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    Fractions II and Decimals: Mixed Numbers

    Uploaded by

    Muralee Veeramalai
    1) Mixed numbers can be compared by looking at either the whole numbers or fractions. Fractions can be converted to improper fractions or mixed numbers by multiplying/dividing the numerator and denominator. 2) Proper fractions have smaller numerators, improper fractions have larger or equal numerators. Mixed numbers can be changed to improper fractions by multiplying the whole number by the denominator and adding. 3) When adding or subtracting fractions, they must have a common denominator or be converted to one first before combining numerators. Whole numbers and mixed numbers can also be added or subtracted using this method.

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    © All Rights Reserved
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    Fractions II and Decimals: Mixed Numbers

    Uploaded by

    Muralee Veeramalai
    107 views6 pages
    1) Mixed numbers can be compared by looking at either the whole numbers or fractions. Fractions can be converted to improper fractions or mixed numbers by multiplying/dividing the numerator and denominator. 2) Proper fractions have smaller numerators, improper fractions have larger or equal numerators. Mixed numbers can be changed to improper fractions by multiplying the whole number by the denominator and adding. 3) When adding or subtracting fractions, they must have a common denominator or be converted to one first before combining numerators. Whole numbers and mixed numbers can also be added or subtracted using this method.

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    fraction

    Original Title

    4. Fraction & Decimal

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    1) Mixed numbers can be compared by looking at either the whole numbers or fractions. Fractions can be converted to improper fractions or mixed numbers by multiplying/dividing the numerator and denominator. 2) Proper fractions have smaller numerators, improper fractions have larger or equal numerators. Mixed numbers can be changed to improper fractions by multiplying the whole number by the denominator and adding. 3) When adding or subtracting fractions, they must have a common denominator or be converted to one first before combining numerators. Whole numbers and mixed numbers can also be added or subtracted using this method.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    107 views6 pages

    Fractions II and Decimals: Mixed Numbers

    Uploaded by

    Muralee Veeramalai
    1) Mixed numbers can be compared by looking at either the whole numbers or fractions. Fractions can be converted to improper fractions or mixed numbers by multiplying/dividing the numerator and denominator. 2) Proper fractions have smaller numerators, improper fractions have larger or equal numerators. Mixed numbers can be changed to improper fractions by multiplying the whole number by the denominator and adding. 3) When adding or subtracting fractions, they must have a common denominator or be converted to one first before combining numerators. Whole numbers and mixed numbers can also be added or subtracted using this method.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    of 6

    Fractions II and Decimals

    By Muralee.V.

    Mixed Numbers
    The values of mixed numbers can be compared in two ways:
    a. A mixed number with the largest whole number has the largest value.
    b. If mixed numbers have the same whole number, then do comparison with their
    fraction values.
    Example 1
    State the largest mixed number for each of the following.
    1 1
    a. 5 and 6
    4 7
    1 2
    b. 7 and 7
    4 5

    Solution
    1 1
    a. 5 and 6
    4 7
    Compare the whole numbers

    1 1
    Therefore, 5 < 6
    4 7
    1 2
    b. 8 and 8
    4 5
    Same whole number
    5 8
    8 and 8
    20 20
    Change the fractions into its equivalent
    with their common denominator
    1 2
    Therefore, 8 < 8
    4 5

    Proper Fractions and Improper Fractions

    A proper fraction has a bigger denominator than its numerator.


    Example
    5 Smaller numerator
    6
    Bigger denominator

    An improper fraction has a smaller or equal denominator than its numerator.


    Example
    8 Bigger numerator
    3
    Smaller denominator
    Equal numerator
    38
    38
    Equal denominator
    A mixed number can be changed into an improper fraction by following these steps:
    I. Multiply the whole number with denominator;
    II. Then, add the product to the numerator;
    III. Leave the denominator unchanged.
    Example

    II
    3 (5 7) 3
    7 =
    5
    I
    5
    35 3
    =
    5
    38
    =
    5

    An improper fraction can be changed into a mixed number by following these steps:
    I. Divide the numerator with the denominator
    II. Leave the denominator unchanged.
    III. The obtained quotient becomes the whole number.
    IV. The remainder becomes the numerator

    Example

    15 Quotient
    3 47
    47 2 3
    = 15 17
    3 3 15
    Denominator 2 Remainder

    Addition and Subtraction of Fractions and Mixed Numbers


    1. Addition or subtraction of fractions with a common denominator can be done by
    adding or subtracting the numerator only.


    2. The denominator remains unchanged
    3. If possible, simplify the answer to its lowest term.

    Example 2
    Solve the following
    3 7
    a)
    11 11
    1 5
    b)
    18 18

    Solution
    3 7 37
    a) =
    11 11 11
    10
    =
    11

    1 5 1 5
    b) =
    18 18 18
    6
    =
    18
    1
    =
    3
    4. Addition or subtraction of fractions with different denominators can be done by
    changing each fraction into its equivalent with a common denominator.
    5. Then, add or subtract the numerator only
    6. If possible, simplify the answer to its lowest term.

    Example 3
    Solve the following
    4 2
    a)
    13 39
    2 4
    b)
    3 7

    Solution
    4 2 43 2
    a) =
    13 39 13 3 39
    12 2
    =
    39 39
    14
    =
    39
    2 4 27 43
    b) = 3 7 73
    3 7
    14 12
    =
    21 21
    2
    =
    21

    7. Addition or subtraction of fractions, whole numbers and mixed numbers.

    Example 4
    4
    a) 5
    9
    5 3
    b) 3
    6 5

    Solution
    4 4
    a) 5 = 4 1
    9 9
    9 4
    =4
    9 9
    5
    =4
    9

    5 3 55 36
    b) 3 =3+
    6 5 65 56
    25 18
    =3+
    30 30
    43
    =3+
    30

    13
    =3+1
    30
    13
    =4
    30

    Multiplication and Division of Fractions


    1. In multiplication:
    I. Multiply numerator by numerator
    II. Multiply denominator by denominator
    III. If possible, simplify the answer to its lowest term.
    * method of cancellation can be used
    Example 5
    3 25 75
    a) =
    5 27 135
    5
    =
    9
    or
    1 5
    3 25 5
    = method of cancellation
    1 5 927 9

    2. In division:
    I. Multiply the fraction with the reciprocal of the second fraction
    (reciprocal of a number or fraction refers to the inverse of the number or
    fraction)
    Example
    1
    3 reciprocal
    3
    3 reciprocal 14
    14 3
    II. If possible, simplify the answer to its lowest term.
    * method of cancellation can be used

    Example 6
    2 8 2 49 reciprocal
    a) =
    7 49 7 8
    1 7
    2 49
    =
    7 8
    1 4

    7
    =
    4
    3
    =1
    4

    3. In multiplication or division of a mixed number by a mixed number:


    I. Change the mixed numbers into improper fractions
    II. Then, carry out the computations.
    III. If possible, simplify the answer to its lowest term.
    * method of cancellation can be used

    Example 6 1 7

    1 2
    3 3 8 35
    a) 1 2 = Change to
    5 16 5 16
    improper fraction
    7
    =
    2
    1
    =3
    2

    Decimals

    Place Tens Ones . Tenths Hundreth Thousanth


    Values s s
    Digits 6 6 Decimal 3 2 1
    Digit 60 6 Point 0.3 0.02 0.001
    Values

    Test Yourself

    4 8
    1) 2 2
    7 14
    2 1 1
    2) 1
    24 4 2
    3) 0.89 x 2.7
    8
    4) 27 x 1.07
    10

    Answers
    1) 1
    1
    2)
    16
    3) 2.403
    4) 26.144

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