Document Sample

Sec 2.4 Change in Quantity and Subtracting Real Numbers Change in Quantity: If you had 15gals of gas in your tank and at the end of your trip you had only 2gals left, then the gas quantity decreased from 15 to 2. This change is called the change in quantity. In our case the quantity of gasoline decreased from 15 to 2 gallons. The actual change in quantity could be calculated by subtracting the starting quantity from the ending: 2 15 13 The change in quantity is the ending amount minus the beginning amount. Change in Quantity = Ending Amount – Beginning amount If the quantity increased the change is positive, if it decreased, the change is negative. Subtraction of Real Numbers. Subtracting some amount of money has the same effect as incurring debt or spending. That means that subtracting is the same as adding negative numbers, which suggests that in general subtracting a number is the same as adding the opposite of that number: a b a b Example: Subtract: 5 2 5 2 3 , which is the same as 5 2 3 , so 5 2 5 2 Subtracting a Negative Number: Example: A helicopter starts from the bottom of the canyon 150 ft below the sea level and rises to the altitude of 423 ft above the sea level. Find the change in altitude. Solution: Since the altitude changed from 150 ft (below the sea level altitude) to 423 ft (above the sea level), the change in altitude is the ending altitude minus the starting altitude: 423 150 the difference should be larger than 423 since the helicopter started from the altitude lower than the sea level. If we recall that a b a b , we get 423 150 423 opposite of 150 423 150 573 ft An opposite of a number is denoted by a negative sign, so the opposite of 5 is 5 . To denote the opposite of 5 we write it 5 . Since we know that the opposite of 5 is 5 we can observe that a a The opposite of an opposite of a number is the number itself. Example: Find an opposite of a number: a) 7 Opposite 7 b) 5 Opposite 5 Subtractive a negative number: 4 5 4 5 9 8 1 8 1 9 Changes of Increasing and Decreasing Quantities. An increasing quantity has a positive change. A decreasing quantity has a negative change. Example: The wolf population in the Greater Yellowstone area for various years is shown in the table. Year Population Change in population from each year to next 1996 40 - 1997 86 46 1998 112 26 1999 118 6 2000 177 59 2001 218 31 a. From what year to the next the changes in population were the greatest? What was that change? The change was the largest from year 1999 to 2000, The change was 59. b. From what year to the next the changes in population were the least? What was that change? The change was least from year 1998 to 1999, The change was 6. Group Exploration: A set of points is given in the table (by x- and y- coordinates). x y Change in y (current value minus previous) 0 3 - 1 5 2 7 3 9 4 11 5 13 a. Plot the points from the table. Do they lie on one line? b. Complete the third column in the table. Describe any patterns.

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 3 |

posted: | 2/21/2012 |

language: | |

pages: | 2 |

OTHER DOCS BY xiagong0815

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.