Explain how to add and subtract fractions with different...

Name: Problem 43, Chapter 5: Prealgebra
Uploaded: 2020-05-27T13:25:56-08:00
Duration: 2 min 19 s
Channel: Thao Trinh
Description: Explain how to add and subtract fractions with different denominators. Illustrate your answer with an example using the LCM and an explanation of how prime factorization can be used to add and subtract unlike fractions.

Explain how to add and subtract fractions with different denominators. Illustrate your answer with an example using the LCM and an explanation of how prime factorization can be used to add and subtract unlike fractions.

Key Concepts

Fractions

Fractions represent parts of a whole, consisting of a numerator (the top number) and a denominator (the bottom number). They are foundational in arithmetic when expressing division and comparison of quantities, but when fractions have unlike denominators, extra steps are required to combine them.

Least Common Multiple (LCM)

The Least Common Multiple (LCM) is the smallest number that is a multiple of each of the denominators. It is essential for finding a common denominator when adding or subtracting fractions with different denominators, ensuring that the fractions are expressed in like terms before performing the operations.

Adding and Subtracting Fractions with Unlike Denominators

When adding or subtracting fractions with different denominators, the key step is to convert each fraction to an equivalent fraction with a common denominator. Typically, the LCM of the denominators is used as this common denominator. Once converted, the numerators are added or subtracted accordingly while the denominator remains unchanged, and the result is simplified if necessary.

Prime Factorization

Prime Factorization involves breaking down numbers into their basic prime components. This method helps efficiently determine the LCM by identifying the highest powers of all involved prime factors, thereby creating a common denominator that works for all fractions involved in a calculation.

Transcript

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