Question

respuesta usando fracciones de referencia.
fracciones dadas a continuación escribiendo >, <, o =

Explanation:

Step1: Convert mixed numbers to improper fractions

To compare \( 5\frac{1}{3} \) and \( 5\frac{3}{4} \), first convert them to improper fractions.

For \( 5\frac{1}{3} \):
\[
5\frac{1}{3}=\frac{5\times3 + 1}{3}=\frac{15 + 1}{3}=\frac{16}{3}
\]

For \( 5\frac{3}{4} \):
\[
5\frac{3}{4}=\frac{5\times4+3}{4}=\frac{20 + 3}{4}=\frac{23}{4}
\]

Step2: Find a common denominator

The denominators are 3 and 4. The least common denominator (LCD) of 3 and 4 is \( 3\times4 = 12 \).

Step3: Convert fractions to have the LCD

Convert \( \frac{16}{3} \) to twelfths:
\[
\frac{16}{3}=\frac{16\times4}{3\times4}=\frac{64}{12}
\]

Convert \( \frac{23}{4} \) to twelfths:
\[
\frac{23}{4}=\frac{23\times3}{4\times3}=\frac{69}{12}
\]

Step4: Compare the numerators

Now that both fractions have the same denominator, we compare the numerators. Since \( 64<69 \), we have \( \frac{64}{12}<\frac{69}{12} \).

Answer:

\( 5\frac{1}{3}<5\frac{3}{4} \)