Understanding Fractions and Reciprocals

The video tutorial explains how to divide fractions by converting the division into multiplication using reciprocals. It provides two examples: dividing 3/7 by 12 and 12/27 by 10/21. The process involves writing whole numbers as improper fractions, finding reciprocals, and simplifying using prime factorization. The tutorial emphasizes simplifying fractions to their lowest terms by identifying common factors between numerators and denominators.

What is the reciprocal of a fraction c/d?

• 1/(c+d)

• d/c

• c-d

• c/d

How do you convert a division of fractions into a multiplication?

• Add the fractions

• Divide by the reciprocal of the divisor

• Multiply by the reciprocal of the divisor

• Subtract the fractions

What is the first step in simplifying the multiplication of fractions?

• Identify common factors between numerators and denominators

• Add the numerators

• Multiply the fractions directly

• Subtract the denominators

What is the prime factorization of 12?

• 2 x 2 x 3

• 2 x 6

• 1 x 12

• 3 x 4

In the example of dividing 3/7 by 12, what is the simplified product?

• 1/28

• 3/28

• 1/7

• 3/7

What is the prime factorization of 21?

• 3 x 7

• 3 x 3

• 7 x 1

• 2 x 10

What common factors are identified in the division of 12/27 by 10/21?

• Two factors of 3 and one factor of 2

• One factor of 5 and one factor of 2

• Two factors of 7 and one factor of 3

• One factor of 10 and one factor of 21

What is the simplified result of dividing 12/27 by 10/21?

• 14/15

• 12/21

• 10/27

• 21/10

What is the prime factorization of 27?

• 2 x 3 x 3

• 3 x 3 x 3

• 1 x 27

• 3 x 9

What is the prime factorization of 10?

• 5 x 5

• 2 x 2 x 5

• 1 x 10

• 2 x 5