Which of the following fractions is the largest?

​$$\frac{2}{3}, \frac{9}{87}, \frac{20}{21}, \frac{45}{66}$$​​

Correct option is A

Given: 

Fractions are $$\frac{2}{3}, \quad \frac{9}{87}, \quad \frac{20}{21}, \quad \frac{45}{66}$$  

Solution: 

Simplify each fraction

$$\frac{2}{3}$$ : This fraction is already in its simplest form.​

​$$\frac{9}{87}$$ : Simplify by dividing both numerator and denominator by 3.

           $$\frac{9}{87} = \frac{9 \div 3}{87 \div 3} = \frac{3}{29}$$​​

​$$\frac{20}{21}$$ : This fraction is already in its simplest form.​

​$$\frac{45}{66}$$ : Simplify by dividing both numerator and denominator by 3.

            $$\frac{45}{66} = \frac{45 \div 3}{66 \div 3} = \frac{15}{22}$$

​​Convert each fraction to decimal form 

$$\frac{2}{3} \approx 0.6667$$ 

​$$\frac{3}{29} \approx 0.1034$$ 

$$\frac{20}{21} \approx 0.9524$$ 

$$\frac{15}{22} \approx 0.6818$$  

The largest value is 0.9524, which corresponds to the fraction $$\frac{20}{21}$$ .​

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