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Competition Math

Simplification

This video goes over PEMDAS (also known as “Please Excuse My Dear Aunt Sally). The acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. The acronym gives the order of priority of all operations. However, the priorities of multiplication and division can be switched (based on which comes first), as can the priorities of addition and subtraction.

In this video, we learn about GCF and LCM. GCF stands for Greatest Common Factor.

In order to find the GCF of two or more numbers, list out all the prime factors and find the common ones between all numbers. Multiply these common factors to get the greatest common factor.

In order to find the LCM of two or more numbers, list out all the prime factors, and for each factor, raise it to the power of the maximum number of times it appears in one of the numbers’ prime factorization. In order words, if 3 appears 3 times in 1 prime factorization but only 2 times in another, you need to take three 3’s to find the LCM.

This video covers some competition-level practice problems. Be sure to follow the Order of Operations (PEMDAS). While trying to find a common denominator, be sure to find the LCM of all the original denominators.