Final answer:
To eliminate fractions, multiply numerators and denominators when multiplying, simplify by canceling common factors, and use a common denominator when adding or subtracting. Converting units can require reciprocals to cancel units appropriately.
Step-by-step explanation:
To get rid of the fractions, one method is to find a common denominator when dealing with the addition or subtraction of fractions. For multiplying fractions, simply multiply the numerators (top numbers) and then the denominators (bottom numbers). Simplify the fraction by canceling out any common factors between the numerator and denominator. When conducting unit conversions or solving equations, ensure that the units in the numerator of one fraction cancel out the units in the denominator of another to achieve the correct units in the answer.
For example, to simplify the fraction ½ of ⅓, you multiply 2 (the numerator of the first fraction) by 15 (the numerator of the second fraction) to get 30. Then, multiply the denominators, 1 and 120, to get 120. Simplifying 30/120 by canceling common factors gives you ¼.
If the desired unit conversion requires it, you can flip the fraction to its reciprocal to make the units cancel out properly. This is because dividing by a number is the same as multiplying by its reciprocal. Lastly, remember that when adding fractions such as ¼ and ¾, you must have a common denominator, but do not add the denominators; only the numerators are added to find the sum.