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-

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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.