[\frac{6}{7}+\frac{3}{8}-\frac{1}{2}] \frac{4}{3}
Answer (2)
Find a common denominator for the fractions inside the brackets: 7 6 + 8 3 − 2 1 = 56 48 + 56 21 − 56 28 .
Add and subtract the fractions: 56 48 + 21 − 28 = 56 41 .
Multiply the result by 3 4 : 56 41 × 3 4 = 168 164 .
Simplify the fraction: 168 164 = 42 41 . The final answer is 42 41 .
Explanation
Understanding the Problem We are asked to evaluate the expression [ 7 6 + 8 3 − 2 1 ] 3 4 . This involves adding and subtracting fractions within the brackets, and then multiplying the result by another fraction.
Finding a Common Denominator First, we need to find a common denominator for the fractions inside the brackets: 7 6 , 8 3 , and 2 1 . The least common multiple of 7, 8, and 2 is 56. So we rewrite each fraction with a denominator of 56:
7 6 = 7 × 8 6 × 8 = 56 48
8 3 = 8 × 7 3 × 7 = 56 21 2 1 = 2 × 28 1 × 28 = 56 28
Adding and Subtracting Fractions Now we can add and subtract the fractions inside the brackets:
56 48 + 56 21 − 56 28 = 56 48 + 21 − 28 = 56 69 − 28 = 56 41
Multiplying by 4/3 Next, we multiply the result by 3 4 :
56 41 × 3 4 = 56 × 3 41 × 4 = 168 164
Simplifying the Fraction Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
168 164 = 168 ÷ 4 164 ÷ 4 = 42 41
Final Answer Therefore, the value of the expression is 42 41 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 4 3 cup of flour and you only want to make half the recipe, you need to calculate 2 1 × 4 3 = 8 3 cup of flour. Understanding how to add, subtract, multiply, and simplify fractions is essential for accurate measurements and successful cooking.
To solve [ 7 6 + 8 3 − 2 1 ] ⋅ 3 4 , we find a common denominator, calculate the combined fractions to get 56 41 , and then multiply by 3 4 to result in 42 41 .
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