Which is greater $\frac{1}{3}$ or $\frac{2}{3}$?
Since they have like denominators or the same then we compare the numerators.
1 < 2, so $\frac{1}{3}$ < $\frac{2}{3}$
When comparing fractions we use <, >, or =.
If we have unlike denominators, then one way is to use the Least Common Denominator (LCD).
Least Common Denominator (LCD) is just the least common Multiple (LCM) of the denominators.
Example 1:
We have $\frac{1}{4}$ and $\frac{3}{12}$.
The LCM of 4 and 12 is 12.
Multiples of 4: 4, 8, 12, ...
Multiples of 12: 12, 24, 36, ...
Thus, in order to find 12 as a denominator we multiply the numerator and denominator of $\frac{1}{4}$ by 3.
$\frac{1}{4}$ = $\frac{3}{12}$
Using this we have an equal fraction, $\frac{3}{12}$ = $\frac{3}{12}$.
Example 2:
$\frac{3}{2}$ and $\frac{4}{5}$
LCM of 2 and 5 is 10.
$\frac{3}{2}$ = $\frac{15}{10}$ when 3 and 2 is multiplied by 5 each.
$\frac{4}{5}$ = $\frac{8}{10}$ when 4 and 5 is multiplied by 2 each.
Thus, $\frac{15}{10}$ > $\frac{8}{10}$ so $\frac{3}{2}$ > $\frac{4}{5}$
A shorter way is by using cross multiplication.
$\frac{3}{2}$ and $\frac{4}{5}$
3 x 5 = 15, write on top of $\frac{3}{2}$
2 x 4 = 8, write on top of $\frac{4}{5}$
Since 15 > 8 then $\frac{3}{2}$ > $\frac{4}{5}$ as expected.
How to write fractions from least to greatest?
Use LCD!
$\frac{1}{2}$, $\frac{2}{3}$, $\frac{5}{8}$
The LCD is just the LCM of the denominator:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 8: 8, 16, 24, ...
The LCD is 24.
Thus the equivalent fractions are:
$\frac{1}{2}$ = $\frac{12}{24}$ by multiplying both numerator and denominator by 12.
$\frac{2}{3}$ = $\frac{16}{24}$ by multiplying both numerator and denominator by 8.
$\frac{5}{8}$ = $\frac{15}{24}$ by multiplying both numerator and denominator by 3.
Since 12 < 15 < 16 so $\frac{1}{2}$, $\frac{5}{8}$, $\frac{2}{3}$
