Question

14 7/15-3 3/23×23/27-1 1/5×1/6

Answer 1

14 7/15 - 3 3/23 * 23/27 - 1 1/5 * 1/6 = 11 3/5

1) 3 3/23 * 23/27 = 72/23 * 23/27 = (8*1)/(1*3) = 8/3 = 2 2/3
2) 1 1/5 * 1/6 = 6/5 * 1/6 = 1/5
3) 14 7/15 - 2 2/3 = 14 7/15 - 2 10/15 = 13 22/15 - 2 10/15 = 11 12/15 = 11 4/5
4) 11 4/5 - 1/5 = 11 3/5

Пояснения:
3 3/23 = (3*23+3)/23 = 72/23
1 1/5 = (1*5+1)/5 = 6/5
2/3 = (2*5)/(3*5) = 10/15 - доп.множ. 5
12/15 = (12:3)/(15:3) = 4/5 - сократили на 3

Answer 2

To solve the expression "14 7/15 - 3 3/23 × 23/27 - 1 1/5 × 1/6," we'll follow the order of operations (also known as PEMDAS/BODMAS).

Step 1: Simplify the multiplications and divisions from left to right. 14 7/15 - 3 3/23 × 23/27 - 1 1/5 × 1/6

Let's simplify the first multiplication: 14 7/15 - 3 3/23 × 23/27 - 1 1/5 × 1/6 = 14 7/15 - (3 3/23 × 23/27) - 1 1/5 × 1/6

Now, let's simplify the second multiplication: 14 7/15 - (3 3/23 × 23/27) - 1 1/5 × 1/6 = 14 7/15 - (3 3/23 × 23/27) - (1 1/5 × 1/6)

Step 2: Convert mixed numbers to improper fractions. 14 7/15 can be written as an improper fraction: (14 × 15 + 7)/15 = 217/15 3 3/23 can be written as an improper fraction: (3 × 23 + 3)/23 = 72/23 1 1/5 can be written as an improper fraction: (1 × 5 + 1)/5 = 6/5

The expression becomes: 217/15 - (72/23 × 23/27) - (6/5 × 1/6)

Step 3: Perform the multiplications and divisions from left to right. 217/15 - (72/23 × 23/27) - (6/5 × 1/6) = 217/15 - (72/23 × 1/3) - (6/5 × 1/6) = 217/15 - (72/69) - (6/30)

Step 4: Find a common denominator and combine the fractions. The common denominator for 15, 23, 69, and 30 is 1,035. = (217 × 69)/(15 × 69) - (72 × 15)/(23 × 15) - (6 × 69)/(5 × 69) = 15,013/1,035 - 1,080/1,035 - 414/1,035

Step 5: Subtract the fractions. 15,013/1,035 - 1,080/1,035 - 414/1,035 = (15,013 - 1,080 - 414)/1,035 = 13,519/1,035

The simplified expression is 13,519/1,035.