[tex]\frac{1}{2} \div \frac{3}{4}[/tex]
Answer (1)
Rewrite the division as multiplication by the reciprocal: 2 1 ÷ 4 3 = 2 1 × 3 4 .
Multiply the numerators and denominators: 2 × 3 1 × 4 = 6 4 .
Simplify the fraction: 6 4 = 3 2 .
The result of the division is: 3 2 .
Explanation
Understanding the Problem We are asked to divide the fraction 2 1 by the fraction 4 3 . This is a straightforward division problem involving fractions.
Rewriting the Division To divide fractions, we multiply by the reciprocal of the second fraction. The reciprocal of 4 3 is 3 4 . Therefore, we rewrite the division as a multiplication: 2 1 ÷ 4 3 = 2 1 × 3 4
Multiplying Fractions Now, we multiply the numerators and the denominators: 2 1 × 3 4 = 2 × 3 1 × 4 = 6 4
Simplifying the Fraction Finally, we simplify the fraction 6 4 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 4 = 6 ÷ 2 4 ÷ 2 = 3 2
Final Answer Therefore, 2 1 ÷ 4 3 = 3 2 .
Examples
In baking, if a recipe calls for 4 3 cup of flour and you only have 2 1 cup, you might want to know what fraction of the recipe you can make. Dividing 2 1 by 4 3 tells you that you can make 3 2 of the recipe. This kind of calculation is useful for scaling recipes up or down based on available ingredients.
