Question

How is the process of multiplying fractions different from the process of adding fractions?

A) When adding, you have to add the numerators and then the denominators, but when multiplying you must find a common denominator or use the butterfly method.
B) When adding, you must find a common denominator or butterfly, but when multiplying you must use the reciprocal (also called "Keep-Change-Flip" and "Invert and Multiply").
C) Adding cannot be done straight across (numerator + numerator, then denominator + denominator), but multiplying is done straight across.
D) When multiplying, you must find a common denominator or use the butterfly method, but when adding you must use the reciprocal (also called "Keep-Change-Flip" and "Invert and Add").

Answer 1

When adding fractions, a common denominator is required and only numerators are added; denominators stay the same. For multiplying fractions, numerators and denominators are multiplied straight across without finding a common denominator, followed by simplification.

Step-by-step explanation:

The process of adding fractions is different from multiplying fractions in that when you add fractions, you must find a common denominator before summing the numerators, while the denominators remain the same. This process ensures that the fractions are being added together correctly since you cannot simply add the denominators alongside the numerators. For example, adding ½ and ¼ requires a common denominator of 4, resulting in ¾, not ·½, which would be incorrect.

When multiplying fractions, however, there is no need to find a common denominator. You can multiply the numerators together and the denominators together directly. Simplification of the resulting fraction by canceling out common factors is often required to find the most reduced form of the answer. For instance, multiplying ½ by ½ gives us 1⁄4 or ¼ when simplified.

Therefore, the correct representation differentiating these processes is: Adding cannot be done straight across (numerator + numerator, then denominator + denominator), but multiplying is done straight across.