Squaring a Negative Number and the Order of Operations

It is important that your child understands how to use the order of operations correctly. Remember that PEMDAS stands for

  • Parentheses,
  • Exponents
  • Multiplication/Division (whichever comes first as you are reading left to right)
  • Addition/Subtraction (whichever comes first as you are reading left to right).

An Easy to Make Error

Many students have problems differentiating between (-4)^2 versus -4^ 2 (where ^ means that the number behind it is an exponent).

On (-4)^2, remind the student that parentheses comes before exponents so you are squaring -4 so the answer is 16. However in -4^2, exponents comes before subtraction or negating something so you are only squaring 4, which is 16. THEN you are negating that so the final answer is -16.

What about when you have an Odd exponent

Suppose you have (-2)^3 versus -2^3? Is there a difference. With (-2)^3, you are cubing -2, which is -8. In -2^3, you are cubing 2, which is 8, then you are negating that, so you get -8. So when the exponent is odd, you get the same answer.


20 Possible Holes in Your Child’s Math Education

Is your child in 6th grade or higher, and he is struggling with math?  Do you need help identifying possible holes in your child’s math education?  Check out the ebook 20 Possible Holes in Your Child’s Math Education. Here is a sample page.

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20 Possible Math Holes in Your Child's Math Education



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