What is algebra?

Algebra is all about missing values or numbers.
If you have solved a missing box problem, you have already solved an algebra equation.
Rather than drawing missing boxes or writing the words “missing number”, mathematicians use a letter of the alphabet.
The most commonly used letters are 𝑥 and 𝑦.

Activity: What is algebra?
Complete this interactive activity to better understand algebra. Then put your knowledge to the test.
Missing number problems
Sometimes you can solve a problem just by using your knowledge of how addition and subtraction, or multiplication and division, are connected.
But algebra can also be solved by balancing out an equation, like a set of scales.
To keep things balanced, whatever you do to one side, you do to the other side as well.
Once you have just the missing number on one side, then you have found the answer.
Let's look at a problem.

Image caption, Any missing number box equation is a form of algebra. Algebra uses letters of the alphabet instead of missing number boxes. The most commonly used letters are 𝑥 and 𝑦.

Image caption, You can think of an equation like a set of scales. Both sides of the equals sign must have the same value to be balanced.

Image caption, To get 𝑦 on its own you have to subtract 153 from the right side. But to keep the equation balanced, you must do the same to the left side.

Image caption, Now, this leaves 𝑦 on it's own. So 𝑦 is 26.

Image caption, You can always check your answer, by putting the value back into the original equation.
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Example 1

What is the value of 𝒙?
✓7
Whatever you do to one side of the equation you must do to the other side.
Let's look at how to work this out.

Image caption, You need to get the value of 𝒙 on its own. To do this you subtract 12 from the left-hand side.

Image caption, To keep the balance, you must subtract 12 from the right-hand side as well. 19 − 12 = 7

Image caption, You can then say that you know x is equal to 7.

Image caption, Remember to write out the equation and then re-write it using the number and not the letter 𝒙.
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Example 2

Expand this expression.
✓ Half the value of b added to 9.

Image caption, Division equations are commonly shown as fractions. Any letter written over a 2 like this means that the value of b must be halved.

Image caption, The second part of the equation asks that 9 is added to half the value of b.

Image caption, Where b has a value of 4 then the answer is 13.
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Example 3

Here is a number machine. If you put a number in the top a different number comes out of the bottom.
Can you work out the rule that the machine applies to the numbers?
✓4𝒙 + 7
The number machine applies the same rule to every number that is put into it.
It multiplies the first number by 4 and then adds 7 to it.
For example, the number 4 going into the machine is first multiplied by 4.
4 × 4 = 16
The second part of the rule is to add 7.
16 + 7 = 23
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