Respuesta :
[tex]2 \frac{5}{6}<2 \frac{3}{4}<2 \frac{5}{8}<2 \frac{4}{7}[/tex]
Step-by-step explanation:
Step 1: The given numbers are [tex]2 \frac{5}{6}<2 \frac{3}{4}<2 \frac{5}{8}<2 \frac{4}{7}[/tex]
Step 2: Let us first convert the mixed fraction into whole numbers.
[tex]2 \frac{5}{8}=\frac{(2 \times 8)+5}{8}=\frac{21}{8}[/tex], [tex]2 \frac{5}{6}=\frac{(2 \times 6)+5}{6}=\frac{17}{6}[/tex]
[tex]2 \frac{3}{4}=\frac{(2 \times 4)+3}{4}=\frac{11}{4}[/tex], [tex]2 \frac{4}{7}=\frac{(2 \times 7)+4}{7}=\frac{18}{7}[/tex]
Step 3: Now, take LCM of the denominators and make the fraction into same denominator.
LCM of 8, 6, 4, 7 is 168.
[tex]\frac{21}{8}=\frac{21 \times 21}{8 \times 21}=\frac{441}{168}[/tex], [tex]\frac{17}{6}=\frac{17 \times 28}{6 \times 28}=\frac{476}{168}[/tex]
[tex]\frac{11}{4}=\frac{11 \times 42}{4 \times 42}=\frac{462}{168}[/tex], [tex]\frac{18}{7}=\frac{18 \times 24}{7 \times 24}=\frac{432}{168}[/tex]
Step 4: Arrange the fractions from greatest to least.
[tex]\frac{476}{168}<\frac{462}{168}<\frac{441}{168}<\frac{432}{168}[/tex]
Now, write the corresponding mixed fraction.
[tex]\Rightarrow 2 \frac{5}{6}<2 \frac{3}{4}<2 \frac{5}{8}<2 \frac{4}{7}[/tex]
