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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 For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_03_homeworkhelp.html 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 For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_05_homeworkhelp.html or visit www.khanacademy.com 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│ For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_05_homeworkhelp.html or visit www.khanacademy.com 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 For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_05_homeworkhelp.html or visit www.khanacademy.com 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 For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_05_homeworkhelp.html or visit www.khanacademy.com 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: For more help, go to http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch03_07_homeworkhelp.html or visit www.khanacademy.com 6 7