Math

Question Evaluate the expression (11)(12)(13)321\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1} without a calculator, then simplify the result.

Studdy Solution

STEP 1

Assumptions
1. The expression to be evaluated is (11)(12)(13)321\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1}.
2. The expression should be simplified without using a calculator.

STEP 2

Start by simplifying the numerator of the expression. We have three negative numbers being multiplied together.
(11)(12)(13)(-11) \cdot(-12) \cdot(-13)

STEP 3

When multiplying two negative numbers, the result is positive. Multiply the first two negative numbers.
(11)(12)=1112(-11) \cdot(-12) = 11 \cdot 12

STEP 4

Now multiply the result by the third negative number. Remember that multiplying a positive number by a negative number gives a negative result.
1112(13)11 \cdot 12 \cdot(-13)

STEP 5

Perform the multiplication of the first two positive numbers.
1112=13211 \cdot 12 = 132

STEP 6

Now multiply the positive result by the negative number.
132(13)132 \cdot(-13)

STEP 7

Perform the multiplication to get the numerator.
132(13)=1716132 \cdot(-13) = -1716

STEP 8

Now, simplify the denominator of the expression. The denominator is 3213 \cdot 2 \cdot 1.
321=63 \cdot 2 \cdot 1 = 6

STEP 9

We now have the simplified numerator and denominator.
17166\frac{-1716}{6}

STEP 10

Divide the numerator by the denominator to simplify the fraction.
17166=286\frac{-1716}{6} = -286
The simplified result of the expression (11)(12)(13)321\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1} is 286-286.

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