e) $\frac{2}{3}\left(\frac{1}{2}-\frac{6}{5}+\frac{3}{4}\right) \div(-1+0,4+1,5)=$
Answer (2)
Simplify the expression inside the first parenthesis: 2 1 − 5 6 + 4 3 = 20 1 .
Simplify the expression inside the second parenthesis: − 1 + 0.4 + 1.5 = 10 9 .
Multiply the result from the first parenthesis by 3 2 : 3 2 × 20 1 = 30 1 .
Divide the result from the previous step by the result from the second parenthesis: 30 1 ÷ 10 9 = 27 1 .
The final answer is 27 1 .
Explanation
Understanding the Problem We are asked to evaluate the expression 3 2 ( 2 1 − 5 6 + 4 3 ) ÷ ( − 1 + 0.4 + 1.5 ) . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Simplifying the First Parenthesis First, we simplify the expression inside the parenthesis: 2 1 − 5 6 + 4 3 . To combine these fractions, we need to find a common denominator. The least common multiple of 2, 5, and 4 is 20. So we rewrite the fractions with a denominator of 20: 2 1 = 20 10 , 5 6 = 20 24 , 4 3 = 20 15 . Now we can combine the fractions: 20 10 − 20 24 + 20 15 = 20 10 − 24 + 15 = 20 1 .
Simplifying the Second Parenthesis Next, we simplify the expression inside the second parenthesis: − 1 + 0.4 + 1.5. We can rewrite this as − 1 + 10 4 + 10 15 = − 1 + 10 19 = − 10 10 + 10 19 = 10 9 .
Multiplying by 2/3 Now we multiply the result from the first parenthesis by 3 2 :
3 2 × 20 1 = 60 2 = 30 1 .
Dividing the Results Finally, we divide the result from the previous step by the result from the second parenthesis: 30 1 ÷ 10 9 = 30 1 × 9 10 = 270 10 = 27 1 .
Final Answer Therefore, the value of the expression is 27 1 ≈ 0.037037...
Examples
Understanding how to evaluate expressions with fractions and decimals is essential in many real-life situations, such as calculating proportions in recipes, determining discounts while shopping, or managing finances. For instance, if you want to bake a cake and need to adjust the ingredient quantities, you'll use fractions to scale the recipe up or down. Similarly, when calculating sale prices or figuring out interest rates, you'll encounter decimals and fractions. Mastering these calculations ensures accuracy and efficiency in everyday tasks.
The value of the expression is 27 1 . This is found by simplifying each part of the expression step by step. Finally, the result of dividing and multiplying the simplified fractions gives the answer.
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