# Rearranging Formulas | Math

January 8, 2015
Are you a resourceful mathematician? Resourceful mathematicians know a variety of tips and tricks for working through different types of math problems. You’ve probably learned a few tips from the TASC Test Assessing Secondary Completion™ blog, but the best tip by far is this: formulas can be rearranged. When you know that formulas aren’t fixed – and can manipulate them to solve for the variables that you need – you know how to make a formula work for you. A formula is a special type of equation that shows the relationship between different variables. Formulas are similar to equations, and can be treated the same way. You’ll remember that a variable is a symbol like x. A variable stands for a number that isn’t known but typically can be solved for. To rearrange a formula, you must first know what the subject of your formula is. For example, in the SUVAT formula (used for finding the velocity of an object over time), V is the subject of the formula: V = u + at Here, V is final velocity, u is initial velocity, a is acceleration, and t is time. But what if a question on the TASC test Mathematics portion asks you to solve for acceleration, rather than final velocity? You have to rearrange the formula by isolating a, or in other words making a the only letter on one side of the equation: (V) - u = (u + at) – u V – u = at (V – u)/t = (at)t (V – u)/t = a By subtracting u and dividing by t, we successfully isolated a. Therefore, we know that the product of final velocity subtracted by initial velocity divided by time equals acceleration. Note that in our example, anything we did to one side was also done to the other side. This keeps the formula balanced. You would do the same if you were working with an equation. For example: x + 2 = 42 x + 2 = 16 (x + 2) – 2 = (16) – 2 x = 14 We solve the exponent first, because that step comes first in the Order of Operations. (Which, you might have been taught as PEMDAS in middle school. PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction – the Order of Operations.) The Order of Operations can help you rearrange formulas. Whenever you use an operation to move a section of a formula, you must perform the opposite operation on the other side of the formula. In the above formula, for example, we divided t from at because a and t were being multiplied. The Order of Operations pairs those opposites together – Multiplication and Division, Addition and Subtraction – making it easy for you to remember what you need to do to make the formula work for you. Resourceful, right? Test your skills with this worksheet from the Aquinas College Math Department.
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