Question

(3 1/18 - 2 7/12) • 1 10/17 + 3/11 • (4 3/28 - 3 4/21)

Answer 1

Ответ:

1

Пошаговое объяснение:

Answer 2

To simplify the expression (3 1/18 - 2 7/12) • 1 10/17 + 3/11 • (4 3/28 - 3 4/21), we'll break it down step by step:

Step 1: Subtract the mixed numbers inside the parentheses:

3 1/18 - 2 7/12 First, convert both mixed numbers to improper fractions: 3 1/18 = (18 * 3 + 1) / 18 = 55/18 2 7/12 = (12 * 2 + 7) / 12 = 31/12

Now, subtract: (55/18) - (31/12)

To subtract fractions with different denominators, find a common denominator. In this case, the common denominator is 36 (LCM of 18 and 12).

(55/18) - (31/12) = (55/18) * (2/2) - (31/12) * (3/3) = (110/36) - (93/36)

Now, subtract: (110/36) - (93/36) = 17/36

So, the expression inside the first set of parentheses simplifies to 17/36.

Step 2: Multiply the result from Step 1 by 1 10/17:

1 10/17 = (17 * 1 + 10) / 17 = 27/17

Now, multiply: (17/36) • (27/17)

The '17' in the numerator and denominator cancel out:

(1/36) • 27 = 27/36

Reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

(27/9) / (36/9) = 3/4

So, the expression inside the first set of parentheses simplifies to 3/4.

Step 3: Subtract the mixed numbers inside the second set of parentheses:

4 3/28 - 3 4/21 First, convert both mixed numbers to improper fractions: 4 3/28 = (28 * 4 + 3) / 28 = 115/28 3 4/21 = (21 * 3 + 4) / 21 = 67/21

Now, subtract: (115/28) - (67/21)

To subtract fractions with different denominators, find a common denominator. In this case, the common denominator is 84 (LCM of 28 and 21).

(115/28) - (67/21) = (115/28) * (3/3) - (67/21) * (4/4) = (345/84) - (268/84)

Now, subtract: (345/84) - (268/84) = 77/84

So, the expression inside the second set of parentheses simplifies to 77/84.

Step 4: Multiply the result from Step 3 by 3/11:

(77/84) • (3/11)

Multiply the numerators together and the denominators together:

(77 * 3) / (84 * 11) = 231/924

Reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 231:

(231/231) / (924/231) = 1/4

So, the expression inside the second set of parentheses simplifies to 1/4.

Step 5: Multiply the results from Step 2 and Step 4:

(3/4) • (1/4)

Multiply the numerators together and the denominators together:

(3 * 1) / (4 * 4) = 3/16

So, the final result of the expression is 3/16.