1150 day 8
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    1150 day 8 1150 day 8 Presentation Transcript

    • RationalNumbers
    • Integers: …, -3, -2, -1, 0, 1, 2, 3, …A Rational Number can be written in theform a , where a and b are integers andb ≠ 0. b 2 3 www.visualfractions.com
    • Representing fractions 2 3Area modelNumber Line Model 0 1 2 1 3 3Set model
    • Equivalent (equal) fractions represent the samenumber. 2 2 4 3 2 6 2 3 6 3 3 9 Fundamental Law of Fractions a a c b b c
    • 2 6Show that and are equal by finding 3 9a common denominator. The least common denominator of twofractions is the LCM of their denominators.LCM(3,9) = 9 2 3 6 3 3 9
    • 2 6Show that and are equal by 3 9simplifying both fractions. A fraction is in simplest form if its numerator and denominator have no common factor other than 1. 2 is simplified 6 3 2 3 9 3 3
    • 2 6Show that and 3 9 are equal by crossmultiplying. a c if ad bc b d 18 18 18 = 18 2 6 so 2 6 3 9 3 9
    • Ordering rational numbersPlace <, > or = between the two numbers: 2 3 < 0 1 2 3 4 5 6 1 7 7 7 7 7 7 7 7 7 1 3 > 7 5 5 1 1 1 < 5 5 4 1 4
    • 1 1Find one rational number between and 5 4 1 4 1 5 LCD = 20 5 4 4 5 4 2 5 2 20 2 20 2 9 8 10 40 40 40
    • 1 1Find two rational numbers between and 6 5 1 5 1 6 LCD = 30 6 5 5 6 5 2 6 2 30 2 30 2 10 2 12 2 60 2 60 2 21 22 23 20 24 , , 120 120 120 120 120
    • A mixed number represents the sum of an integerand a fraction. 1 1 1 2 1 2 1 1 1 2 1 2 -2 11 2 -1 0 1 1 1 2 2
    • 2Change 1 3 to an improper fraction.An improper fraction has a numerator that is greater than or equal to its denominator. 2 3 2 1 3 3 3 2 1 3 5 3
    • Change 5 to a mixed number. 2 1 2 2 1 1 1 2 2 2 5 2R1 4 2 1 2 1
    • Adding Rational Numbers 1 1 2 1 4 4 4 2 3 1 1 4 3 4 3 4 3 4 7 12 12 12
    • 2 31 3 2 4 2 4 8 1 3 4 1 12 9 2 3 3 4 3 2 12 17 3 12 5 4 12
    • 2 31 3 2 4 2 5 4 20 1 3 3 4 12 3 11 3 33 2 4 4 3 12 53 12 5 4 12
    • Subtracting Rational Numbers 4 2 1 3 8 3 5 4 9 12 3 36 36 36 2 2 1 5 4 5 1 2 5 2 5 10 10 10
    • 1 24 5 1 3 1 3 3 3 18 4 5 3 4 15 2 5 10 1 3 5 1 15 8 2 15
    • 1 2 4 5 1 33 21 5 53 5 3 5 63 25 15 15 38 8 2 15 15
    • Multiplication of Rational Numbers 3·2 =6 3 groups of 2 3·½ = 3 = 1 ½ or 2 3 groups of ½
    • 2 1 2 a c a c = 3 4 12 b d b d Rectangle model 1 423
    • 1 1 1 12 4 1 2 (2 4 )(1 2 )9 3 274 2 8 3 3 8
    • Dividing rational numbers 6 3 =2 3 3 How many threes are in six? 6 2 =3 2 2 2 How many twos are in six?
    • 6 ½= 12 How many one-halfs are in six?6 ¼= 24 How many one-fourths are in six?
    • 1 13 6 =2 How many one-sixths are in one-third? a c a d b d b c 1 1 1 6 6 2 3 6 3 1 3
    • Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:a) 2 yards of fabric 20 2 = 10 blouses
    • Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:b) 2 ½ yards of fabric 8 blouses 1 5 20 2 40 20 2 2 20 2 1 5 5 =8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
    • Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:c) 2 1 yards of fabric 8 blouses 3 1 7 20 3 60 4 20 2 3 20 3 1 7 7 8 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20d) How many yards of fabric is left over? 1 7 56 2 Fabric used: 8 2 3 8 3 3 18 3 yards Fabric left: 20 18 2 1 1 yards 3 3