Find each product or quotient where possible. -10/17 / (-12/5)
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1
Identify the operation: This is a division problem involving two fractions: and .
Recall the rule for dividing fractions: To divide by a fraction, multiply by its reciprocal.
Find the reciprocal of the divisor: The reciprocal of is .
Rewrite the division as multiplication: .
Multiply the numerators and the denominators: Multiply by for the numerator and by for the denominator.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Division of Fractions
Dividing fractions involves multiplying by the reciprocal of the divisor. To divide by a fraction, you flip the second fraction and change the division sign to multiplication. For example, dividing -10/17 by -12/5 means you multiply -10/17 by the reciprocal of -12/5, which is 5/-12.
When multiplying fractions, you multiply the numerators together and the denominators together. For instance, if you have two fractions a/b and c/d, the product is (a*c)/(b*d). This concept is essential for simplifying the result after converting a division problem into a multiplication problem.
Simplifying fractions involves reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). This process makes fractions easier to work with and understand. For example, if the result of a calculation is 10/20, it can be simplified to 1/2.