SAMPLE 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 . However, between any two integers (..., − 3, − 2, − 1, 0, 1, 2, 3, ...) (such as 0 and 1 or and ) is an entirely new set of numbers (rational) known as − 5 − 4 fractions. When we discuss fractions, we will refer to a number such as one-fourth as a 1 4 ( ) fraction rather than the decimal notation 0.25. The term fraction, however, simply tells us how many parts of a whole we have - whether it is written as a decimal, percentage, or with traditional fraction notation. Fractions are written in the form , where and and are both real numbers. The top ≠0 number is referred to as the numerator , and the bottom number is the denominator ( ) ( ) (remember "D" for the number down below). 34 ←← 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).

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