Equivalent Fractions

Dividing the numerator and denominator by their greatest common divisor, 5, gives $15÷5=3$ and $20÷5=4$, resulting in $\frac{3}{4}$.

Dividing the numerator and denominator by their greatest common divisor, 9, gives $18÷9=2$ and $27÷9=3$, resulting in $\frac{2}{3}$.

$\frac{5}{7}$ is already in its simplest form because 5 and 7 have no common divisors other than 1.

Expanding by a factor of 6 means multiplying both the numerator and denominator by 6: $7\times 6=42$ and $9\times 6=54$, giving $\frac{42}{54}$.

The greatest common divisor of 105 and 150 is 15. Dividing both by 15 gives $105÷15=7$ and $150÷15=10$, so the simplified fraction is $\frac{7}{10}$.

Divide both the numerator and denominator by 8 to undo the expansion: $96÷8=12$ and $144÷8=18$. Simplifying $\frac{12}{18}$ by dividing both parts by 6 gives $\frac{2}{3}$.