\[\left(-\frac{6}{11}\right) \times\left(-\frac{2}{3}\right)\]
Answer (2)
Multiply the numerators and denominators: 11 6 × 3 2 = 11 × 3 6 × 2 .
Simplify the fraction by canceling the common factor of 3: 11 × 3 6 × 2 = 11 2 × 2 .
Calculate the final result: 11 2 × 2 = 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. Since both fractions are negative, their product will be positive. Thus, we have
( − 11 6 ) × ( − 3 2 ) = 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 in the numerator and the denominator:
11 × 3 2 × 3 × 2 = 11 2 × 2 = 11 4
Final Answer Therefore, the result of the multiplication is 11 4 .
Examples
Fractions are used in everyday life, such as when calculating proportions in recipes, determining discounts while shopping, or understanding probabilities in games. For example, if a recipe calls for 3 2 cup of flour and you only want to make half the recipe, you need to multiply 3 2 by 2 1 to find the new amount of flour needed, which is 3 1 cup. Understanding how to multiply fractions is essential for accurate measurements and adjustments in various real-world scenarios.
The product of ( − 11 6 ) × ( − 3 2 ) is 11 4 after simplifying the fraction. Both negative fractions result in a positive product. This method involves multiplying the numerators and denominators, followed by simplification.
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