Changing the Subject of a Formula worksheet

Changing the subject of a formula

We use formulae to work out the value of a variable given the values of other variables. For example, the formula Speed = Distance ÷ Time allows us to calculate speed given distance and time. Sometimes we want to work out one of the variables within the formula and to help us do this, we can rearrange the formula to make that variable the subject of the formula. We do this using inverse operations to move variables from one side of the equation to the other. For example, from Speed = Distance ÷ Time, we can multiply by time to get Speed × Time = Distance .

Let’s look at changing the subject of the following formula: a=frac{bx+c}{3}. We could make x the subject. The denominator on the right hand side is 3 so we first need to multiply by 3 to give us 3a=bx+c . Next, subtracting c gives us 3a-c=bx . Finally, dividing by b we get frac{3a-c}{b} = x. Notice now that the right hand side of the formula is just x and the left hand side is the algebraic expression x is equal to. We can swap these and write x=frac{3a-c}{b}.

Looking forward, students can then progress to additional rearranging equations worksheet or more algebra worksheets, for example a sequences worksheet, or a simultaneous equations worksheet.

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