Question

Compare the fractions and put an appropriate sign.
a) $\frac{3}{6}\square \frac{5}{6}$
b) $\frac{1}{7}\square \frac{1}{4}$
c) $\frac{4}{5}\square \frac{5}{5}$
d) $\frac{3}{5}\square \frac{3}{7}$

Answer 1

a) Given $\frac{3}{6}\square \frac{5}{6}$
Here, the denominator are same, Therefore, The fraction having the greater numerator will be greater.
Hence, $\frac{3}{6}<\frac{5}{6}$
b) Since, the given fractions denominators are not same, so we will make the denominators are same by multiplying $\frac{4}{4}$ and $\frac{7}{7}$ with given fractions as
$\frac{1}{7}=\frac{1\times 4}{7\times 4}=\frac{4}{28}$
$\frac{1}{4}=\frac{1\times 7}{4\times 7}=\frac{7}{28}$
Now, we can compare their numerators as $4<7$
$\therefore \frac{4}{28}<\frac{7}{28}$
c) $\frac{4}{5}<\frac{5}{5}$
Since, the denominators are same,
Therefore the fraction having the greater numerator will be greater.
Hence, $\frac{4}{5}<\frac{5}{5}$

d) Given $\frac{3}{5}$ and $\frac{3}{7}$
Since, the denominators are not same, so let us make the denominators are same by multiplying $\frac{7}{7}$ and $\frac{5}{5}$ with given fractions.
Thus, $\frac{3\times 7}{5\times 7}=\frac{21}{35}$
$\frac{3\times 5}{7\times 5}=\frac{15}{35}$
Now we can compare their numerator's as $21>15$
$\therefore \frac{21}{35}>\frac{15}{35}$