Question

(3 1/14 - 2 5/21) * (2 7/15-2 13/18)

Answer 1

(3 1/14 - 2 5/21) · (2 7/15 - 2 13/18) = -23/108

1) 3 1/14 - 2 5/21 = 3 3/42 - 2 10/42 = 2 45/42 - 2 10/42 = 35/42 = 5/6

2) 2 7/15 - 2 13/18 = 2 42/90 - 2 65/90 = -(2 65/90 - 2 42/90) = -23/90

3) 5/6 · (-23/90) = -(1·23)/(6·18) = -23/108

Ответ: (-23/108).

Answer 2

To calculate the expression (3 1/14 - 2 5/21) * (2 7/15 - 2 13/18), we'll first convert the mixed numbers into improper fractions and then perform the calculations step by step.

1. Convert the mixed numbers to improper fractions:

   • 3 1/14 = (3 * 14 + 1)/14 = (42 + 1)/14 = 43/14
   • 2 5/21 = (2 * 21 + 5)/21 = (42 + 5)/21 = 47/21
   • 2 7/15 = (2 * 15 + 7)/15 = (30 + 7)/15 = 37/15
   • 2 13/18 = (2 * 18 + 13)/18 = (36 + 13)/18 = 49/18

2. Now, let's rewrite the expression with the improper fractions: (43/14 - 47/21) * (37/15 - 49/18)

3. Next, find the common denominators for both sets of fractions, which are 14 for the first set and 18 for the second set.

4. Adjust the fractions to have the common denominators:

   • For the first set: Multiply the first fraction by 3/3 (to make the denominator 14) and the second fraction by 2/2 (to make the denominator 14).
   • For the second set: Multiply the first fraction by 18/18 (to make the denominator 18) and the second fraction by 15/15 (to make the denominator 18).

The expression becomes: (43/14 * 3/3 - 47/21 * 2/2) * (37/15 * 18/18 - 49/18 * 15/15)

5. Now, calculate each part of the expression:

   • For the first part: (43/14 * 3/3 - 47/21 * 2/2) = (129/42 - 94/42) = (129 - 94)/42 = 35/42

   • For the second part: (37/15 * 18/18 - 49/18 * 15/15) = (666/270 - 735/270) = (666 - 735)/270 = -69/270

6. Finally, multiply the results from the first and second parts together: (35/42) * (-69/270)

7. Simplify the result. First, find the greatest common divisor (GCD) of 35 and 270, which is 5: (35/42) * (-69/270) = (5/6) * (-69/270)

8. Divide both the numerator and denominator of the second fraction by 5: (5/6) * (-69/270) = (1/6) * (-69/54)

9. Now, multiply the fractions: (1/6) * (-69/54) = -69/324

So, the final result of the expression (3 1/14 - 2 5/21) * (2 7/15 - 2 13/18) is -69/324.