Questions: Order 4/5 - 10/3 using < or >.

Order 4/5 - 10/3 using < or >.
Transcript text: Order $\frac{4}{5}-\frac{10}{3}$ using $<$ or $>$.
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Solution

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Solution Steps

Step 1: Convert Fractions to a Common Denominator

To compare the fractions \(\frac{4}{5}\) and \(\frac{10}{3}\), we first need to convert them to a common denominator. The least common multiple of 5 and 3 is 15.

Convert \(\frac{4}{5}\) to a fraction with a denominator of 15: \[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \]

Convert \(\frac{10}{3}\) to a fraction with a denominator of 15: \[ \frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15} \]

Step 2: Compare the Numerators

Now that both fractions have the same denominator, compare their numerators:

  • \(\frac{12}{15}\) has a numerator of 12.
  • \(\frac{50}{15}\) has a numerator of 50.

Since 12 is less than 50, we have: \[ \frac{12}{15} < \frac{50}{15} \]

Final Answer

Thus, \(\frac{4}{5} < \frac{10}{3}\).

\[ \boxed{<} \]

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