Ch 3 – Addition and Subtraction Equations€¦ · Web viewCh 3 – Addition and Subtraction...
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Ch 3 – Addition and Subtraction Equations
3.1 – Rational Numbers
Rational Numbers:
Rational Number:
Graphing on a number line:
Inequality:
Comparison Property:
Example: Replace each with <, >, or = to make a true sentence.
-1
-3(2)(0) 7 + (-8)
-1 -14.2
-5(0) 16 + (-16)
Cross Products:
Comparison Property for Rational Numbers:
Examples: Replace each with <, >, or = to make a true sentence.
Example: Write the following numbers in order from least to greatest:
Example: Write the following numbers in order from least to greatest:
Unit Cost:
Example: Latisha needs to buy snacks for her art club. A package of 12 granola bars costs $2.69 and a package of 18 granola bars costs $3.55. Which is the better buy? Explain.
Example: Rolanda needs to buy colored pencils. The cost of a package of 12 pencils is $6.39. A package of 24 pencils costs $12.89. Which is the better buy? Explain.
3.2 – Adding and Subtracting Rational Numbers
Rules-
-
Example: Find each sum.
Example: Suppose the water level in a pond was measured over a 4-year period. The level above or below average for this pond for each of the 4 years is given in the table. Find the net change in the water level of this pond.
Example: Find the difference.
Example: Evaluate c – d if and .
Example: Evaluate x – y if x = 25.8 and y = -13.9.
3.3 – Mean, Median, Mode, and Range
Measures of Central Tendency:
Mean:
Example: Find the mean of the snack food data.
Median:
Example: The stem-and-leaf plot shows the number of children enrolled in each of 9 gymnastics classes offered at a local recreation center.
Find the mean of the gymnastics data.
Find the median of the gymnastics data.
Example: Find the median of each set of data.4, 6, 12, 5, 8
10, 3, 17, 1, 8, 6, 12, 15
Mode:
Example: Find the mode of the gymnastics data.
Example: Find the mode of each set of data.7, 19, 9, 4, 7, 2
300, 34, 40, 50, 60
Measures of Variation:
Range:
Example: Find the range of the gymnastics data.
Example: Find the range of each set of data
4, 6, 12, 5, 8
Example: The table shows the test results of two different classes on the same test. How do the results for Class A compare to the results for Class B?
Types of Data:Univariate:
Categorical:
Bivariate:
Measurement:
3.4 – Equations
Statement:
Open Sentences:
Replacement Set:
Solving:
Solution:
Example: Find the solution of 13 = 33 + 4d if the replacement set is {-6, -5, -4, -3}.
Example: Find the solution of if the replacement set is {0, 1, 2, 3}.
Example: The temperature C, in degrees Celsius, that is equivalent to a temperature of F degree Fahrenheit
is given by . If the thermometer reads 25° C, what is the temperature in degrees Fahrenheit: 76° F, 77° F, 78° F, or 79° F.
Example: Solve each equation.
3.6 – Solving Addition and Subtraction Equations
Addition Property of Equality:
Examples:
Subtraction Property of Equality:
Example: Yoko was born in 1982 and her great-grandfather Hideo was born in 1917. Use the equation 1917 + n = 1982 to find the number of years between their births.
3.7 – Solving Equations Involving Absolute Values
Absolute Value Reminder:
Examples: Solve and check each equation.
|x – 3| = 5
|d – 4| = 3
|c – 4| = 2
6 = |5 + h|
|a + 6| + 5 = 12
|g + 3| - 2 = 6
|m + 5| - 4 = 18
13 = |-8 + d| + 2
Empty Set:
Example: solve and check each equation
|d| + 7 = 2
|w| - 18 = -6
|y + 5| - 2 = -7
Example: In a survey, it was found that 78% of voters in a school district favored building a new high school. It is estimated that the actual number of voters that favor building the school differs from 78% by 5%. Write and then solve an equation that could be used to find the least and greatest percentage of voters that favor building a new high school.