Multiply. Express numbers as integers or simplified fractions.
$\left(-\frac{2}{3}\right) \cdot\left(-\frac{18}{13}\right)$
Part 1 of 2
Same signs. The product is $\square$
Answer (2)
The product of − 3 2 and − 13 18 is positive 13 12 after multiplying and simplifying the result. The multiplication involves both determining the sign and calculating the product of the absolute values before simplification. Thus, the final answer is 13 12 .
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Determine the sign: Since both fractions are negative, the product is positive.
Multiply the fractions: 3 2 ⋅ 13 18 = 39 36 .
Simplify the fraction: 39 36 = 13 12 .
The final answer is: 13 12 .
Explanation
Determine the sign We are asked to multiply two negative fractions: − 3 2 and − 13 18 . The first step is to determine the sign of the product. Since the product of two negative numbers is positive, the product will be positive.
Multiply the fractions Next, we multiply the absolute values of the two fractions: 3 2 ⋅ 13 18 = 3 × 13 2 × 18 = 39 36
Simplify the fraction Now, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 36 and 39 is 3. So, we divide both the numerator and the denominator by 3: 39 ÷ 3 36 ÷ 3 = 13 12
Final Answer Since the product of two negative numbers is positive, the final answer is 13 12 .
Examples
Understanding fraction multiplication is crucial in many real-life scenarios. 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, which is 3 1 cup. Similarly, if you are calculating discounts, such as 20% off an item that costs $50 , yo u w o u l d m u lt i pl y 0.20 ( or \frac{1}{5} ) b y 50 t o f in d t h e am o u n t o f t h e d i sco u n t , w hi c hi s $10. These calculations help in everyday tasks like cooking, shopping, and managing finances.
