Question

1/3 = 3/9 = 6/18. 1/4=4/16=3/12 Ms. White's students are working on generating equivalent fractions like the ones shown. She asks her students to write a set of instructions for how to generate equivalent fractions. One student writes, "You have to multiply the bottom and the top of the fraction by a number." Which of the following revisions most improves the student statement in terms of validity and generalizability?

A) "You have to multiply only the top of the fraction by a number."
B) "You have to multiply only the bottom of the fraction by a number."
C) "You have to multiply both the bottom and the top of the fraction by the same nonzero number."
D) "You have to divide both the bottom and the top of the fraction by the same nonzero number."

Answer 1

The most accurate way to create equivalent fractions is to multiply or divide both the numerator and denominator by the same nonzero number, which maintains the fraction's value. The corrected student statement is: "You have to multiply both the bottom and the top of the fraction by the same nonzero number."

Step-by-step explanation:

To generate equivalent fractions, the student's statement needs a revision for validity. Among the options provided, choice C offers the most accurate and generalizable instruction.

The correct way to create equivalent fractions is to multiply (or divide) both the numerator (top) and the denominator (bottom) of the original fraction by the same nonzero number.

Doing this ensures the value of the fraction remains unchanged, which is the essence of equivalent fractions. For example, if we multiply the numerator and denominator of 1/2 by 3, we get 3/6, which is equivalent to 1/2.

Multiplying or dividing by different numbers would not produce an equivalent fraction but rather would change the value of the fraction.

So, the revision that most improves the student statement by being both valid and generalizable is C: "You have to multiply both the bottom and the top of the fraction by the same nonzero number."