Question

Which statement is true about the meaning of the equation 2=3×23? The fraction 23 is half the size of 3. The number 3 is twice the size of 23 . The number 2 is 3 times the size of 23 . The fraction 23 is twice the size of 3.

Answer 1

Solution: The equation is , 2 =3 ×$\frac{2}{3}$

Out of the given options :

 The number 2 is 3 times the size of 2/3.

For example, if and b are any two real numbers, a≠0,∧b≠0 then

→a= b×(a/b).

Or

A/B=k, then A=Bk→A=B×A/B replacing k by A/B.

Answer 2

Answer:

3rd statement is true.

Step by step explanation:

We have been given an equation $2=3\times\frac{2}{3}$ and we are asked to select the correct statement from given options.

Let us see our given statements one by one.

1. The  fraction $\frac{2}{3}$ is half the size of 3.

Half of 3 will be $\frac{3}{2}$.  

$\frac{2}{3}\neq\frac{3}{2}$

Therefore, first statement is false.

2. The number 3 is twice the size of $\frac{2}{3}$.

Twice the size of $\frac{2}{3}$ will be $\frac{2\cdot2}{3}=\frac{4}{3}$.

$\frac{4}{3}\neq3$

Therefore, we can see that 2nd statement is not true either.

3. The number 2 is 3 times the size of $\frac{2}{3}$.

Three times the size of $\frac{2}{3}$ will be $3\times\frac{2}{3}$.

Upon cancelling 3 from numerator and denominator we will get,

$3\times\frac{2}{3}=2$

We can see that $2=2$, therefore, third statement is true.

4. The fraction $\frac{2}{3}$ is twice the size of 3.

Two times of 3 will be $2\times3=6$

$\frac{2}{3}\neq6$    

Therefore, 4th statement is false.