[tex]\frac{2}{5} \times\left(-\frac{3}{7}\\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}[/tex]
Answer (2)
Multiply the first term: 5 2 × ( − 7 3 ) = − 35 6 .
Multiply the second term: 6 1 × 2 3 = 4 1 .
Multiply the third term: 14 1 × 5 2 = 35 1 .
Combine the results: − 35 6 − 4 1 + 35 1 = − 28 11 .
− 28 11
Explanation
Understanding the Expression We are asked to evaluate the expression: 5 2 × ( − 7 3 ) − 6 1 × 2 3 + 14 1 × 5 2 To do this, we will perform each multiplication separately and then combine the results.
Calculating Each Term First, we calculate the value of the first term: 5 2 × ( − 7 3 ) = − 5 × 7 2 × 3 = − 35 6 Next, we calculate the value of the second term: 6 1 × 2 3 = 6 × 2 1 × 3 = 12 3 = 4 1 Then, we calculate the value of the third term: 14 1 × 5 2 = 14 × 5 1 × 2 = 70 2 = 35 1
Combining the Terms Now, we substitute these values back into the original expression: − 35 6 − 4 1 + 35 1 To add these fractions, we need to find a common denominator. The least common multiple of 35 and 4 is 140. So we rewrite each fraction with the denominator 140: − 35 6 = − 35 × 4 6 × 4 = − 140 24 − 4 1 = − 4 × 35 1 × 35 = − 140 35 35 1 = 35 × 4 1 × 4 = 140 4 So the expression becomes: − 140 24 − 140 35 + 140 4 = 140 − 24 − 35 + 4 = 140 − 59 + 4 = 140 − 55 We can simplify this fraction by dividing both the numerator and the denominator by 5: 140 − 55 = 140 ÷ 5 − 55 ÷ 5 = 28 − 11 Thus, the final result is − 28 11 .
Final Answer Therefore, the value of the expression is: 5 2 × ( − 7 3 ) − 6 1 × 2 3 + 14 1 × 5 2 = − 28 11
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 5 2 of a cup of flour and you want to make half of the recipe, you would need to calculate 2 1 × 5 2 to determine the new amount of flour needed. Understanding how to perform operations with fractions is essential for accurate measurements and successful outcomes in various practical situations.
The value of the expression is − 28 11 after performing the required multiplications and combining the fractions. Each term was carefully calculated and simplified to arrive at the final result. Understanding how to work with fractions and find common denominators is essential for this calculation.
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