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

3rd statement is true.

Step by step explanation:

We have been given an equation
`2=3*(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
`(2)/(3)` is half the size of 3.

Half of 3 will be
`(3)/(2)`.

`(2)/(3)\\eq(3)/(2)`

Therefore, first statement is false.

2. The number 3 is twice the size of
`(2)/(3)`.

Twice the size of
`(2)/(3)` will be
`(2\cdot2)/(3)=(4)/(3)`.

`(4)/(3)\\eq3`

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

3. The number 2 is 3 times the size of
`(2)/(3)`.

Three times the size of
`(2)/(3)` will be
`3*(2)/(3)`.

Upon cancelling 3 from numerator and denominator we will get,

`3*(2)/(3)=2`

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

4. The fraction
`(2)/(3)` is twice the size of 3.

Two times of 3 will be
`2*3=6`

`(2)/(3)\\eq6`

Therefore, 4th statement is false.

Answer 2

Solution: The equation is , 2 =3 ×
`(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.