Question

Simplify.

1/4 (1 - 2/3)² + 1/3.

The answer must be a simplified fraction.

Answer 1

`(13)/(36)`

Explanation:

I took the test ~~>.<~~

Answer 2

`\large\boxed{(13)/(36)}`

Explanation:

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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`(1)/(4)\left(1-(2)/(3)\right)^2+(1)/(3)=(1)/(4)\left((3)/(3)-(2)/(3)\right)^2+(1)/(3)=(1)/(4)\left((3-2)/(3)\right)^2+(1)/(3)\\\\=(1)/(4)\left((1)/(3)\right)^2+(1)/(3)=(1)/(4)\cdot(1^2)/(3^2)+(1)/(3)=(1)/(4)\cdot(1)/(9)+(1)/(3)=(1)/(36)+(1)/(3)\qquad(*)\\\\\text{the common denominator is}\ 36.\\\\36=3\cdot12\to(1)/(3)=(1\cdot12)/(3\cdot12)=(12)/(36)\\\\(*)\qquad=(1)/(36)+(12)/(36)=(1+12)/(36)=(13)/(36)`