\left(\frac{13}{18} \times \frac{-12}{39}\right)-\left(\frac{8}{9} \times \frac{-3}{4}\right)+\left[-\frac{7}{-9} \div \frac{63}{-36}\right]
Answer (2)
Simplify the first term: 18 13 × 39 − 12 = − 9 2 .
Simplify the second term: 9 8 × 4 − 3 = − 3 2 .
Simplify the third term: − − 9 7 ÷ − 36 63 = − 9 4 .
Calculate the final result: − 9 2 − ( − 3 2 ) + ( − 9 4 ) = 0 . The final answer is 0 .
Explanation
Understanding the Problem We are asked to evaluate the expression ( 18 13 × 39 − 12 ) − ( 9 8 × 4 − 3 ) + [ − − 9 7 ÷ − 36 63 ] . This involves multiplication, subtraction, and division of fractions. We will follow the order of operations (PEMDAS/BODMAS).
Simplifying the First Term First, let's simplify the expression inside the first parenthesis: 18 13 × 39 − 12 . We can simplify this as follows: 18 13 × 39 − 12 = 3 × 6 13 × 3 × 13 − 6 × 2 = 3 1 × 3 − 2 = − 9 2
Simplifying the Second Term Next, let's simplify the expression inside the second parenthesis: 9 8 × 4 − 3 . We can simplify this as follows: 9 8 × 4 − 3 = 3 × 3 2 × 4 × 4 − 3 = 3 2 × − 1 = − 3 2
Simplifying the Third Term Now, let's simplify the expression inside the brackets: − − 9 7 ÷ − 36 63 . Remember that dividing by a fraction is the same as multiplying by its reciprocal. So we have: − − 9 7 ÷ − 36 63 = 9 7 × 63 − 36 = 9 7 × 9 × 7 − 4 × 9 = 1 1 × 9 − 4 = − 9 4
Subtracting the First Two Terms Now, we perform the subtraction between the result of the first and second parenthesis: − 9 2 − ( − 3 2 ) = − 9 2 + 3 2 = − 9 2 + 3 × 3 2 × 3 = − 9 2 + 9 6 = 9 4
Adding the Results Finally, we add the result of the subtraction to the result of the brackets: 9 4 + ( − 9 4 ) = 9 4 − 9 4 = 0
Final Answer Therefore, the final result is 0.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to perform operations with fractions is essential for accurate calculations in these situations. For example, if you are halving a recipe that calls for 3 2 cup of flour, you need to calculate 2 1 × 3 2 to determine the new amount of flour needed. This problem demonstrates the importance of mastering fraction operations for practical applications.
The value of the expression simplifies to 0 after evaluating the individual terms. Each multiplication and division of fractions was simplified step by step. When combined, the result leads to a final answer of 0 .
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