How do you write division as multiplication?

You can write division as multiplication by multiplying by the reciprocal of the divisor.

Here's a breakdown:

• Understanding Reciprocals: The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 2 is 1/2, and the reciprocal of 3/4 is 4/3. To find the reciprocal of a fraction, simply flip the numerator and the denominator. The reciprocal of a whole number can be expressed as 1 over that number.

• The Transformation: Instead of dividing by a number, you multiply by its reciprocal.

  • Example: 8 / 2 is the same as 8 * (1/2). Both equal 4.
  • General Form: a / b = a * (1/b)

• Why This Works: Division essentially asks, "How many times does 'b' fit into 'a'?" Multiplying by the reciprocal (1/b) is the same as finding a fraction of 'a' equivalent to one "unit" of 'b'.

• Using Variables:

  • If you have an equation like 8 / 2 = X, this is equivalent to 2 * X = 8. This formulation highlights what multiplication factor yields the dividend from the divisor.

• Fractions: Dividing by a fraction is the same as multiplying by its reciprocal.

  • Example: 4 / (1/2) is the same as 4 (2/1), which simplifies to 4 2 = 8.

• Applications: This principle is fundamental in algebra and higher mathematics for simplifying expressions and solving equations.

In summary, dividing by a number is mathematically equivalent to multiplying by its reciprocal. This concept is essential for simplifying calculations and solving equations involving division.