What is the product of $-\frac{5}{6} \times \frac{2}{3}$?
A. $-\frac{7}{9}$
B. $-\frac{5}{9}$
C. $\frac{5}{9}$
D. $\frac{7}{9}$
Answer (1)
Multiply the numerators: $5
imes 2 = 10$ and the denominators: $6
imes 3 = 18 , res u lt in g in -\frac{10}{18}$.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: − 18 10 = − 9 5 .
The product of − 6 5 and 3 2 is − 9 5 .
The final answer is − 9 5 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, specifically − 6 5 and 3 2 . Our goal is to multiply these fractions and simplify the result to match one of the given options.
Multiplying the Fractions To multiply two fractions, we multiply the numerators together and the denominators together. So, we have − 6 5 × 3 2 = − 6 × 3 5 × 2 = − 18 10 .
Simplifying the Fraction Now, we need to simplify the fraction − 18 10 . Both the numerator and the denominator are divisible by 2. Dividing both by 2, we get − 18 10 = − 18 ÷ 2 10 ÷ 2 = − 9 5 .
Finding the Answer Comparing our simplified fraction − 9 5 with the given options, we see that it matches option B. Therefore, the product of − 6 5 and 3 2 is − 9 5 .
Examples
Understanding fraction multiplication is crucial in many real-life scenarios. For instance, if you are baking a cake and a recipe calls for 3 2 of a cup of flour, but you only want to make 6 5 of the recipe, you need to calculate 6 5 × 3 2 to determine how much flour to use. This type of calculation ensures that you maintain the correct proportions and achieve the desired outcome in your baking endeavor. Similarly, in construction or engineering, multiplying fractions is essential for scaling designs and calculating material requirements.
