# Bayesian latent variable models for mixed discrete outcomes by Dunson D.B., Herring A.H. PDF By Dunson D.B., Herring A.H.

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49 FRACTIONS Types of fractions A proper fraction—where the numerator is smaller than the denominator—is just one type of fraction. When the number of parts is greater than the whole, the result is a fraction that can be written in two ways— either as an improper fraction (also known as a top-heavy fraction) or a mixed fraction. numerator has higher value than denominator numerator has lower value than denominator 1 4 35 4 ◁ Proper fraction In this fraction the number of parts examined, shown on top, is less than the whole.

It cannot accurately be written out in full, so it is most simply expressed as the surd √5. △Not a surd The square root of 4 is not a surd. It is the number 2, a whole, or rational, number. Simplifying surds Some surds can be made simpler by taking out factors that can be written as whole numbers. A few simple rules can help with this. ▷ Square roots A square root is the number that, when multiplied by itself, equals the number inside the root. a × a = a 3× 3 = 3 multiply the surd by itself to get the number inside the square root ▷ Multiplying roots Multiplying two numbers together and taking the square root of the result equals the same answer as taking the square roots of the two numbers and mutiplying them together.

49 FRACTIONS Types of fractions A proper fraction—where the numerator is smaller than the denominator—is just one type of fraction. When the number of parts is greater than the whole, the result is a fraction that can be written in two ways— either as an improper fraction (also known as a top-heavy fraction) or a mixed fraction. numerator has higher value than denominator numerator has lower value than denominator 1 4 35 4 ◁ Proper fraction In this fraction the number of parts examined, shown on top, is less than the whole.