Question

4 7/9•1 13/14-3 7/12•1 13/14+1 13/14•1 13/18

Answer 1

$4 \frac{7}{9} * 1 \frac{13}{14} - 3 \frac{7}{12} * 1 \frac{13}{14} + 1 \frac{13}{14} * 1 \frac{13}{18} = 1 \frac{13}{14} *( 4\frac{7}{9} - 3\frac{7}{12} +1 \frac{13}{18} )=$
$\frac{27}{14} *( \frac{43}{9} - \frac{43}{12} + \frac{31}{18} )= \frac{27}{14} * \frac{172-129+62}{36} = \frac{27}{14} * \frac{105}{36} = \frac{27}{14} * \frac{35}{12} =$
$\frac{9}{2} * \frac{5}{4} = \frac{45}{8} = 5 \frac{5}{8} = 5,625$

Answer 2

To calculate the expression:

4 7/9 * 1 13/14 - 3 7/12 * 1 13/14 + 1 13/14 * 1 13/18

Let's break it down step by step:

Step 1: Convert mixed numbers to improper fractions. 4 7/9 = (4 * 9 + 7)/9 = 43/9 1 13/14 = (1 * 14 + 13)/14 = 27/14 3 7/12 = (3 * 12 + 7)/12 = 43/12 1 13/14 = 27/14 1 13/18 = (1 * 18 + 13)/18 = 31/18

So the expression becomes:

(43/9) * (27/14) - (43/12) * (27/14) + (27/14) * (31/18)

Step 2: Perform the multiplications and subtractions.

(43/9) * (27/14) = (43 * 27) / (9 * 14) = 1161/126

(43/12) * (27/14) = (43 * 27) / (12 * 14) = 1161/168

(27/14) * (31/18) = (27 * 31) / (14 * 18) = 837/252

Now, let's put it all together:

(1161/126) - (1161/168) + (837/252)

Step 3: Find a common denominator, which is 252 (the least common multiple of 126, 168, and 252).

Now, adjust the fractions:

(1161/126) * (2/2) - (1161/168) * (3/3) + (837/252) * (1/1)

(2322/252) - (3483/252) + (837/252)

Step 4: Combine the fractions with the same denominator:

(2322 - 3483 + 837) / 252

Step 5: Perform the addition and subtraction:

(2322 - 3483 + 837) = -324

So the final result is:

-324/252

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12:

-324/252 = (-324/12) / (252/12) = -27/21

Finally, reduce the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 3:

-27/21 = (-27/3) / (21/3) = -9/7

So the result of the expression is:

-9/7