Dividing a fraction is the same thing as which of the following?

Dividing a fraction is the same thing as which of the following?

• A. Adding it to the denominator
• B. Multiplying it by the inverse of that number
• C. Subtracting it from the numerator
• D. Dividing it by the numerator

Answer: (B)

Dividing a fraction by another number is fundamentally rooted in the concept of multiplying by the reciprocal, or inverse, of that number. When you divide by a fraction, you can rewrite this operation as multiplying by its reciprocal. For example, if you have a fraction \( \frac{a}{b} \) and you want to divide it by a number \( c \), this can be expressed as \( \frac{a}{b} \div c \). To divide by \( c \), you multiply by its inverse, which is \( \frac{1}{c} \). This can be rearranged to \( \frac{a}{b} \times \frac{1}{c} \), and it leads to a new fraction of \( \frac{a}{bc} \). This principle applies universally to both whole numbers and fractions, which makes it a foundational rule in arithmetic and algebra. Using this method simplifies calculations and ensures accurate results when working with divisions involving fractions.

Dividing a fraction by another number is fundamentally rooted in the concept of multiplying by the reciprocal, or inverse, of that number. When you divide by a fraction, you can rewrite this operation as multiplying by its reciprocal.

For example, if you have a fraction ( \frac{a}{b} ) and you want to divide it by a number ( c ), this can be expressed as ( \frac{a}{b} \div c ). To divide by ( c ), you multiply by its inverse, which is ( \frac{1}{c} ). This can be rearranged to ( \frac{a}{b} \times \frac{1}{c} ), and it leads to a new fraction of ( \frac{a}{bc} ).

This principle applies universally to both whole numbers and fractions, which makes it a foundational rule in arithmetic and algebra. Using this method simplifies calculations and ensures accurate results when working with divisions involving fractions.