Give your answer in its simplest form.
Dividing by [tex]\frac{3}{4}[/tex] is the same as multiplying by $\square$
Answer (1)
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 4 3 is 3 4 . Therefore, dividing by 4 3 is the same as multiplying by 3 4 .
Explanation
Understanding Division by a Fraction Let's think about what it means to divide by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
Finding the Reciprocal In this case, we want to find the reciprocal of the fraction 4 3 . To find the reciprocal, we simply swap the numerator (3) and the denominator (4). This gives us the fraction 3 4 .
The Answer Therefore, dividing by 4 3 is the same as multiplying by 3 4 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to divide by a fraction is useful in situations like scaling a recipe. For example, if a recipe calls for 4 3 cup of flour and you only want to make half the recipe, you would multiply the amount of flour by 2 1 , which is the same as dividing by 2. Knowing that dividing by a fraction is the same as multiplying by its reciprocal can simplify these calculations.
