What is 190 divided by 2/3
The Correct Answer and Explanation is:
To divide 190 by ( \frac{2}{3} ), we can follow a method that involves multiplication by the reciprocal.
Step-by-Step Solution
- Write the problem as a division of fractions:
[
190 \div \frac{2}{3}
] - Convert 190 into a fraction:
[
\frac{190}{1} \div \frac{2}{3}
] - Change the division to multiplication by the reciprocal:
Dividing by a fraction is the same as multiplying by its reciprocal (i.e., flipping the numerator and the denominator). So,
[
\frac{190}{1} \times \frac{3}{2}
] - Multiply the fractions:
Multiply the numerators and then the denominators.
[
\frac{190 \times 3}{1 \times 2} = \frac{570}{2}
] - Simplify the fraction:
[
\frac{570}{2} = 285
]
Thus, the correct answer is 285.
Explanation
When dividing a whole number by a fraction, you can think of it in terms of “how many of the fraction fit into the whole number?” Dividing by a fraction is effectively the same as multiplying by its reciprocal because you are seeing how many times that fraction can be contained within the whole.
In this case, 190 divided by ( \frac{2}{3} ) asks how many ( \frac{2}{3} ) parts fit into 190. To calculate this, we flip ( \frac{2}{3} ) to get ( \frac{3}{2} ) and then multiply. Multiplying by ( \frac{3}{2} ) gives the same outcome as dividing 190 by ( \frac{2}{3} ).
After converting and multiplying, simplifying (\frac{570}{2}) yields 285. This process of changing division by a fraction into multiplication by the reciprocal is a standard method in fraction operations, ensuring accuracy and simplifying calculations. This approach applies generally to any division involving fractions and whole numbers, making it a versatile and useful tool in mathematics.