Simplifying Fractions and Prime Factorization

The video tutorial explains how to subtract fractions by finding a common denominator. It starts with a simple example using denominators of 2 and 10, demonstrating how to rewrite fractions with a common denominator and simplify the result. The tutorial then progresses to a more complex example, using prime factorization to find the least common denominator for fractions with denominators of 42 and 70. The video concludes with simplifying the resulting fraction by identifying common factors.

What is the first step in subtracting fractions?

• Find a common denominator

• Find a common numerator

• Divide the fractions

• Multiply the fractions

In Example 1, what is the least common denominator for the fractions 1/2 and 3/10?

• 10

• 20

• 5

• 2

How do you simplify the fraction 2/10?

• Subtract 2 from both numerator and denominator

• Divide both numerator and denominator by 2

• Multiply both numerator and denominator by 2

• Add 2 to both numerator and denominator

What is the purpose of using prime factorization in the second example?

• To find the greatest common factor

• To divide the fractions

• To find the least common denominator

• To multiply the fractions

In Example 2, what is the prime factorization of 42?

• 2 * 3 * 7

• 2 * 5 * 7

• 2 * 3 * 5

• 3 * 5 * 7

What additional factor is needed for the first fraction in Example 2 to match the second fraction's denominator?

• 3

• 7

• 2

• 5

What is the result of subtracting 95/210 and 39/210?

• 56/105

• 56/210

• 39/210

• 95/210

What is the prime factorization of 56?

• 2^3 * 7

• 2^2 * 7

• 2^3 * 5

• 2^2 * 5

What is the simplified form of 56/210?

• 2/15

• 8/30

• 7/30

• 4/15

Which factors cancel out when simplifying 56/210?

• 3 and 5

• 2 and 7

• 5 and 7

• 2 and 3