Question

Arrange the following in descending order.

$3\frac{4}{5},1\frac{1}{2},3\frac{1}{2}$

Answer 1

Step 1. Comparing the whole number part of the mixed fraction:

In mixed fractions, the fraction having a larger whole number part is the larger and vice-versa.

$3\frac{4}{5}$ and $3\frac{1}{2}$ have $3$ in their whole number part and $1\frac{1}{2}$ has $1$ in its whole number part, so $1\frac{1}{2}$ is the smallest among $3\frac{4}{5},1\frac{1}{2},3\frac{1}{2}$.

Now let us compare $3\frac{4}{5}$ and $3\frac{1}{2}$.

$3\frac{4}{5}$ and $3\frac{1}{2}$ have the same whole number part that is $3$. So, let us compare their fractional part only that is $\frac{4}{5}$ and $\frac{1}{2}$.

Step 2. Converting into like fractions:

Like fractions means the fractions have the same denominator. So, in order to convert fractions into like fractions, first, we have to find the LCM of the denominators of the given fractions.

Here LCM of the denominators that is of $5,2$:

$5,2$ are both prime numbers so their LCM $=5\times 2=10$

Now, write the equivalent fractions of $\frac{4}{5},\frac{1}{2}$ with $10$ as the denominator.

$\frac{4}{5}=\frac{4\times 2}{5\times 2}=\frac{8}{10}$

$\frac{1}{2}=\frac{1\times 5}{2\times 5}=\frac{5}{10}$

So, the obtained like fractions are $\frac{8}{10},\frac{5}{10}$

Step 3. Comparing the like fractions:

We know among the like fractions the fraction having a larger numerator is also larger and vice-versa.

So, now among $\frac{8}{10},\frac{5}{10}$, as $8>5\Rightarrow \frac{8}{10}>\frac{5}{10}$

$\Rightarrow \frac{4}{5}>\frac{1}{2}$

$\Rightarrow 3\frac{4}{5}>3\frac{1}{2}$

$\Rightarrow 3\frac{4}{5}>3\frac{1}{2}>1\frac{1}{2}\left(Fromstep1,wegetthat1\frac{1}{2}isthesmallest\right)$

Hence, the fractions are in descending order $3\frac{4}{5},3\frac{1}{2},1\frac{1}{2}$.