and work it out

7 .

It takes a person five minutes to pick a sack of potatoes. How long will it take z people to pick 20 sacks of potatoes? You may assume that all the people work together to fill the same sack before moving onto the next sack. Give your answer in minutes.

20 + z minutes

20 x 5 / z minutes

20z minutes

z - 20 minutes

If it takes 5 min for one man, then 2 men will take 1/2 that time, 3 men will take 1/3 that time,... z men will take 1/z of that time - that is 5/z min for each sack. Therefore, 20 sacks will take 20 x 5/z min. Of course, if they each filled their own sack, it would only take 5 min to fill 20 sacks

8 .

Joseph has x rabbits and Sam has three more rabbits than Joseph. How many rabbits have they between them?

x + 3

x + x + 3

x + x - 3

If Joseph has x rabbits then Sam has x + 3 so, between them, Joseph and Sam have x + x + 3 or 2x + 3

9 .

Five people each start the day with x sweets. During the day, each of them eat two of their sweets. What is the total number of sweets that have not been eaten at the end of the day?

5(x - 2)

5 - x

10 - x

x - 10

If you answered x - 10 then you need to remember that EACH PERSON started with x sweets. x sweets DOES NOT represent the total number of sweets at the start

10 .

There were x pens in the cupboard. Paula took out three pens, John took out two pens and Pamela put seven pens back into the cupboard. How would you write the number of pens now in the cupboard?

2x + 3x

x - 3 - 2 + 7

x + 3 + 2 - 7

x + 3 + 2 + 7

There are now x + 2 pens in the cupboard

You can find more about this topic by visiting BBC Bitesize - Expressions and formulae

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)