[tex]\frac{5}{6} \times(-\frac{2}{3})-\frac{16}{5} \times \frac{3}{4}+\frac{3}{2} \times(-\frac{7}{9})[/tex]
Answer (2)
Perform each multiplication: 6 5 × ( − 3 2 ) = − 9 5 , 5 16 × 4 3 = 5 12 , 2 3 × ( − 9 7 ) = − 6 7 .
Rewrite the expression: − 9 5 − 5 12 − 6 7 .
Find a common denominator: The least common multiple of 9, 5, and 6 is 90.
Perform the subtraction: − 90 50 − 90 216 − 90 105 = − 90 371 .
The final answer is − 90 371 .
Explanation
Understanding the Problem We are asked to evaluate the expression 6 5 × ( − 3 2 ) − 5 16 × 4 3 + 2 3 × ( − 9 7 ) . This involves performing multiplication and subtraction of fractions.
Performing Multiplications First, we perform the multiplication operations: 6 5 × ( − 3 2 ) = − 6 × 3 5 × 2 = − 18 10 = − 9 5 5 16 × 4 3 = 5 × 4 16 × 3 = 20 48 = 5 12 2 3 × ( − 9 7 ) = − 2 × 9 3 × 7 = − 18 21 = − 6 7
Substituting Back Now we substitute these results back into the original expression: − 9 5 − 5 12 − 6 7
Finding Common Denominator To perform the subtraction, we need to find a common denominator for the fractions. The least common multiple of 9, 5, and 6 is 90. So we convert each fraction to have a denominator of 90: − 9 5 = − 9 × 10 5 × 10 = − 90 50 − 5 12 = − 5 × 18 12 × 18 = − 90 216 − 6 7 = − 6 × 15 7 × 15 = − 90 105
Performing Subtraction Now we can perform the subtraction: − 90 50 − 90 216 − 90 105 = 90 − 50 − 216 − 105 = 90 − 371
Final Answer The final result is − 90 371 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to perform arithmetic operations with fractions is essential for accurately calculating quantities and ensuring fair distribution. For example, if you are baking a cake and need to halve a recipe that calls for 3 2 cup of flour, you need to calculate 2 1 × 3 2 to determine the correct amount of flour to use.
The expression calculates to − 90 371 after performing the necessary multiplications and common denominator adjustments for subtraction of the fractions.
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