For decades, if not longer, we've all learned to use "Please excuse my dear Aunt Sally" (PEMDAS) to remember the order of operations. A couple years ago, I sensed a need to develop another mnemonic to assist students in solving multi-step equations. With assistance from my wife, we came up with FEAST on DELICIOUS LASAGNA and VEGETABLES; AUNT SALLY MADE DESSERT. (Not all equations will use all of the steps. If a step doesn't apply, just skip it!)
1. FEAST - Fractions and Decimals
- If there are two or more terms with fractions or decimals, it will almost always be easier to solve the equation if you get rid of them first.
- If the equation includes two or more decimals, multiply EACH AND EVERY TERM in the whole equation (decimal or not) by the power of 10 which will clear all of them. For example, if you have a variable term with a coefficient of 2.5 and a constant of 2.75, multiply each and every term by 100.
- If the equation has two or more fractions, multiply EACH AND EVERY TERM of the whole equation (fraction or not) by the least common multiple (LCM) of the denominators. For example, if you have a variable term with a coefficient of 1/3 and a constant of 1/5, multiply each and every term by 15.
2. on DELICIOUS - Distributive Property
- Distribute the factor outside the parentheses to each of the terms inside the parentheses.
3. LASAGNA - Like Terms
- Working on ONLY ONE SIDE of the equal sign, combine like terms. When you've simplified as much as you can on that side of the equal sign, do the same to the other side.
4. and VEGETABLES - Variable Terms
- Combine variable terms if they are on both sides of the equation. It will be easiest in the end to get rid of the variable term with the smallest coefficient.
- If both variable term coefficients are positive (or addition), subtract the lesser coefficient from both variable terms. For example, if the left side has a 5x term and the right 2x, you will SUBTRACT 2x from both sides.
- If one variable term coefficient is positive (or addition) and the other is negative (or subtraction), add the opposite of the negative coefficient to both variable terms. For example, if the left side has a 7x term and the right -3x, you would ADD 3x to both sides.
5. AUNT SALLY - Addition or Subtraction (of course)
- At this point, one side of the equation should have a positive variable term and a constant. If the constant is added to the variable term, subtract that value from BOTH SIDES. If the constant is subtract, you do the opposite.
6. MADE DESSERT - Multiplication or Division
- The variable term should now be alone on one side of the equation. Unless there is no coefficient, you will need to multiply or divide BOTH SIDES such that the coefficient becomes one.