Points to Remember:
- Order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
- Fraction addition/subtraction: Requires a common denominator.
- Fraction multiplication: Multiply numerators and denominators separately.
- Converting improper fractions to mixed fractions: Divide the numerator by the denominator; the quotient is the whole number part, and the remainder is the numerator of the fractional part.
Introduction:
This question tests the understanding of basic arithmetic operations involving fractions. It requires a sequential application of multiplication and subtraction of fractions. The final answer needs to be expressed as a mixed fraction, a combination of a whole number and a proper fraction. We will follow the order of operations (PEMDAS/BODMAS) to arrive at the correct solution.
Body:
1. Multiplication:
First, we calculate the product of -5/7 and 3/4:
(-5/7) * (3/4) = (-5 * 3) / (7 * 4) = -15/28
2. Addition:
Next, we find the sum of 7/5 and 4/3. To do this, we need a common denominator, which is 15:
7/5 = (7 * 3) / (5 * 3) = 21/15
4/3 = (4 * 5) / (3 * 5) = 20/15
21/15 + 20/15 = (21 + 20) / 15 = 41/15
3. Subtraction:
Finally, we subtract the sum (41/15) from the product (-15/28):
-15/28 – 41/15. Again, we need a common denominator, which is 28 * 15 = 420:
-15/28 = (-15 * 15) / (28 * 15) = -225/420
41/15 = (41 * 28) / (15 * 28) = 1148/420
-225/420 – 1148/420 = (-225 – 1148) / 420 = -1373/420
4. Converting to a Mixed Fraction:
To express -1373/420 as a mixed fraction, we perform the division:
-1373 ÷ 420 = -3 with a remainder of -113
Therefore, -1373/420 = -3 113/420
Conclusion:
Following the order of operations, we first multiplied -5/7 and 3/4 to get -15/28. Then, we added 7/5 and 4/3 to obtain 41/15. Subtracting the sum from the product resulted in -1373/420. Finally, converting this improper fraction to a mixed fraction gave us the answer: -3 113/420. This problem highlights the importance of mastering fundamental arithmetic operations with fractions and adhering to the correct order of operations to arrive at an accurate solution. There are no policy recommendations or best practices applicable to this purely mathematical problem. The focus should remain on accurate calculation and understanding of fractional arithmetic.