Question

(24 4/9:8-15:7 1/5) *9-1 1/4​

Answer 1

(24 4/9 : 8 - 15 : 7 1/5) · 9 - 1 1/4 = 7 1/2

1) 24 4/9 : 8 = 220/9 · 1/8 = (55·1)/(9·2) = 55/18 = 3 1/18

2) 15 : 7 1/5 = 15 : 36/5 = 15/1 · 5/36 = (5·5)/(1·12) = 25/12 = 2 1/12

3) 3 1/18 - 2 1/12 = 3 2/36 - 2 3/36 = 2 38/36 - 2 3/36 = 35/36

4) 35/36 · 9/1 = (35·1)/(4·1) = 35/4 = 8 3/4

5) 8 3/4 - 1 1/4 = 7 2/4 = 7 1/2

Ответ: 7 целых 1/2 (или 7,5 в десятичных дробях).

Answer 2

Let's break down the expression step by step:

1. First, let's simplify the fractions within the parentheses: 24 4/9 = 24 + 4/9 = (24*9 + 4) / 9 = 220/9 15:7 1/5 = 15 + 7 1/5 = 15 + 7 + 1/5 = 22 1/5

2. Now, substitute these simplified fractions back into the expression: (220/9:8 - 22 1/5) * 9 - 1 1/4

3. Perform the division within the parentheses: (220/9:8 - 22 1/5) = (220/9 * 1/8 - 22 1/5)

4. Calculate the values inside the parentheses step by step:

   a. 220/9 * 1/8 = (220 * 1) / (9 * 8) = 220/72 = 55/18

   b. Now subtract 22 1/5 from 55/18:

   To subtract fractions with different denominators, you need to find a common denominator, which in this case is 18. So, convert 22 1/5 to an equivalent fraction with a denominator of 18:

   22 1/5 = (22 * 5 + 1) / 5 = 111/5

   Now, subtract 111/5 from 55/18:

   (55/18 - 111/5)

5. To subtract these fractions, you need to have a common denominator, which is 18 * 5 = 90:

   (55/18 - 111/5) = (55/18 * 5/5 - 111/5 * 18/18)

6. Perform the subtraction:

   (55/90 - 198/90)

7. Subtract the numerators:

   (55 - 198)/90 = -143/90

8. Now, let's simplify the expression:

   (-143/90) * 9 - 1 1/4

9. Multiply (-143/90) by 9:

   (-143/90) * 9 = (-143 * 9) / 90 = -1287/90

10. Now, subtract 1 1/4 from -1287/90:

    To subtract a mixed number from a fraction, convert the mixed number to an improper fraction with a common denominator of 90:

    1 1/4 = (1 * 4 + 1) / 4 = 5/4

    (-1287/90 - 5/4)

11. To subtract these fractions, you need a common denominator of 90:

    (-1287/90 - 5/4) = (-1287/90 * 10/10 - 225/90)

12. Perform the subtraction:

    (-12870/90 - 225/90) = (-13195/90)

So, the final result is -13195/90. You can simplify this fraction further:

-13195/90 = -4399/30 = -1466 1/3