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Simplify these fractions: 1. (18)/(8) x (15)/(3) x (16)/(4) 2. (12)/(4) x (16)/(12) x (y)/(8)

Mathematics

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Step-by-step solution

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Here are the solutions for the fraction multiplication problems:

: 188×153×164\frac{18}{8} \times \frac{15}{3} \times \frac{16}{4}

  1. Simplify the fractions by cross-cancellation.

    188×153×164\frac{18}{8} \times \frac{15}{3} \times \frac{16}{4}

    Cancel 15 and 3: 15÷3=515 \div 3 = 5, 3÷3=13 \div 3 = 1.
    Cancel 16 and 4: 16÷4=416 \div 4 = 4, 4÷4=14 \div 4 = 1.
    The expression becomes:

    188×51×41\frac{18}{8} \times \frac{5}{1} \times \frac{4}{1}

    Cancel 18 and 8 by dividing by 2: 18÷2=918 \div 2 = 9, 8÷2=48 \div 2 = 4.
    The expression becomes:

    94×51×41\frac{9}{4} \times \frac{5}{1} \times \frac{4}{1}

    Cancel 4 (denominator of the first fraction) and 4 (numerator of the third fraction): 4÷4=14 \div 4 = 1.
    The expression becomes:

    91×51×11\frac{9}{1} \times \frac{5}{1} \times \frac{1}{1}
  2. Multiply the remaining numerators and denominators.

    9×5×11×1×1=451=45\frac{9 \times 5 \times 1}{1 \times 1 \times 1} = \frac{45}{1} = 45

    The final answer is 45\boxed{\text{45}}.

    : 124×1612×y8\frac{12}{4} \times \frac{16}{12} \times \frac{y}{8}

  3. Simplify the fractions by cross-cancellation.

    124×1612×y8\frac{12}{4} \times \frac{16}{12} \times \frac{y}{8}

    Cancel 12 (numerator of the first fraction) and 12 (denominator of the second fraction): 12÷12=112 \div 12 = 1.
    The expression becomes:

    14×161×y8\frac{1}{4} \times \frac{16}{1} \times \frac{y}{8}

    Cancel 16 (numerator of the second fraction) and 4 (denominator of the first fraction): 16÷4=416 \div 4 = 4, 4÷4=14 \div 4 = 1.
    The expression becomes:

    11×41×y8\frac{1}{1} \times \frac{4}{1} \times \frac{y}{8}

    Cancel 4 (numerator of the second fraction) and 8 (denominator of the third fraction): 4÷4=14 \div 4 = 1, 8÷4=28 \div 4 = 2.
    The expression becomes:

    11×11×y2\frac{1}{1} \times \frac{1}{1} \times \frac{y}{2}
  4. Multiply the remaining numerators and denominators.

    1×1×y1×1×2=y2\frac{1 \times 1 \times y}{1 \times 1 \times 2} = \frac{y}{2}

    The final answer is y2\boxed{\frac{y}{2}}.

    : 189×169×124\frac{18}{9} \times \frac{16}{9} \times \frac{12}{4}

  5. Simplify the fractions by cross-cancellation.

    189×169×124\frac{18}{9} \times \frac{16}{9} \times \frac{12}{4}

    Cancel 18 and 9: 18÷9=218 \div 9 = 2, 9÷9=19 \div 9 = 1.
    The expression becomes:

    21×169×124\frac{2}{1} \times \frac{16}{9} \times \frac{12}{4}

    Cancel 12 and 4: 12÷4=312 \div 4 = 3, 4÷4=14 \div 4 = 1.
    The expression becomes:

    21×169×31\frac{2}{1} \times \frac{16}{9} \times \frac{3}{1}

    Cancel 3 (numerator of the third fraction) and 9 (denominator of the second fraction): 3÷3=13 \div 3 = 1, 9÷3=39 \div 3 = 3.
    The expression becomes:

    21×163×11\frac{2}{1} \times \frac{16}{3} \times \frac{1}{1}
  6. Multiply the remaining numerators and denominators.

    2×16×11×3×1=323\frac{2 \times 16 \times 1}{1 \times 3 \times 1} = \frac{32}{3}

    The final answer is 323\boxed{\frac{32}{3}}.

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