Question

b. arrange the fractions from least to greatest

1. 6/15, 2/12, 10/15 3. 3/5, 8/15, 1/3 5. 5/6, 4/12, 3/8
2. 7/8, 5/4, 1/2 4. 9/2, 9/10, 9/6

c. arrange the fractions from greatest to least

1. 3/2, 3/9, 5/6 3. 4/5, 6/15, 1/3
2. 7/12, 3/9, 5/6 4. 4 3/4, 3 4/5, 4 1/2
3. 1/2, 9/7, 5/14

Explanation:

Let's solve part B, question 1: Arrange \(\frac{6}{15}\), \(\frac{2}{12}\), \(\frac{10}{15}\) from least to greatest.

Step 1: Simplify or find common denominators

First, simplify the fractions if possible. \(\frac{2}{12}=\frac{1}{6}\), \(\frac{6}{15}=\frac{2}{5}\), \(\frac{10}{15}=\frac{2}{3}\). Alternatively, find a common denominator. The least common denominator (LCD) of 15, 12, and 15 is 60.

• \(\frac{6}{15}=\frac{6\times4}{15\times4}=\frac{24}{60}\)
• \(\frac{2}{12}=\frac{2\times5}{12\times5}=\frac{10}{60}\)
• \(\frac{10}{15}=\frac{10\times4}{15\times4}=\frac{40}{60}\)

Step 2: Compare the numerators

Now that the fractions have the same denominator, we compare the numerators. \(10 < 24 < 40\), so \(\frac{10}{60} < \frac{24}{60} < \frac{40}{60}\).

Step 1: Find a common denominator

The LCD of 8, 4, and 2 is 8.

• \(\frac{7}{8}=\frac{7}{8}\)
• \(\frac{5}{4}=\frac{5\times2}{4\times2}=\frac{10}{8}\)
• \(\frac{1}{2}=\frac{1\times4}{2\times4}=\frac{4}{8}\)

Step 2: Compare the numerators

\(4 < 7 < 10\), so \(\frac{4}{8} < \frac{7}{8} < \frac{10}{8}\).

Step 1: Find a common denominator

The LCD of 5, 15, and 3 is 15.

• \(\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}\)
• \(\frac{8}{15}=\frac{8}{15}\)
• \(\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}\)

Step 2: Compare the numerators

\(5 < 8 < 9\), so \(\frac{5}{15} < \frac{8}{15} < \frac{9}{15}\).

Answer:

\(\frac{2}{12}\), \(\frac{6}{15}\), \(\frac{10}{15}\)

Let's solve part B, question 2: Arrange \(\frac{7}{8}\), \(\frac{5}{4}\), \(\frac{1}{2}\) from least to greatest.