State which of the following is true:1. 2. $19\frac{1}{2}\times \frac{2}{39}=1$3. $5\frac{1}{7}\times \frac{3}{4}=5+\frac{1}{7}\times \frac{3}{4}$4. $\frac{8}{9}\times \frac{5}{6}=\frac{8\times 5}{6\times 9}$5. $2\frac{1}{3}\times 2\frac{1}{3}=4\frac{1}{9}$"

Given :

Multiple expressions are given.

To do :

We have to state which of the expressions are true.

Solution :

1. $\frac{5}{6} \times \frac{7}{8} = \frac{5 \times 7}{6 \times 8}$

It is true.

2. $19 \frac{1}{2} \times \frac{2}{39} = \frac{(19\times 2+1)}{2} \times \frac{2}{39} = \frac{39}{2} \times \frac{2}{39}$

 $19 \frac{1}{2} \times \frac{2}{39} = 1$.

It is true.

3. $5 \frac{1}{7} \times \frac{3}{4} = 5+\frac{1}{7} \times \frac{3}{4}$

$\frac{(5\times 7+1)}{7} \times \frac{3}{4} = \frac{36}{7} \times \frac {3}{4} = \frac{36\times 3}{7\times4} = \frac{108}{28}$

$5+\frac{1}{7} \times \frac{3}{4} = 5 + \frac{1\times 3}{7\times 4} = 5 + \frac{3}{28} = \frac{(28\times5+3)}{28} = \frac{(140+3)}{28} = \frac{143}{28}$

Therefore,

$5 \frac{1}{7} \times \frac{3}{4} = 5+\frac{1}{7} \times \frac{3}{4}$ is false.

4. $\frac{8}{9} \times \frac{5}{6}  = \frac{8\times 5}{9\times 6} = \frac{8\times 5}{6\times 9}$

It is true.

5. $2 \frac{1}{3} \times 2 \frac{1}{3} = \frac{(2\times 3+1)}{3} \times \frac{(2\times 3+1)}{3} = \frac{7}{3} \times \frac{7}{3} = \frac{49}{9}$.

$4\frac{1}{9} = \frac{(4\times 9+1)}{9} = \frac{37}{9}$

 $2 \frac{1}{3} \times 2 \frac{1}{3} = 4 \frac{1}{9}$ is false.

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Updated on: 10-Oct-2022

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