\(\left(-\frac{6}{11}\right) \times\left(-\frac{2}{3}\right)\)
Answer (2)
Multiply the numerators and denominators: 11 × 3 6 × 2 .
Simplify the fraction by canceling the common factor 3: 11 2 × 2 .
Calculate the final result: 11 4 .
The final answer is 11 4 .
Explanation
Understanding the Problem We are asked to evaluate the expression ( − 11 6 ) × ( − 3 2 ) . This involves multiplying two negative fractions.
Multiplying the Fractions When multiplying fractions, we multiply the numerators together and the denominators together. Also, recall that the product of two negative numbers is a positive number. Therefore, we have
( − 11 6 ) × ( − 3 2 ) = 11 × 3 6 × 2
Simplifying the Fraction Now, we simplify the fraction by canceling common factors. We can write 6 as 2 × 3 , so we have
11 × 3 6 × 2 = 11 × 3 2 × 3 × 2
We can cancel the common factor of 3 from the numerator and the denominator:
11 × 3 2 × 3 × 2 = 11 2 × 2
Final Calculation Finally, we multiply the remaining numbers in the numerator:
11 2 × 2 = 11 4
So, the result of the multiplication is 11 4 .
Examples
Understanding how to multiply fractions is essential in many real-life situations. For example, if you are baking a cake and need to halve a recipe that calls for 3 2 cup of flour, you would multiply 2 1 × 3 2 to find the new amount of flour needed. This skill is also useful in calculating proportions, discounts, and many other everyday tasks.
The product of ( − 11 6 ) × ( − 3 2 ) is 11 4 after calculating the multiplication of the numerators and denominators and simplifying the fraction. Multiplying two negative fractions results in a positive value. Therefore, the final answer is 11 4 .
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