Question

choose all fractions equivalent to each given fraction.

given fraction	check all fractions that are equivalent to the given fraction.

given fraction	check all fractions that are equivalent to the given fraction.

Explanation:

Step1: Recall the rule for equivalent fractions with negative signs

The rule is that \(\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\), and \(-\frac{a}{b}=\frac{-a}{b}=\frac{a}{-b}\).

Step2: Solve part (a)

Given fraction \(\frac{-5}{8}\).

• For \(-\frac{5}{8}\): By the rule, \(\frac{-5}{8}=-\frac{5}{8}\), so this is equivalent.
• For \(\frac{5}{-8}\): \(\frac{5}{-8}=\frac{-5}{8}\) (since dividing a positive by a negative gives a negative), so this is equivalent.
• For \(\frac{-5}{-8}\): \(\frac{-5}{-8}=\frac{5}{8}\) (negative divided by negative is positive), which is not equivalent to \(\frac{-5}{8}\).
• For \(\frac{5}{8}\): This is positive, while the given fraction is negative, so not equivalent.

Step3: Solve part (b)

Given fraction \(-\frac{3}{10}\).

• For \(\frac{3}{10}\): This is positive, while the given fraction is negative, so not equivalent.
• For \(\frac{-3}{-10}\): \(\frac{-3}{-10}=\frac{3}{10}\) (negative divided by negative is positive), not equivalent to \(-\frac{3}{10}\).
• For \(\frac{3}{-10}\): \(\frac{3}{-10}=-\frac{3}{10}\), so this is equivalent.
• For \(\frac{-3}{10}\): \(\frac{-3}{10}=-\frac{3}{10}\), so this is equivalent.

Answer:

(a) The equivalent fractions are \(-\frac{5}{8}\), \(\frac{5}{-8}\) (i.e., the first and second options).
(b) The equivalent fractions are \(\frac{3}{-10}\), \(\frac{-3}{10}\) (i.e., the third and fourth options).