[tex]\frac{2}{3} \div \frac{4}{5}[/tex]
Answer (2)
To divide 3 2 by 5 4 , we multiply 3 2 by the reciprocal of 5 4 , which is 4 5 .
Multiply the numerators and denominators: 3 × 4 2 × 5 = 12 10 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, 2: 12 ÷ 2 10 ÷ 2 = 6 5 .
The final answer is 6 5 .
Explanation
Understanding the Problem We are asked to divide two fractions, 3 2 and 5 4 .
Finding the Reciprocal To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 5 4 is 4 5 .
Rewriting the Division as Multiplication Therefore, 3 2 ÷ 5 4 = 3 2 × 4 5 .
Multiplying the Fractions Multiply the numerators and the denominators: 3 × 4 2 × 5 = 12 10 .
Simplifying the Fraction Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 12 ÷ 2 10 ÷ 2 = 6 5 .
Final Answer The result of dividing 3 2 by 5 4 is 6 5 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 3 2 cup of flour and you only want to make half of the recipe, you need to divide 3 2 by 2, which is the same as multiplying 3 2 by 2 1 . This gives you 3 1 cup of flour. Understanding how to divide fractions is essential for accurately adjusting recipes and other measurements.
To divide 3 2 by 5 4 , you multiply 3 2 by the reciprocal of 5 4 , which is 4 5 . This gives you 12 10 , which simplifies to 6 5 . Therefore, the answer is 6 5 .
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