\(\left(-\frac{7}{4}\right) \div 4 \frac{2}{3}\)
Answer (2)
Convert the mixed number to an improper fraction: 4 3 2 = 3 14 .
Rewrite the division as multiplication by the reciprocal: ( − 4 7 ) ÷ 3 14 = ( − 4 7 ) × 14 3 .
Multiply the fractions: − 4 × 14 7 × 3 = − 56 21 .
Simplify the fraction: − 56 21 = − 8 3 . The final answer is − 8 3 .
Explanation
Understanding the Problem We are asked to evaluate the expression ( − 4 7 ) ÷ 4 3 2 . This involves dividing a negative fraction by a mixed number.
Converting to Improper Fraction First, we need to convert the mixed number 4 3 2 into an improper fraction. To do this, we multiply the whole number part (4) by the denominator (3) and add the numerator (2): 4 3 2 = 3 4 × 3 + 2 = 3 12 + 2 = 3 14 So, the expression becomes ( − 4 7 ) ÷ 3 14 .
Rewriting as Multiplication Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3 14 is 14 3 . Therefore, we can rewrite the expression as a multiplication: ( − 4 7 ) ÷ 3 14 = ( − 4 7 ) × 14 3
Multiplying the Fractions Now, we multiply the fractions: ( − 4 7 ) × 14 3 = − 4 × 14 7 × 3 = − 56 21
Simplifying the Fraction Finally, we simplify the fraction. Both the numerator and the denominator are divisible by 7: 56 21 = 56 ÷ 7 21 ÷ 7 = 8 3 Therefore, the simplified expression is − 8 3
Final Answer Thus, ( − 4 7 ) ÷ 4 3 2 = − 8 3 .
Examples
Understanding fraction division is crucial in many real-life scenarios, such as scaling recipes. For instance, if a recipe calls for 4 7 cups of flour and you only want to make 3 2 of the recipe, you would need to divide 4 7 by 4 3 2 to find out how much flour you need. This ensures that all the ingredients are in the correct proportion, maintaining the recipe's integrity.
To evaluate ( − 4 7 ) ÷ 4 3 2 , first convert the mixed number to an improper fraction, resulting in 3 14 . Then, rewrite the division as multiplication by the reciprocal, multiply the fractions, and simplify to get − 8 3 . The final answer is − 8 3 .
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