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Which fraction is equivalent to [tex]\frac{2}{3}[/tex]?

A. [tex]\frac{6}{10}[/tex]
B. [tex]\frac{26}{39}[/tex]
C. [tex]\frac{28}{39}[/tex]
D. [tex]\frac{24}{30}[/tex]

Answer :

We want to determine which fraction is equivalent to
[tex]$$\frac{2}{3} \approx 0.6666667.$$[/tex]

Let’s evaluate each option:

1. Option 1:
[tex]$$\frac{6}{10} = 0.6,$$[/tex]
which is different from [tex]$0.6666667$[/tex].

2. Option 2:
[tex]$$\frac{26}{39}.$$[/tex]
Notice that dividing both the numerator and denominator by [tex]$13$[/tex] gives:
[tex]$$\frac{26 \div 13}{39 \div 13} = \frac{2}{3} \approx 0.6666667.$$[/tex]
This option is exactly the same as [tex]$\frac{2}{3}$[/tex].

3. Option 3:
[tex]$$\frac{28}{39} \approx 0.7179487,$$[/tex]
which is not equal to [tex]$0.6666667$[/tex].

4. Option 4:
[tex]$$\frac{24}{30} = 0.8,$$[/tex]
which is also different from [tex]$0.6666667$[/tex].

Since only
[tex]$$\frac{26}{39}$$[/tex]
simplifies exactly to
[tex]$$\frac{2}{3},$$[/tex]
this is the fraction equivalent to [tex]$\frac{2}{3}$[/tex].

Thus, the fraction equivalent to [tex]$\frac{2}{3}$[/tex] is
[tex]$$\frac{26}{39}.$$[/tex]

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