Algebra: Expressions, Equations and Formulae

The language of algebra

Algebra uses letters to stand for numbers we do not yet know, and once you read it as a language it stops being mysterious. A letter such as x is a variable, standing for a number. A single part like 3x or 5 is a term, and terms with the same letter part, such as 2x and 5x, are like terms that can be added together. A set of terms with no equals sign, such as 2x plus 3, is an expression, which you can simplify. When two things are set equal, such as 2x plus 3 equals 11, you have an equation, which you can solve to find the letter. A rule connecting quantities, such as area equals length times width, is a formula. This module covers terms and expressions, solving equations, and using formulae, with operators written in words throughout.

Algebra words

Learn these terms before the expressions are matched up. They name the parts of algebra.

Match each algebra term to its meaning

An expression against an equation

These two look similar but are used very differently, and the equals sign is the tell.

How do you simplify this?

How do you simplify the expression 3x plus 5x?

• 8x, by adding the like terms
• 15x, by multiplying them
• 8x squared
• It cannot be simplified

Do the same to both sides

Solving an equation means finding the value of the letter that makes both sides equal, and the golden rule is simple: whatever you do to one side, do to the other, so the equation stays balanced. To solve 2x plus 3 equals 11, you subtract 3 from both sides to get 2x equals 8, then divide both sides by 2 to get x equals 4. Work in steps, undoing what has been done to the letter, and keep the two sides equal at every stage. This one habit, keeping the balance, solves every linear equation you will meet. It is also the idea behind rearranging a formula: you change both sides in the same way until the letter you want is on its own. Balance in, balance out.

Pick the like terms

Select every term that is a like term with 3x.

• 5x
• x
• 8x
• 5
• 5x squared

Order the steps to solve an equation

Put the steps of solving 2x plus 3 equals 11 in order.

• Write the equation: 2x plus 3 equals 11
• Subtract 3 from both sides to get 2x equals 8
• Divide both sides by 2 to get x equals 4
• Check by putting x equals 4 back in
• State the solution

Complete the algebra facts

A single part of an expression, such as 3x, is a _____. Terms with the same letter part are _____ terms. A statement with an equals sign is an _____. A rule connecting quantities is a _____.

Solve for x

Solve the equation 3x plus 4 equals 19. Subtract 4 from both sides, then divide by 3, and give the value of x.

The hunt for a hidden number

A puzzle in algebra is a clue. It does not hand you the hidden number outright, but it pins it down so tightly that only one value can be true. Say a number is doubled and then three is added, and the result is thirteen. You do not have to guess wildly; you can work backwards. Take away the three, which leaves ten; undo the doubling, which leaves five. The hidden number was five all along, and the clue led you straight to it. Algebra is that detective work written in shorthand, with a letter standing in for the number you are hunting. Read the puzzle as a set of instructions done to a hidden number, then undo them one at a time, and the answer gives itself up.

Tap the two like terms

Tap the TWO terms that are like terms with 2y.

• 5y
• y
• 5x
• 5

Work through each algebra step

Read each situation and choose the correct answer.

• You need to simplify 4a plus 3a. What do you get?
• To solve 2x equals 10, what do you do to both sides?
• A formula says area equals length times width. If the length is 6 and the width is 4, what is the area?

Build an algebra sentence

Choose the word for each gap to complete one point about algebra.

Explain the basics of algebra

A friend says algebra is just letters that make no sense. Using what you have learned, explain the basics of algebra.

• Explain what a term and like terms are
• Explain the difference between an expression and an equation
• Explain how to simplify an expression by collecting like terms
• Explain how to solve a simple equation by doing the same to both sides
• Explain what a formula is and how to use one