Question

9 1/6 : 11 / 24 - 3 1 / 9 × 1 2 / 7

Answer 1

Ответ:

$14\frac{2}{3}$

Пошаговое объяснение:

$9\frac{1}{6}:\frac{11}{24}-3\frac{1}{9}*\frac{12}{7}=\\\frac{55}{6}*\frac{24}{11}-\frac{28}{9}*\frac{12}{7}=\\\frac{5}{1}*\frac{4}{1}-\frac{4}{3}*\frac{4}{1}=\\20-\frac{16}{3}=\\20-\frac{16}{3}=20-5\frac{1}{3}=14\frac{2}{3}$

Answer 2

To solve the expression, let's break it down step by step.

Given expression: 9 1/6 : 11/24 - 3 1/9 × 12/7

Step 1: Simplify the mixed fractions: 9 1/6 can be converted to an improper fraction as follows: 9 1/6 = (9 * 6 + 1) / 6 = 55/6

3 1/9 can be converted to an improper fraction as follows: 3 1/9 = (3 * 9 + 1) / 9 = 28/9

Step 2: Convert the division and multiplication into fractions: 9 1/6 : 11/24 - 3 1/9 × 12/7 can be written as: (55/6) : (11/24) - (28/9) × (12/7)

Step 3: Perform multiplication: (55/6) : (11/24) - (28/9) × (12/7) = (55/6) : (11/24) - (336/63)

Step 4: Simplify the fractions: To simplify the fractions, we need to find the least common denominator (LCD) for the denominators of the fractions involved. In this case, the LCD is 72.

(55/6) : (11/24) - (336/63) can be rewritten with the LCD of 72 as follows: (55/6) × (24/24) : (11/24) - (336/63) × (72/72) = (1320/144) : (11/24) - (24192/4536)

Step 5: Perform division: (1320/144) : (11/24) - (24192/4536) can be simplified as: (1320/144) ÷ (11/24) - (24192/4536)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (1320/144) ÷ (11/24) = (1320/144) × (24/11) = (1320/11) × (4/1) = 480

So, the expression becomes: 480 - (24192/4536)

Step 6: Simplify the remaining fraction: To simplify the remaining fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.

The GCD of 24192 and 4536 is 48.

24192/48 = 504 4536/48 = 94

So, the expression simplifies to: 480 - (504/94) = 480 - 5.3617 (rounded to 4 decimal places)

Therefore, the result is approximately 474.6383.