Question

3/4 + 3 3/5 *( 5/18- 7/24 )- 1/5

Answer 1

3/4 + 3 3/5 · (5/18 - 7/24) - 1/5 = 1/2

1) 5/18 - 7/24 = 20/72 - 21/72 = -1/72

2) 3 3/5 · (-1/72) = 18/5 · (-1/72) = -(1·1)/(5·4) = -1/20

3) 3/4 + (-1/20) = 15/20 - 1/20 = 14/20 = 7/10

4) 7/10 - 1/5 = 7/10 - 2/10 = 5/10 = 1/2

Ответ: 1/2.

Answer 2

To solve this expression, follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the given expression step by step:

1. Start with the innermost operation within the parentheses: 5/18 - 7/24 = (20 - 21) / 72 = -1 / 72

2. Now substitute this result back into the original expression: 3/4 + 3 3/5 * (-1/72) - 1/5

3. Convert the mixed fraction 3 3/5 into an improper fraction: 3 3/5 = (5 * 3 + 3) / 5 = 18/5 + 3/5 = 21/5

4. Substitute the improper fraction back into the expression: 3/4 + 21/5 * (-1/72) - 1/5

5. Perform the multiplication: 21/5 * (-1/72) = -21/360 = -7/120

6. Substitute the multiplication result back into the expression: 3/4 - 7/120 - 1/5

7. Convert the fractions so that they have a common denominator, which is 120: 3/4 = 90/120 1/5 = 24/120

8. Substitute the equivalent fractions back into the expression: 90/120 - 7/120 - 24/120

9. Combine the fractions: (90 - 7 - 24) / 120 = 59/120

10. Simplify the fraction if possible: 59/120 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1: 59/120

So, the final result of the given expression is 59/120. This fraction can also be expressed as a mixed fraction or decimal if needed.