Simplifying Fractions and Prime Factorization

The video tutorial explains how to simplify fractions by using the prime factorization method. It begins by defining a fraction in its simplest form and highlights the difficulty in identifying common factors by inspection. The tutorial then demonstrates the prime factorization method with two examples: simplifying 24/108 and 75/105. The process involves breaking down the numerator and denominator into their prime factors, identifying common factors, and simplifying the fraction. The video emphasizes the efficiency of this method, especially for larger numbers, compared to relying solely on multiplication tables.

What is the simplest form of a fraction?

• When the numerator is larger than the denominator

• When the fraction is a mixed number

• When the numerator and denominator have no common factors

• When both numerator and denominator are even numbers

What is the first step in the prime factorization method?

• Multiply the numerator and denominator

• Determine the prime factorization of the numerator and denominator

• Convert the fraction to a decimal

• Add the numerator and denominator

What is the prime factorization of 24?

• 5 * 5 * 2

• 2 * 3 * 4

• 3 * 3 * 3

• 2 * 2 * 2 * 3

Which common factor can be used to simplify 24/108 directly?

• 8

• 6

• 12

• 24

What is the simplified form of 24/108?

• 1/4

• 2/9

• 3/8

• 4/9

What is the prime factorization of 75?

• 5 * 5 * 5

• 3 * 5 * 5

• 2 * 5 * 5

• 3 * 3 * 5

What is the prime factorization of 105?

• 5 * 5 * 7

• 3 * 3 * 7

• 2 * 5 * 7

• 3 * 5 * 7

What is the simplified form of 75/105?

• 5/7

• 3/7

• 7/5

• 5/3

Which common factor can be used to simplify 75/105 directly?

• 25

• 20

• 15

• 10

Why is the prime factorization method useful for larger numbers?

• It makes addition easier

• It helps in identifying common factors

• It converts fractions to decimals

• It simplifies multiplication