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  1. Thunguyet
    0
    2021-08-31T13:45:34+00:00
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    1 \frac{1}{9} \times 4 \frac{1}{2} + (3 \frac{1}{5} - \frac{1}{3} ) = \\

    \frac{9 + 1}{9} \times \frac{8 + 1}{2} + ( \frac{15 + 1}{5} - \frac{1}{3} ) = \\

    \frac{10}{9} \times \frac{9}{2} + ( \frac{16 \times 3}{5 \times 3} - \frac{1 \times 5}{3 \times 5} ) = \\

    \frac{9 \times 10}{9 \times 2} + ( \frac{48}{15} - \frac{5}{15} ) = \\

    \frac{10}{2} +( \frac{48 - 5}{15} ) = \\

    5 + ( \frac{43}{15} ) = \\

    \frac{75}{15} + \frac{43}{15} = \frac{118}{15} \\

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  2. Giakhanh
    0
    2021-08-31T13:46:14+00:00
    Reply

    Answer:

    118/15 or 7.8666666666666666666666666666666666666666666666666666666666666666… decimal

    Step-by-step explanation:

    Simplify the following:

    (1 + 1/9) (4 + 1/2) + 3 + 1/5 – 1/3

    Put 1 + 1/9 over the common denominator 9. 1 + 1/9 = 9/9 + 1/9:

    9/9 + 1/9 (4 + 1/2) + 3 + 1/5 – 1/3

    9/9 + 1/9 = (9 + 1)/9:

    (9 + 1)/9 (4 + 1/2) + 3 + 1/5 – 1/3

    9 + 1 = 10:

    10/9 (4 + 1/2) + 3 + 1/5 – 1/3

    Put 4 + 1/2 over the common denominator 2. 4 + 1/2 = (2×4)/2 + 1/2:

    10/9 (2×4)/2 + 1/2 + 3 + 1/5 – 1/3

    2×4 = 8:

    10/9 (8/2 + 1/2) + 3 + 1/5 – 1/3

    8/2 + 1/2 = (8 + 1)/2:

    10/9 (8 + 1)/2 + 3 + 1/5 – 1/3

    8 + 1 = 9:

    10/9×9/2 + 3 + 1/5 – 1/3

    10/9×9/2 = (10×9)/(9×2):

    (10×9)/(9×2) + 3 + 1/5 – 1/3

    (10×9)/(9×2) = 9/9×10/2 = 10/2:

    10/2 + 3 + 1/5 – 1/3

    The gcd of 10 and 2 is 2, so 10/2 = (2×5)/(2×1) = 2/2×5 = 5:

    5 + 3 + 1/5 – 1/3

    Put 5 + 3 + 1/5 – 1/3 over the common denominator 15. 5 + 3 + 1/5 – 1/3 = (15×5)/15 + (15×3)/15 + 3/15 – 5/15:

    (15×5)/15 + (15×3)/15 + 3/15 – 5/15

    15×5 = 75:

    75/15 + (15×3)/15 + 3/15 – 5/15

    15×3 = 45:

    75/15 + 45/15 + 3/15 – 5/15

    75/15 + 45/15 + 3/15 – 5/15 = (75 + 45 + 3 – 5)/15:

    (75 + 45 + 3 – 5)/15

    | 1 |  

    | 7 | 5

    | 4 | 5

    + | | 3

    1 | 2 | 3:

    (123 – 5)/15

    | | 1 | 13

    | 1 | 2 | 3

    – | | | 5

    | 1 | 1 | 8:

    Answer: 118/15

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