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Sometimes algebra gets in the way of us taking a good Physics beginning to problem solving and the solution. Here are some reminders and common error to make sure to avoid.
Use Reverse PEMDAS to rearrange equations
Use Reverse PEMDAS to rearrange equations
Remember the order of operations, P E MD AS? It tells that when we are calculating values we need to deal with things in parentheses first, then exponents, then multiplication and division, and we add and subtract last.
When re-arranging an equation to solve for a variable, either in a derivation or in preparation to substitute values in an equation, you will work backwards through the order of operations.
For example, how would you solve for x in this equation that follows? Use the arrows to reveal the steps to reverse the PEMDAS operations and isolate x.
Common Errors to Avoid
Common Errors to Avoid
Solving for a variable in the bottom or a fraction
Solving for a variable in the bottom or a fraction
If the variable you solve is in the bottom of a fraction you need to focus on getting that out of the bottom of the fraction ASAP. Too often students will move the variables from the top of the fraction and forget that the target is still in the denominator.
Can you detect the correct solution for each of the 2 examples in the tiles above? Use the arrows to see which is right and find the 2nd example.
Cancelling variables with addition or subtraction
Cancelling variables with addition or subtraction
When there is addition or subtraction any variable to be cancelled out has to be part of both terms (groups of multiplication or division on either side of the addition or subtraction symbol).
One way to be sure you are cancelling properly is that you should be able to factor our any term that can be cancelled out by division.
Can you detect which equations in the tiles above can be reduced by canceling the repeated variable? Use the arrows to see which is right and find the 2nd example.
Division and multiplication with fractions
Division and multiplication with fractions
When a fraction is multiplied by a quantity, that quantity can be integrated into the numerator of the fraction.
When a fraction is divided by a quantity, that quantity can be integrated into the bottom of the fraction.
When a fraction is multiplied by a fraction the numerators and denominators can be combined.
Dividing by a fraction is best done by multiplying by the reciprocal of the fraction.
See if you can detect correct applications of these rules in the examples in the tiles above. Use the right arrows to see answers and find additional examples.
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