Download Unit 1c – The Number System – Rational Numbers Class Notes

Unit 1c – The Number System – Rational Numbers
Class Notes
Date
Locating a point and its opposite on a number line
Learning Target: I can locate a point and its opposite on a number line.
Important Terms:
 Positive Number: Any number greater than 0. They may be written with a positive sign (+) but they are usually
without it. Ex 8 or +8
 Negative Number: Any number less than 0. They are always written with a negative sign (-). Ex. -8
 Opposite: Numbers that are the same distance from 0 on a number line but on different sides of 0. Ex. 3 and -3
 Integer: A set of all numbers and their opposites.
o Whole Numbers: Includes all whole numbers and their opposites. Ex. 0, 1, 2, 3, 4, …
Examples:
Graph each integer and its opposite on the number line.
1)
7
2)
-3
3) 0
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0r visit www.khanacademy.com
1
Date
Describe quantities using positive and negative numbers
Learning Target: I can describe quantities using positive and negative numbers.
Important Information:


Positive Number: Any number greater than 0. They may be written with a positive sign (+) but they are usually
without it. Ex 8 or +8
Negative Number: Any number less than 0. They are always written with a negative sign (-). Ex. -8
Examples:
Name a positive or negative number for each situation.
1) Earning $50
3) 7 feet above sea level
2) 20° below zero
4) a decrease of 39 points
Write a situation that each integer could represent.
5)
+49
6) -83
7) -7
8) +15
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2
Date
Absolute Value
Learning Target: I can identify and explain the absolute value of a number.
Important Terms:
 Absolute Value: The distance a number is from 0 on a number line. The symbol for absolute value is ││.
Ex. │-5│ = 5 and │3│ = 3
Important Information:
 Absolute values are never negative.
 Opposite integers have the same absolute value. Ex. │-5│ = 5 and │5│ = 5
 The absolute value of zero is zero. Ex. │0│ = 0
Examples:
Use the number line to find the absolute value of each integer.
1) │-9│
3) │6│
2) │3│
4) │-2│
Find each absolute value.
5) │419│
8) │96│
6) │-295│
9) │723│
7) │-806│
10) │-150│
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3
Date
Converting between decimals and fractions
Learning Target: I can convert between decimals and fractions.
Writing Fractions as Decimals
 Divide the numerator by the denominator.
o 3/4 becomes 3 ÷ 4 or 0.75
o 1/3 becomes 1 ÷ 3 or 0.3333…..
 If you have a mixed number, the whole numbers goes before the decimal, and then divide out the fraction.
o 6 ¼ becomes 1 ÷ 4 or 0.25, when placed with the whole number you get, 6.25.
o 8 7/8 becomes 7 ÷ 8 or 0.875, when placed with the whole number you get, 8.875.
Writing Decimals as Fractions



Make sure your final answer is reduced, or in simplest form.
Examples:
Write each fraction or mixed number as a decimal.
1) 2/5
2) 2 7/8
3) 2 5/6
4) 17/20
Write each decimal as a fraction or mixed number.
1) 0.15
2) 2.6
3) 0.625
4) 3.375
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4
Date
Compare Rational Numbers
Learning Target: I can compare rational numbers, including integers, fractions and decimals.
Important Information:
 >, is the symbol for great than.
 <, is the symbol for less than.
 =, is the symbol for equal to.
Steps:
1) Rewrite all fractions as decimals.
2) Compare digits to determine the order.
Examples:
Compare. Write <, > or =.
1) 0.75
¾
2) 5/8
3) 0.78
7/9
4) 0.65
0.5
2/3
Order the fractions and decimals from least to greatest.
1) 0.11, 1/10, 0.13
2) 3/7, -0.76, 0.31
3) 0.38, ¾, 1/5
4) 2/5, 0.7, -2/3
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5
Date
Graph/Identify Points
Learning Target: I can graph and identify point on the coordinate plane in all four quadrants.
Important Terms:
 Coordinate grid (plane): A plane formed by the intersection of a horizontal line called the x-axis and a vertical
line called the y-axis.
 Ordered pair: A pair of numbers that can be used to locate a point on a coordinate plane.
 Origin: The point where the x-axis and y-axis intersect on the coordinate plane. (0,0)
 Quadrant: The x-axis and y-axis divide the coordinate plane into four regions. Each region is called a quadrant.
 x-coordinate: The first number in an ordered pair. It tells the distance to move right or left from the origin.
 y-coordinate: The second number in an ordered pair. It tells the distance to move up or down from the origin.
Examples:
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