by The Open University
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Now, we will look at rearranging an equation. Before we do this, we would like you to look at some general rules for adding, subtracting, multiplying and dividing positive and negative numbers. Symbols like a or x are simply ‘standing in? for numerical values, so where a term is positive or negative, it should be treated in the same way as the rules below.
Positive and negative numbers
Numbers which have a plus sign attached to them, such as + 7, are referred to as positive numbers. Numbers which have a minus sign attached to them, such as−5, are referred to as negative numbers.
Addition of numbers with the same sign
When adding numbers with the same sign, the sign of the sum is the same as the sign on each of the numbers.
When adding numbers with the same sign, you can omit the brackets and the + sign for the addition. When the first number is positive, it is usual to omit its + sign.
Addition of numbers with different signs
To add numbers whose signs are different, subtract the numerically smaller from the larger. The sign of the result is the same as the sign of the numerically larger number.
When dealing with several numbers of different signs, separately add the positive and negative numbers together. The set of numbers then becomes two numbers, one positive and one negative, which you can add in the usual way.
Subtraction
To subtract numbers, change the sign of the number being subtracted and add the resulting number.
Multiplication
The product of two numbers with similar signs is positive, while the product of two numbers with different signs is negative.
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If you multiply any number by zero, the answer is always zero.
Division
When dividing, numbers with similar signs give a positive answer and numbers with different signs give a negative answer.
For example, 
If you divide a number by zero, you will always get an error, as this is impossible.
We may wish to rearrange an equation, to change its subject. Some equations may have more than one algebraic symbol that is an unknown. The equation may be expressed in terms of x, say x = y + 4. We may wish to know what the equation would look like if it were expressed in terms of y. The critical thing with any equation is that you must always carry out the same calculations to each side of the equation. If, for example, you deduct x from one side of the equation but not from the other, it changes the equation completely. Since the quantities on each side of an equation are the same, anything done to one side must be done to the other to maintain the equality.
Say we wish to rearrange x = y + 3 so that y becomes the subject of the equation.
We can subtract 3 from both sides of the equation, and simplify.
As another example, say we wish to rearrange 
so that y becomes the subject of the equation.
First, we multiply both sides by 5: 5x = y − 10
Then we add 10 to both sides: 5x + 10 = y
Now try some rearrangement exercises for yourself. In all cases, make x the subject of the equation.
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