How to solve algebra problems

This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in Maths and get you ready for the exciting next step into Year 8!

Don't let the letters scare you! Algebra is just a special way of solving puzzles.

In this guide, you will learn:

• that algebra is just using letters (like n or x) to stand for an unknown number

• how to write an expression (a rule) for a real-life problem

• how to solve an equation (a full sum) to find a missing value

• how to solve algebra problems that use large numbers and decimals

You use algebra all the time without even knowing it. An expression is just a set of rules or instructions.

Think about cooking a turkey. The instructions might be: "30 minutes per kg, plus 20 minutes at the end."

If we use the letter k to stand for the number of kilograms, we can write this as an algebraic expression: 30 k + 20

30 k means 30 x k (30 minutes times the number of kg)

20 means add 20 minutes at the end.

This is a rule. If your turkey is 2kg, you put '2' where k is: (30 x 2) + 20 = 60 + 20 = 80 minutes.

An equation is when you have a full sum and you need to find the missing number. An equation always has an equals sign (=).

This is just like the 'missing box' problems you've seen before.

The problem: "Caoimhe buys 4 drinks and a newspaper that costs £2.50. The total bill is £12.50. What is the cost of one drink ( c )?"

We can write this as an equation: 4c + 2.50 = 12.50

How to solve it (the method): To find c, we must work backwards (use the inverse). We need to get the letter c all by itself.

Start with the total: 12.50

Undo the '+ 2.50': The inverse is subtract 2.50.

12.50 - 2.50 = 10.00

Now our equation is simpler: 4c = 10.00

Undo the '4 x c': The inverse is divide by 4.

10.00 ÷ 4 = 2.50

The answer: c = 2.50. One drink costs £2.50.

Well done! You've learned that algebra is just using letters to find missing numbers.

You now know how to:

• write an expression (like 30k + 20) which is a rule.

• solve an equation (like 4c + 2.50 = 12.50) by working backwards to find the unknown value.

Think about these questions to stretch your thinking and sharpen your skills!

• What is the difference between an expression and an equation? (Hint: look for an equals sign!)

• How would you write this as an expression: "A taxi costs £3.00, plus £2.00 for every mile (m)"?

• How would you start to solve this equation: 2x - 10 = 40? What is the first inverse operation you would use?

Have a chat about your answers with a parent, teacher or your class.