Question

find 3 ratios that are equivalent to the given ratio
\\(\frac{7}{8}\\)
find 3 ratios that are equivalent to the given ratio.
\\(\square\\) a. \\(\frac{14}{16}\\) \\(\square\\) b. \\(\frac{28}{32}\\)
\\(\square\\) c. \\(\frac{21}{24}\\) \\(\square\\) d. \\(\frac{21}{16}\\)
\\(\square\\) e. \\(\frac{21}{32}\\) \\(\square\\) f. \\(\frac{28}{24}\\)
\\(\square\\) g. \\(\frac{14}{24}\\) \\(\square\\) h. \\(\frac{14}{32}\\)

Explanation:

To find equivalent ratios to \(\frac{7}{8}\), we can multiply or divide both the numerator and the denominator by the same non - zero number.

Step 1: Analyze Option A (\(\frac{14}{16}\))

We multiply the numerator and denominator of \(\frac{7}{8}\) by 2. Using the rule \(\frac{a}{b}=\frac{a\times k}{b\times k}\) (where \(k = 2\), \(a = 7\), \(b = 8\)), we get \(\frac{7\times2}{8\times2}=\frac{14}{16}\). So, \(\frac{14}{16}\) is equivalent to \(\frac{7}{8}\).

Step 2: Analyze Option B (\(\frac{28}{32}\))

We multiply the numerator and denominator of \(\frac{7}{8}\) by 4. Using the rule \(\frac{a}{b}=\frac{a\times k}{b\times k}\) (where \(k = 4\), \(a = 7\), \(b = 8\)), we get \(\frac{7\times4}{8\times4}=\frac{28}{32}\). So, \(\frac{28}{32}\) is equivalent to \(\frac{7}{8}\).

Step 3: Analyze Option F (\(\frac{28}{24}\)) Wait, no, let's re - check. Wait, Option F is \(\frac{28}{24}\)? No, wait the original ratio is \(\frac{7}{8}\). Wait, let's check Option F: \(\frac{28}{24}\) simplifies to \(\frac{7}{6}\), which is not equivalent. Wait, maybe I made a mistake. Wait, let's check Option C: \(\frac{21}{24}\). We multiply numerator and denominator of \(\frac{7}{8}\) by 3. \(\frac{7\times3}{8\times3}=\frac{21}{24}\), so \(\frac{21}{24}\) is equivalent.

Wait, let's go through each option:

• Option A: \(\frac{14}{16}\), divide numerator and denominator by 2, we get \(\frac{7}{8}\), so equivalent.
• Option B: \(\frac{28}{32}\), divide numerator and denominator by 4, we get \(\frac{7}{8}\), so equivalent.
• Option C: \(\frac{21}{24}\), divide numerator and denominator by 3, we get \(\frac{7}{8}\), so equivalent.
• Option D: \(\frac{21}{16}\), this is not equivalent to \(\frac{7}{8}\) since \(\frac{21}{16}=1.3125\) and \(\frac{7}{8} = 0.875\)
• Option E: \(\frac{21}{32}\), \(\frac{21}{32}=0.65625

eq0.875\), not equivalent.

• Option F: \(\frac{28}{24}=\frac{7}{6}\approx1.1667

eq0.875\), not equivalent.

• Option G: \(\frac{14}{24}=\frac{7}{12}\approx0.583

eq0.875\), not equivalent.

• Option H: \(\frac{14}{32}=\frac{7}{16}=0.4375

eq0.875\), not equivalent.

Wait, maybe the intended correct options are A, B, C. Let's verify again:

For \(\frac{7}{8}\):

• A: \(\frac{14}{16}\), \(7\times2 = 14\), \(8\times2=16\), so equivalent.
• B: \(\frac{28}{32}\), \(7\times4 = 28\), \(8\times4 = 32\), so equivalent.
• C: \(\frac{21}{24}\), \(7\times3=21\), \(8\times3 = 24\), so equivalent.

Answer:

A. \(\frac{14}{16}\), B. \(\frac{28}{32}\), C. \(\frac{21}{24}\)