Question

question 2 of 5
choose all fractions equivalent to each given fraction.
given fraction check all fractions that are equivalent to the given fraction.
(a) $-\frac{3}{8}$ $\frac{-3}{8}$ $\frac{3}{8}$ $\frac{3}{-8}$ $\frac{-3}{-8}$
given fraction check all fractions that are equivalent to the given fraction.
(b) $\frac{-7}{-10}$ $-\frac{7}{10}$ $\frac{-7}{10}$ $\frac{7}{-10}$ $\frac{7}{10}$

Explanation:

Part (a)

Step 1: Recall the rule of signs for fractions

The rule is that \(\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\), where \(a,b\) are positive real numbers. For the given fraction \(-\frac{3}{8}\):

• For \(\frac{-3}{8}\): Using the rule \(-\frac{a}{b}=\frac{-a}{b}\) (here \(a = 3,b = 8\)), so \(-\frac{3}{8}=\frac{-3}{8}\).
• For \(\frac{3}{8}\): The sign is positive, while the given fraction is negative, so they are not equivalent.
• For \(\frac{3}{-8}\): Using the rule \(-\frac{a}{b}=\frac{a}{-b}\) (here \(a = 3,b = 8\)), so \(-\frac{3}{8}=\frac{3}{-8}\).
• For \(\frac{-3}{-8}\): The product of two negative signs is positive, so \(\frac{-3}{-8}=\frac{3}{8}\), which is not equal to \(-\frac{3}{8}\).

Step 2: Identify equivalent fractions

From the above analysis, the fractions equivalent to \(-\frac{3}{8}\) are \(\frac{-3}{8}\) and \(\frac{3}{-8}\).

Part (b)

Step 1: Simplify the given fraction

First, simplify \(\frac{-7}{-10}\). The rule for dividing two negative numbers is that \(\frac{-a}{-b}=\frac{a}{b}\) (where \(a,b>0\)). So \(\frac{-7}{-10}=\frac{7}{10}\). Now we check each option:

• For \(-\frac{7}{10}\): The sign is negative, while \(\frac{7}{10}\) is positive, so not equivalent.
• For \(\frac{-7}{10}\): The sign is negative, while \(\frac{7}{10}\) is positive, so not equivalent.
• For \(\frac{7}{-10}\): \(\frac{7}{-10}=-\frac{7}{10}\), which is not equal to \(\frac{7}{10}\), so not equivalent.
• For \(\frac{7}{10}\): We already found that \(\frac{-7}{-10}=\frac{7}{10}\), so this is equivalent.

Answer:

(a) The equivalent fractions are \(\boldsymbol{\frac{-3}{8}}\) and \(\boldsymbol{\frac{3}{-8}}\)
(b) The equivalent fraction is \(\boldsymbol{\frac{7}{10}}\)