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Chapter 3 Fractions, Part 1 3-1 Introducing Fractions and Mixed Numbers Whole numbers and integers can be plotted on number lines such as those shown in Figure 3-1. Fractions, however, allow us to plot points between the numbers—half way between 2 and 3, for example; or between -1 and -2. There is no limit to how finely you can divide the space between two whole numbers or integers. 
Figure 3-1. Fractions allow you to plot values between whole numbers and integers. A First Look at Fractions The square in Figure 3-2 is divided into four tiles. - In the first example, one of the four tiles is red. This can be written as the fraction 1/4.
- In the second instance, two of the four tiles are red. This can be written as the fraction 2/4.
- In the third instance, three of the four tiles are red. This can be written as the fraction 3/4.
- In the fourth instance, four of the four tiles are red. This can be written as the fraction 4/4.
The fraction 1/4 is spoken as "one over four" or "one fourth" The fraction 3/4 is spoken as "three over four" or "three fourths." Fractions are written as two numbers, one over the other, and separated by a bar. Definition - The upper number in a fraction is the numerator.
- The lower number in a fraction is the denominator
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Figure 3-2. Fractions of four. | Exercises Express the following statements as fractions.
Click the ? symbol to see the correct answer. | 1. One out of three = ? | 2. Two out of five = ? | 3. Three out of five = ? | | 4. Four fifths = ? | 5. One eighth = ? | 6. Three sevenths = ? | | 7. Three sixteenths = ? | 8. 99 out of a hundred = ? | 9. Four out of seven = ? | | 10. Seven over nine = ? | | | Definitions - A proper fraction is one where the numerator is smaller than the denominator.
Examples: 1/2, 1/3, 2/3, -5/8 - An improper fraction is one where the absolute value of the numerator is greater than, or equal to, the denominator.
Examples: 3/2, 8/3, -16/5, 7/7 - A mixed number is one that includes an integer as well as a fractional part.
Examples: 11/2, 2 3/4, 6 5/8, -4 1/4 | 3-1.2 A First Look at Mixed Numbers | A mixed number expresses fractional parts that are equal or greater than 1. In Figure 3-3, for example, the blue tiles represent a total of three halves. There are two sets of tiles. Both halves of the first tile are colored blue. | 
Figure 3-3. Three halves of these tiles are colored blue.
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