Prime Factorization and Simplifying Fractions

This video tutorial covers the process of simplifying fractions, both numerically and geometrically. It introduces two methods: prime factorization and divisibility, providing examples for each. The video also demonstrates how to verify simplified fractions using a graphing calculator. Additionally, it explains how to simplify fractions that include variables, emphasizing the ease of using the prime factorization method.

What is the main goal when simplifying fractions?

• To make the fraction larger

• To add more terms to the fraction

• To express the fraction in its simplest form

• To change the fraction to a decimal

Which method involves breaking down numbers into their prime factors?

• Addition method

• Graphing method

• Prime factorization method

• Divisibility method

What is the first step in the prime factorization method for simplifying 18/24?

• Convert the fraction to a decimal

• Multiply the numbers together

• Create a factor tree for both numbers

• Divide both numbers by 2

When using the divisibility method, what is a common first step?

• Multiply the numerator and denominator

• Divide both by the smallest prime number

• Add the numerator and denominator

• Subtract the numerator from the denominator

How can you verify a simplified fraction using a graphing calculator?

• By adding it to another fraction

• By converting it to a decimal and back to a fraction

• By subtracting it from another fraction

• By multiplying it by another fraction

What is the simplified form of 84/96 using the prime factorization method?

• 2/3

• 5/6

• 3/4

• 7/8

Why is the prime factorization method preferred when variables are involved?

• It requires less calculation

• It is faster

• It avoids decimals

• It is easier to see common factors

What is the prime factorization of 25?

• 5 x 5

• 2 x 12

• 3 x 8

• 4 x 6

In the expression x^2, what does it represent?

• x + x

• x divided by x

• x - x

• x times x

What is the simplified form of the fraction with variables: 25x^2y^3/55x^3y?

• 11y/5x^2

• 11x/5y^2

• 5x^2/11y

• 5y^2/11x