Question

homework 4 - (2nd quarter)
select the two fractions that are equivalent to
$-dfrac{1}{4}$.

Explanation:

Step1: Recall Equivalent Fractions Rule

To find equivalent fractions, we multiply or divide the numerator and denominator by the same non - zero number. For the fraction \(-\frac{1}{4}\), if we multiply the numerator and denominator by 2, we get \(-\frac{1\times2}{4\times2}=-\frac{2}{8}\). If we multiply the numerator and denominator by 3, we get \(-\frac{1\times3}{4\times3}=-\frac{3}{12}\), and so on. Also, we can consider the sign: \(\frac{-1}{4}=-\frac{1}{4}=\frac{1}{-4}\). For example, \(\frac{-2}{8}\) (since \(\frac{-2\div2}{8\div2}=\frac{-1}{4}\)) and \(\frac{3}{-12}\) (since \(\frac{3\div(- 3)}{-12\div(-3)}=\frac{-1}{4}\)) are equivalent to \(-\frac{1}{4}\).

Step2: Identify Equivalent Fractions

Suppose we have a set of fractions (even though the options are not fully shown here, the general method is as above). Let's assume some common equivalent fractions. For example, if the options include \(-\frac{2}{8}\) and \(\frac{-3}{12}\), we can check:

• For \(-\frac{2}{8}\): Divide numerator and denominator by 2, \(\frac{-2\div2}{8\div2}=-\frac{1}{4}\).
• For \(\frac{-3}{12}\): Divide numerator and denominator by 3, \(\frac{-3\div3}{12\div3}=-\frac{1}{4}\).

(Note: Since the full set of options is not provided in the image, the above is a general method. If we assume typical options, for example, if the options are A. \(-\frac{2}{8}\), B. \(\frac{1}{4}\), C. \(\frac{-3}{12}\), D. \(\frac{4}{16}\), then the equivalent fractions to \(-\frac{1}{4}\) are A. \(-\frac{2}{8}\) and C. \(\frac{-3}{12}\) because:

• For A: \(-\frac{2}{8}=\frac{-2\div2}{8\div2}=-\frac{1}{4}\)
• For C: \(\frac{-3}{12}=\frac{-3\div3}{12\div3}=-\frac{1}{4}\)
• For B: \(\frac{1}{4}\) has a positive sign while the original is negative, so not equivalent.
• For D: \(\frac{4}{16}=\frac{4\div4}{16\div4}=\frac{1}{4}\), positive, not equivalent.)

Answer:

(Assuming the options are as above) A. \(-\frac{2}{8}\), C. \(\frac{-3}{12}\) (The answer depends on the actual options provided, but the method is to use the rule of equivalent fractions: multiply/divide numerator and denominator by the same non - zero number and consider the sign.)