Forming expressions

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

This lesson includes:

• two videos
• 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

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.