Question

4 2/3:6 1/15+1 1/14-1 39/73•(5 5/7-5 1/16=

Answer 1

$4 \frac{2}{3} \div 6 \frac{1}{15} + 1 \frac{1}{14} - 1 \frac{39}{73} \times (5 \frac{5}{7} - 5 \frac{1}{16} ) = \frac{233}{1890}$

Answer 2

Let's break down the expression step by step:

1. Start with the addition and subtraction inside the parentheses: (6 1/15 + 1 1/14 - 1 39/73)

   First, find a common denominator for 15, 14, and 73, which is 2190.

   (6 * 146 + 1 * 156 - 1 * 30) / 2190

   Now, calculate the numerator:

   (876 + 156 - 30) / 2190

   Combine the numerators:

   (1002) / 2190

   Simplify the fraction by finding the greatest common divisor (GCD) of 1002 and 2190, which is 6:

   (1002 / 6) / (2190 / 6)

   Now, divide both the numerator and denominator by 6:

   (167) / (365)

2. Now, subtract this result from 4 2/3:

   4 2/3 - (167 / 365)

   To subtract mixed numbers, you'll need to find a common denominator. In this case, it's 3 * 365 = 1095.

   Convert 4 2/3 to an improper fraction:

   (4 * 3 + 2) / 3 = 14/3

   Now, subtract the fractions:

   (14/3 * 365 - 167) / 1095

   Calculate the numerator:

   (5110 - 167) / 1095

   Subtract the numerators:

   4943 / 1095

3. Next, multiply this result by the expression in the last set of parentheses: (5 5/7 - 5 1/16)

   First, find a common denominator for 7 and 16, which is 112.

   Convert 5 5/7 to an improper fraction:

   (5 * 7 + 5) / 7 = 40/7

   Convert 5 1/16 to an improper fraction:

   (5 * 16 + 1) / 16 = 81/16

   Now, subtract the fractions:

   (40/7 - 81/16)

   Find a common denominator of 112:

   (40/7 * 16/16 - 81/16 * 7/7) / 112

   Calculate the numerator:

   (640/112 - 567/112) / 112

   Subtract the numerators:

   (73/112) / 112

   To divide fractions, you can multiply by the reciprocal:

   (73/112) * (1/112)

   Multiply the numerators and denominators:

   (73 * 1) / (112 * 112)

   Simplify:

   73 / 12544

4. Finally, multiply the result from step 2 by the result from step 3:

   (4943 / 1095) * (73 / 12544)

   Multiply the numerators:

   (4943 * 73) / (1095 * 12544)

   Calculate the products:

   360839 / 1374640

So, the final result of the expression is approximately:

360839 / 1374640