Multiply: 1/2 x 1 3/5 x 2 7/9=

Multiply: 1/2 x 1 3/5 x 2 7/9=

A.
2 2/9

B.
20/9

C.
3 11/16

D.
2 21/90

The Correct answer and Explanation is:

o solve the multiplication problem 12×135×279\frac{1}{2} \times 1 \frac{3}{5} \times 2 \frac{7}{9}21​×153​×297​, we will follow these steps:

1. Convert Mixed Numbers to Improper Fractions:
   • For 1351 \frac{3}{5}153​:
     • Multiply the whole number 111 by the denominator 555 and add the numerator 333: 1×5+3=81 \times 5 + 3 = 81×5+3=8.
     • So, 135=851 \frac{3}{5} = \frac{8}{5}153​=58​.
   • For 2792 \frac{7}{9}297​:
     • Multiply the whole number 222 by the denominator 999 and add the numerator 777: 2×9+7=252 \times 9 + 7 = 252×9+7=25.
     • So, 279=2592 \frac{7}{9} = \frac{25}{9}297​=925​.
2. Multiply the Fractions:First, convert all mixed numbers into improper fractions:
   • 12\frac{1}{2}21​
   • 85\frac{8}{5}58​
   • 259\frac{25}{9}925​
   Now, multiply these fractions together:12×85×259\frac{1}{2} \times \frac{8}{5} \times \frac{25}{9}21​×58​×925​To multiply fractions, multiply the numerators together and the denominators together:
   • Numerators: 1×8×25=2001 \times 8 \times 25 = 2001×8×25=200
   • Denominators: 2×5×9=902 \times 5 \times 9 = 902×5×9=90
   So,20090\frac{200}{90}90200​
3. Simplify the Result:Simplify 20090\frac{200}{90}90200​ by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 200 and 90 is 10:200÷1090÷10=209\frac{200 \div 10}{90 \div 10} = \frac{20}{9}90÷10200÷10​=920​
4. Convert the Improper Fraction to a Mixed Number (if desired):209\frac{20}{9}920​ as a mixed number is 2292 \frac{2}{9}292​:
   • Divide 20 by 9 to get 2 with a remainder of 2.

Thus, the correct answer is B. 209\frac{20}{9}920​.