Do bracket first or division first?

Algebra Level 2

Which of the following three has a different value?

2 ÷ 2 ÷ ( 2 ÷ 2 ) 2\div 2 \div (2 \div 2) 2 ÷ ( 2 ÷ 2 ) ÷ 2 2\div (2 \div 2) \div 2 ( 2 ÷ 2 ) ÷ 2 ÷ 2 (2\div 2) \div 2 \div 2

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1 solution

2 ÷ 2 ÷ ( 2 ÷ 2 ) = 2 × 1 2 × 1 = 1 2 ÷ ( 2 ÷ 2 ) ÷ 2 = 2 × 1 × 1 2 = 1 ( 2 ÷ 2 ) ÷ 2 ÷ 2 = 1 × 1 2 × 1 2 = 1 4 \begin{aligned} 2÷2÷(2÷2)&=2 \times {\dfrac{1}{2}} \times 1 = 1 \\ 2÷(2÷2)÷2&=2 \times 1 \times {\dfrac{1}{2}}= 1 \\ (2÷2)÷2÷2&= 1 \times {\dfrac{1}{2}} \times {\dfrac{1}{2}}=\boxed{{\dfrac{1}{4}}} \\ \end{aligned}

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