Question

4) (5 8/9÷1 17/36+1 1/4)×5/21​

Answer 1

Точный ответ: 5/4
или 1,25

Answer 2

To solve the expression (5 8/9 ÷ 1 17/36 + 1 1/4) × 5/21, we'll follow the order of operations (also known as PEMDAS/BODMAS) to simplify it step by step.

Step 1: Convert mixed numbers to improper fractions 5 8/9 can be written as an improper fraction: (5 × 9 + 8) / 9 = 53/9 1 17/36 can be written as an improper fraction: (1 × 36 + 17) / 36 = 53/36 1 1/4 can be written as an improper fraction: (1 × 4 + 1) / 4 = 5/4

Now the expression becomes: (53/9 ÷ 53/36 + 5/4) × 5/21

Step 2: Simplify the division Dividing by a fraction is equivalent to multiplying by its reciprocal. (53/9 ÷ 53/36) can be rewritten as (53/9 × 36/53) = (53 × 36) / (9 × 53) = 36/9 = 4

Now the expression becomes: (4 + 5/4) × 5/21

Step 3: Add the fractions To add fractions, we need a common denominator, which in this case is 4. (4 + 5/4) can be rewritten as (16/4 + 5/4) = (16 + 5) / 4 = 21/4

Now the expression becomes: (21/4) × 5/21

Step 4: Multiply the fractions (21/4) × (5/21) = (21 × 5) / (4 × 21) = 105/84

Step 5: Simplify the fraction (if possible) 105/84 can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 21. 105/84 = (105 ÷ 21) / (84 ÷ 21) = 5/4

Therefore, the value of the expression (5 8/9 ÷ 1 17/36 + 1 1/4) × 5/21 is 5/4.