# Forming expressions

## Home learning focus

In this lesson you will learn about algebraic expressions. This is the first of four lessons this week.

This lesson includes:

- two videos
- two downloadable activities
- an interactive quiz

# Learn

Algebraic expressions are mathematical expressions that have operations (+ - x ÷), numbers and variables.

Algebra is used in Maths when we do not know the exact number(s) in a calculation.

In algebra we use letters to represent unknown values or values that can change.

Algebra is commonly used in formulas when we do not know at least one of the numbers, or when one of the numbers can change.

Algebra can be used in many real-life contexts, for example in business when predicting sales, growth and profit.

## How does algebraic notation work?

Let's say that **x = 5** and **y = 10** in the following equations.

Therefore...

- x + 2 = 7
- 3x = 15 (when multiplying don't include the multiplication symbol)
- 3x + 2 = 17
- x² = 25
- 4x² = 100
- xy = 50
- 2xy = 100

### This video illustrates some algebraic expressions, and shows how they can be written down.

## How is algebra used in business?

Algebra can be used to predict sales and how much a customer will spend. Algebra is used to estimate the life-time value of a customer, which calculates the percentage of annual spend.

**Example**

A company uses the formula below to estimate the life-time value of a customer:

y = 12 + 8x

Algebra is used because **x** (the number of months a customer has shopped with the company) can change. **y** represents the percentage that a customer will spend in a year.

Imagine that a customer spends £50 in their first 2 months. We have to include their first month as **x = 0**, so their 2nd month will be **x = 1**.

Now we know **x = 1**, we can substitute it into y = 12 + 8x.

Therefore:

y = 12 + (8 × 1)

y = **20%**

If 20% = £50. Then over a full year, 100% will equal £250 (5 × £50). This means we can predict a customer will spend £250 a year.

# Practise

## Activity 1

**Making and using word formulae - Part A**

Download the activity below from Dynamic Learning . You can print it out, or use a pen and paper to answer the questions.

The answers can be found below, after Activity 2.

## Activity 2

**Making and using word formulae - Part B**

You can print it out, or use a pen and paper to answer the questions on making and using word formulae.

Find the answers to both worksheets part A and B by clicking here to download the answer sheet .

## Activity 3

**Forming expressions quiz**

Test your knowledge with this quick quiz.

# There's more to learn

Have a look at these other resources around the BBC and the web.