Question

1. \\(\frac{3}{4}\\) and \\(\frac{2}{5}\\) 3. \\(\frac{4}{7}\\) and \\(\frac{2}{3}\\) 6. \\(\frac{5}{4}\\) and \\(\frac{11}{16}\\) 7. \\(\frac{6}{7}\\) and \\(\frac{1}{5}\\)

Explanation:

Assuming the problem is to compare the pairs of fractions (e.g., find which is larger or convert to like fractions), we'll solve each sub - question:

Sub - question 2: Compare $\boldsymbol{\frac{3}{4}}$ and $\boldsymbol{\frac{2}{5}}$

Step 1: Find a common denominator

The least common denominator of 4 and 5 is $4\times5 = 20$.

Step 2: Convert the fractions

For $\frac{3}{4}$, multiply numerator and denominator by 5: $\frac{3\times5}{4\times5}=\frac{15}{20}$.
For $\frac{2}{5}$, multiply numerator and denominator by 4: $\frac{2\times4}{5\times4}=\frac{8}{20}$.

Step 3: Compare the numerators

Since $15>8$, $\frac{15}{20}>\frac{8}{20}$, so $\frac{3}{4}>\frac{2}{5}$.

Step 1: Find a common denominator

The least common denominator of 7 and 3 is $7\times3 = 21$.

Step 2: Convert the fractions

For $\frac{4}{7}$, multiply numerator and denominator by 3: $\frac{4\times3}{7\times3}=\frac{12}{21}$.
For $\frac{2}{3}$, multiply numerator and denominator by 7: $\frac{2\times7}{3\times7}=\frac{14}{21}$.

Step 3: Compare the numerators

Since $12 < 14$, $\frac{12}{21}<\frac{14}{21}$, so $\frac{4}{7}<\frac{2}{3}$.

Step 1: Find a common denominator

The least common denominator of 4 and 16 is 16.

Step 2: Convert the fraction

For $\frac{5}{4}$, multiply numerator and denominator by 4: $\frac{5\times4}{4\times4}=\frac{20}{16}$.

Step 3: Compare the numerators

Since $20>11$, $\frac{20}{16}>\frac{11}{16}$, so $\frac{5}{4}>\frac{11}{16}$.

Answer:

$\frac{3}{4}>\frac{2}{5}$ (or if converting to like fractions: $\frac{15}{20}$ and $\frac{8}{20}$)

Sub - question 3: Compare $\boldsymbol{\frac{4}{7}}$ and $\boldsymbol{\frac{2}{3}}$