Question

1\4 x 4 3\4 x 16\37 + (4 3\7 + 1 2\3) x 16\21 + 2\27 x 4 1\2

Answer 1

........................=8  5/6  (или  8 76/111)

1)   1/4 * 4 3/4 * 16/37=1/4 * 19/4 * 16/37=19/37  ( если 16/38, то получается 19/38=1/2)
2)   4 3/7+1 2/3=4 9/21+1 14/21=5 23/21=6 2/21
3)   6 2/21 : 16/21=128/21 * 21/16=8
4)   2/27 * 4 1/2=2/27 * 9/2=1/3
5)   19/37+ 8 + 1/3=57/111+8+19/111=8 76/111  (  или   1/2+8+1/3=3/6+8+2/6=8 5/6)

Answer 2

To solve the expression, let's break it down step by step:

1. Calculate 1/4 multiplied by 4 3/4: 1/4 x 4 3/4 = (1/4) x (4 + 3/4) = (1/4) x (16/4 + 3/4) = (1/4) x (19/4) = 19/16

2. Calculate (4 3/7 + 1 2/3) multiplied by 16/21: First, let's find the sum of 4 3/7 and 1 2/3: 4 3/7 + 1 2/3 = (4 + 3/7) + (1 + 2/3) = (28/7 + 3/7) + (3/3 + 2/3) = 31/7 + 5/3

   Now, multiply the above result by 16/21: (31/7 + 5/3) x 16/21 = [(31/7) x (16/21)] + [(5/3) x (16/21)] = (31 x 16)/(7 x 21) + (5 x 16)/(3 x 21) = 496/147 + 80/63 = (496 x 3)/(147 x 3) + (80 x 7)/(63 x 7) = 1488/441 + 560/441 = (1488 + 560)/441 = 2048/441

3. Calculate 2/27 multiplied by 4 1/2: 2/27 x 4 1/2 = (2/27) x (4 + 1/2) = (2/27) x (8/2 + 1/2) = (2/27) x (9/2) = 18/54 = 1/3

Now, let's add up the results we obtained:

19/16 + 2048/441 + 1/3

To add fractions, we need a common denominator. The least common multiple of 16, 441, and 3 is 3,168. Let's convert each fraction to have this denominator:

(19/16) x (198/198) = 3612/3168 (2048/441) x (72/72) = 147456/3168 (1/3) x (1056/1056) = 1056/3168

Now, we can add the fractions:

(3612/3168) + (147456/3168) + (1056/3168) = 149124/3168

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, we get:

149124/3168 = 47/1

Therefore, the final result is 47.