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Solution: Convert the mixed numbers to improper fractions:
Find a common denominator (LCD = 4):
Question: A mammalogist notes that one troop of primates contains 84 individuals and another contains 126. What is the greatest common factor of these two numbers?
Question: A cartographer measures two distances on a map: $ 2
Solution: Convert to improper fractions:
Solution: Multiply both sides by $ 2a - 1 $ to eliminate the denominator:
Bring all terms involving $ a $ to one side and constants to the other:
Solution: First, factor out the greatest common factor:
Now factor the quadratic inside the parentheses. We look for two numbers that multiply to $ -5 $ and add to $ 4 $. These are $ 5 $ and $ -1 $:
So the fully factored expression is: