Question

Use computation to determine which of the following statements is true A 1/10 • 5/2 < 1/10 B 13/6 • 4/7 > 13/6 C 11/13 • 1/8 < 11/13 D 4/7 • 10/3 < 4/7

Answer 1

Let's compute each statement one by one:

**A.** \( \frac{1}{10} \cdot \frac{5}{2} < \frac{1}{10} \)

Calculating the left side:

\[
\frac{1}{10} \cdot \frac{5}{2} = \frac{1 \cdot 5}{10 \cdot 2} = \frac{5}{20} = \frac{1}{4}
\]

Now we compare \( \frac{1}{4} < \frac{1}{10} \).

Since \( \frac{1}{4} = 0.25 \) and \( \frac{1}{10} = 0.1 \), \( 0.25 \) is not less than \( 0.1 \).

So **A is false**.

---

**B.** \( \frac{13}{6} \cdot \frac{4}{7} > \frac{13}{6} \)

Calculating the left side:

\[
\frac{13}{6} \cdot \frac{4}{7} = \frac{13 \cdot 4}{6 \cdot 7} = \frac{52}{42} = \frac{26}{21}
\]

Now we compare \( \frac{26}{21} > \frac{13}{6} \):

Convert \( \frac{13}{6} \) to a fraction over 21:

\[
\frac{13}{6} = \frac{13 \cdot 21/13}{6 \cdot 21/13} = \frac{13 \cdot 21}{6 \cdot 21} = \frac{65}{42}
\]

Now we compare:

Since \( 26/21 = 52/42 \) and \( \frac{65}{42} > \frac{52}{42} \), it shows \( \frac{26}{21} < \frac{13}{6} \).

So **B is false**.

---

**C.** \( \frac{11}{13} \cdot \frac{1}{8} < \frac{11}{13} \)

Calculating the left side:

\[
\frac{11}{13} \cdot \frac{1}{8} = \frac{11 \cdot 1}{13 \cdot 8} = \frac{11}{104}
\]

Now we compare \( \frac{11}{104} < \frac{11}{13} \).

Convert \( \frac{11}{13} \) to a fraction over 104:

\[
\frac{11}{13} = \frac{11 \cdot 8}{13 \cdot 8} = \frac{88}{104}
\]

Now we compare:

Since \( \frac{11}{104} < \frac{88}{104} \), this is indeed true.

So **C is true**.

---

**D.** \( \frac{4}{7} \cdot \frac{10}{3} < \frac{4}{7} \)

Calculating the left side:

\[
\frac{4}{7} \cdot \frac{10}{3} = \frac{4 \cdot 10}{7 \cdot 3} = \frac{40}{21}
\]

Now we compare \( \frac{40}{21} < \frac{4}{7} \).

Convert \( \frac{4}{7} \) to a fraction over 21:

\[
\frac{4}{7} = \frac{4 \cdot 3}{7 \cdot 3} = \frac{12}{21}
\]

Now we compare:

Since \( \frac{40}{21} > \frac{12}{21} \), this inequality is false.

So **D is false**.

---

In summary:

- A is false
- B is false
- C is true
- D is false

The only true statement is **C**: \( \frac{11}{13} \cdot \frac{1}{8} < \frac{11}{13} \).