Question

Arrange the following fractions in asscending order (top to bottom):

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{4}{5}$
• D. $\frac{5}{6}$

Answer 1

Comparing $\frac{1}{2}$, $\frac{5}{6}$, and $\frac{4}{5}$ and $\frac{2}{3}$.
These fractions have different denominator, so convert them into like fractions.
To convert them into like fractions, they need to have the same denominator.
The multiples 2, 6, 5, and 3 are

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30...
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
5: 5, 10, 15, 20, 25, 30...
6: 6, 12, 18, 24, 30...
The common multiple of 2, 3, 5, and 6 is 30

$\frac{1}{2}$ = $\frac{1\times 15}{2\times 15}$ = $\frac{15}{30}$

$\frac{5}{6}$ = $\frac{5\times 5}{6\times 5}$ = $\frac{25}{30}$

$\frac{4}{5}$ = $\frac{4\times 6}{5\times 6}$ = $\frac{24}{30}$

$\frac{2}{3}$ = $\frac{2\times 10}{3\times 10}$ = $\frac{20}{30}$

Look at the fractions $\frac{15}{30}$, $\frac{25}{30}$, $\frac{24}{30}$, $\frac{20}{30}$.
When the denominator is the same, the fraction with lower numerator will have lesser value.
Here, $15<20<24<25$

So, $\frac{15}{30}<\frac{20}{30}<\frac{24}{30}<\frac{25}{30}$

Therefore, $\frac{1}{2}<\frac{2}{3}<\frac{4}{5}<\frac{5}{6}$