Question

10×(3 2/15-2 5/18)+12×(1 5/6+5 3/4)​

Answer 1

Ответ:

99 5/9

Пошаговое объяснение:

1) 3 2/15 - 2 5/18 = 3 12/90 - 2 25/90 = 77/90

2) 77/90 * 10 = 77/9 = 8 5/9

3) 1 5/6 + 5 3/4 = 1 10/12 + 5 9/12 = 6 19/12 = 7 7/12

4) 7 7/12 * 12 = 91/12 * 12 = 91

5) 8 5/9 + 91 = 99 5/9

Answer 2

To solve the expression:

10 × (3 2/15 - 2 5/18) + 12 × (1 5/6 + 5 3/4)

First, let's simplify the expressions inside the parentheses:

1. 3 2/15 - 2 5/18

To subtract mixed numbers, we need to find a common denominator, which in this case would be 90 (the least common multiple of 15 and 18). So, we'll rewrite the fractions with a common denominator:

(3 * 6/6) - (2 * 5/5) = (18/15) - (10/18)

Now, subtract the fractions:

(18/15) - (10/18) = (24/18) - (10/18) = 14/18

To simplify further, you can reduce the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

(14/2) / (18/2) = 7/9

So, 3 2/15 - 2 5/18 = 7/9.

2. 1 5/6 + 5 3/4

To add mixed numbers, we'll find a common denominator, which in this case is 12 (the least common multiple of 6 and 4). So, we'll rewrite the fractions with a common denominator:

(1 * 2/2) + (5 * 3/3) = (2/12) + (15/12)

Now, add the fractions:

(2/12) + (15/12) = (2 + 15)/12 = 17/12

So, 1 5/6 + 5 3/4 = 17/12.

Now, we can substitute these simplified values back into the original expression and calculate:

10 × (7/9) + 12 × (17/12)

Now, multiply:

(10 × 7/9) + (12 × 17/12)

(70/9) + (17/1)

To add these fractions, we need a common denominator, which is 9 in this case:

(70/9) + (17/1) = (70/9) + (17/1) * (9/9)

Now, add the fractions:

(70/9) + (17 * 9/9) = (70/9) + (153/9)

Now, add the numerators:

(70 + 153)/9 = 223/9

So, the final result is:

10 × (3 2/15 - 2 5/18) + 12 × (1 5/6 + 5 3/4) = 223/9