Math

QuestionSimplify the expression: 13(114)2\frac{1}{3}\left(1-\frac{1}{4}\right)^{2}.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression 13(114)\frac{1}{3}\left(1-\frac{1}{4}\right)^{}. The operations in the expression should be performed following the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

STEP 2

First, we simplify the expression inside the parentheses.
1141-\frac{1}{4}

STEP 3

Subtract the fraction from1.
11=11-\frac{1}{} = \frac{}{} - \frac{1}{}

STEP 4

Calculate the result of the subtraction.
4414=34\frac{4}{4} - \frac{1}{4} = \frac{3}{4}

STEP 5

Now, we have to square this result. We replace the expression inside the parentheses with the result we just calculated.
(34)2\left(\frac{3}{4}\right)^{2}

STEP 6

Calculate the square of the fraction.
(34)2=916\left(\frac{3}{4}\right)^{2} = \frac{9}{16}

STEP 7

Now, we multiply this result by1/3.
13×916\frac{1}{3} \times \frac{9}{16}

STEP 8

Multiply the fractions.
13×16=1×3×16\frac{1}{3} \times \frac{}{16} = \frac{1 \times}{3 \times16}

STEP 9

Calculate the result of the multiplication.
×93×16=948\frac{ \times9}{3 \times16} = \frac{9}{48}

STEP 10

Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is3.
948=9/348/3=316\frac{9}{48} = \frac{9/3}{48/3} = \frac{3}{16}The simplified form of the given expression is 316\frac{3}{16}.

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