Solution: The equation is , 2 =3 ×[tex]\frac{2}{3}[/tex]
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:
3rd statement is true.
Step by step explanation:
We have been given an equation [tex]2=3\times\frac{2}{3}[/tex] and we are asked to select the correct statement from given options.
Let us see our given statements one by one.
1. The fraction [tex]\frac{2}{3}[/tex] is half the size of 3.
Half of 3 will be [tex]\frac{3}{2}[/tex].
[tex]\frac{2}{3}\neq\frac{3}{2}[/tex]
Therefore, first statement is false.
2. The number 3 is twice the size of [tex]\frac{2}{3}[/tex].
Twice the size of [tex]\frac{2}{3}[/tex] will be [tex]\frac{2\cdot2}{3}=\frac{4}{3}[/tex].
[tex]\frac{4}{3}\neq3[/tex]
Therefore, we can see that 2nd statement is not true either.
3. The number 2 is 3 times the size of [tex]\frac{2}{3}[/tex].
Three times the size of [tex]\frac{2}{3}[/tex] will be [tex]3\times\frac{2}{3}[/tex].
Upon cancelling 3 from numerator and denominator we will get,
[tex]3\times\frac{2}{3}=2[/tex]
We can see that [tex]2=2[/tex], therefore, third statement is true.
4. The fraction [tex]\frac{2}{3}[/tex] is twice the size of 3.
Two times of 3 will be [tex]2\times3=6[/tex]
[tex]\frac{2}{3}\neq6[/tex]
Therefore, 4th statement is false.
