Question

4 5/12 - 1 1/2÷ (2 1/6 +8/15)×1 4/5​

Answer 1

Ответ:3 5/12

Подробнное решение в картинке

Answer 2

To solve this expression, you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).

Let's break down the expression step by step:

1. Start with the addition and subtraction within each mixed number:

   4 5/12 - 1 1/2 = (4 + 1) + (5/12 - 1/2) = 5 + (5/12 - 6/12) = 5 - 1/12

2. Now, let's simplify the fractions:

   5 - 1/12 = 60/12 - 1/12 = 59/12

So, the expression becomes:

59/12 ÷ (2 1/6 + 8/15) × 1 4/5

3. Now, deal with the addition within the parentheses:

   2 1/6 + 8/15 = (12/6 + 1/6) + 8/15 = 13/6 + 8/15

4. Find a common denominator for 6 and 15, which is 30:

   (13/6) * (5/5) + (8/15) * (2/2) = (65/30) + (16/30) = (65 + 16)/30 = 81/30

5. Now, divide 59/12 by 81/30:

   (59/12) ÷ (81/30)

   To divide fractions, invert the second fraction and multiply:

   (59/12) * (30/81)

6. Simplify the fraction multiplication:

   (59 * 30) / (12 * 81) = 1770 / 972

7. Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of 1770 and 972, which is 18:

   (1770 ÷ 18) / (972 ÷ 18) = 98/54

8. Finally, multiply by 1 4/5, which is equivalent to 9/5:

   (98/54) * (9/5)

   Multiply the numerators together and the denominators together:

   (98 * 9) / (54 * 5) = 882 / 270

9. Simplify the fraction by finding the GCD of 882 and 270, which is 18:

   (882 ÷ 18) / (270 ÷ 18) = 49/15

So, the final result of the expression is:

49/15 or 3 4/15