Question

The shopping list included $3kg$ of potatoes,$3\frac{1}{2}kg$ of apples, $2\frac{3}{4}kg$ of oranges and $\frac{1}{3}kg$ of pears. Find the total weight of fruits purchased.

Answer 1

The weight of potatoes is $3kg$

The weight of apples is $3\frac{1}{2}kg$

The improper fraction of $3\frac{1}{2}kg$ is

$$\begin{gathered} 3\frac{1}{2} \\ \frac{3\times 2+1}{2} \\ \frac{6+1}{2} \\ \frac{7}{2} \end{gathered}$$

Now, The weight of apples is $\frac{7}{2}kg$

The weight of oranges is $2\frac{3}{4}kg$

The improper fraction of $2\frac{3}{4}kg$ is

$$\begin{gathered} 2\frac{3}{4} \\ \frac{2\times 4+3}{4} \\ \frac{8+3}{4} \\ \frac{11}{4} \end{gathered}$$

Now, The weight of oranges is $\frac{11}{4}kg$

The weight of pears is $\frac{1}{3}kg$

To find the total weight purchased

Total weight $=$ The weight of potatoes $+$The weight of apples $+$ The weight of oranges $+$ The weight of pears

$=$ $3kg$$+$$\frac{7}{2}kg$$+$$\frac{11}{4}kg$$+$$\frac{1}{3}kg$

Now consider the denominator of $=$ $3kg$$+$$\frac{7}{2}kg$$+$$\frac{11}{4}kg$$+$$\frac{1}{3}kg$ i.e, $2,4,3$

The LCM of $2,4,3$ is $12$

The fraction become

$$\begin{gathered} =\frac{3\times 12+\frac{7}{2}\times 12+\frac{11}{4}\times 12+{\displaystyle \frac{1}{3}}\times 12}{12} \\ =\frac{36+7\times 6+11\times 3+1\times 4}{12} \\ =\frac{36+42+33+4}{12} \\ =\frac{115}{12} \end{gathered}$$

Hence, Total weight purchased is $\frac{115}{12}kg$