Fundamentals of Math

Fundamentals of Mathematics

Chapter 2: Fractions, Decimals, and Percentages Now that have you have a thorough understanding of integers and order of operations, you may have noticed some difficulty when dividing certain numbers. For instance, 18 divided by 6 or 10 divided by 2 may be relatively simple, but something like 24 divided by 5 causes some trouble: 5 doesn't go into 24 evenly--the quotient is somewhere between 4 and 5! (We would, therefore, say that 24 is not divisible by 5.) This uncertainty with the divisibility is definitely a conundrum, but this type of division is not far-fetched from what people experience in the real world. Such as a recipe calling for one and a half pound of beef or a pizzaiolo needing to cut the pizza into eighths. 2.1 Introduction to Fractions From our previous chapter, we know Integers are all the counting positive and negative counting numbers (. . . , −3, −2, −1, 0, 1, 2, 3, . . . ) . However, between any two integers (such as 0 and 1 or −5 and −4 ) is an entirely new set of numbers (rational) known as fractions. When we discuss fractions, we will refer to a number such as one-fourth ( 1 4 ) as a fraction rather than the decimal notation 0.25. The term fraction, however, simply tells us howmany parts of a whole we have - whether it is written as a decimal, percentage, or with traditional fraction notation. ≠ 0 and and are both real numbers. The top number ( ) is referred to as the numerator , and the bottom number ( ) is the denominator (remember "D" for the number down below). 3 ← Numerator 4 ← Denominator The line seen between the numerator and denominator is treated as the division operator (like ÷ ). Let's take a look at this relationship. Imagine a circle divided into six equal parts (the denominator), and we shaded in one part (the numerator), then we are left with one-sixth of the circle (the shaded portion). Fractions are written in the form , where

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