Write each of the following as a common fraction or mixed number. Write your answer in lowest terms.
28. 15.35
Complete each of the following statements, using the symbol < or >
30. 5/16 0.313
34. Statistics. The following table gives the winning percentages of the top five coaches in NFL history. What fraction of his games has each coach won?
Coach Percentage
Don Shula 0.676
George Halas 0.672
Tom Landry 0.606
Curly Lambeau 0.624
Paul Brown 0.667
To write each of the given numbers as a common fraction or mixed number, we need to understand their decimal representations.
1. 28 can be written as a common fraction by putting it over the denominator 1: 28/1.
2. To write 15.35 as a common fraction or mixed number, we can start by observing that it is a decimal with two decimal places. Therefore, we can write it as a fraction by placing the decimal part (35) over 100, which represents two decimal places: 35/100. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 35 and 100 is 5. By dividing both 35 and 100 by 5, we get 7/20.
So, 15.35 can be written as the common fraction 7/20.
Now, let's move on to completing the statements using the comparison symbols < or >.
3. To compare 5/16 and 0.313, we need to convert the decimal 0.313 to a fraction. Since 0.313 has three decimal places, we can express it as 313/1000. Now, we have 5/16 and 313/1000 as fractions.
To compare these fractions, we can find a common denominator. The least common multiple (LCM) of 16 and 1000 is 8000. Therefore, we can convert both fractions to have denominators of 8000.
For 5/16, we can multiply both the numerator and denominator by 500 to get an equivalent fraction with a denominator of 8000: (5/16) * (500/500) = 2500/8000.
For 313/1000, we can multiply both the numerator and denominator by 8 to get an equivalent fraction with a denominator of 8000: (313/1000) * (8/8) = 2504/8000.
Now, we can compare these fractions. Since 2504/8000 is greater than 2500/8000, we can conclude that 5/16 < 0.313.
Therefore, the completed statement is 5/16 < 0.313.
Finally, let's calculate the fraction of games won for each coach in the given table.
4. Don Shula has won 67.6% of his games. To express this as a fraction, we can write it as the fraction 67.6/100. Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 0.8), we get 8/10 or 4/5.
Similarly, for the other coaches:
- George Halas: 67.2% = 67.2/100 = 672/1000 = 84/125
- Tom Landry: 60.6% = 60.6/100 = 606/1000 = 303/500
- Curly Lambeau: 62.4% = 62.4/100 = 624/1000 = 312/500
- Paul Brown: 66.7% = 66.7/100 = 667/1000 = 667/1000.
Therefore, the fractions of games won for each coach are:
Don Shula: 4/5
George Halas: 84/125
Tom Landry: 303/500
Curly Lambeau: 312/500
Paul Brown: 667/1000.