3/8 divided by 2/3 PLEASE PUT IN FRACTION FORM
The Correct Answer and Explanation is:
To divide two fractions, you can use the rule of multiplying by the reciprocal. Here’s how to solve the problem ( \frac{3}{8} \div \frac{2}{3} ):
- Identify the problem: You need to divide ( \frac{3}{8} ) by ( \frac{2}{3} ).
- Find the reciprocal of the second fraction: The reciprocal of ( \frac{2}{3} ) is ( \frac{3}{2} ). This is done by flipping the numerator and the denominator.
- Rewrite the division as multiplication: Now, instead of dividing by ( \frac{2}{3} ), you can multiply ( \frac{3}{8} ) by ( \frac{3}{2} ): [
\frac{3}{8} \div \frac{2}{3} = \frac{3}{8} \times \frac{3}{2}
] - Multiply the numerators and denominators: Multiply the numerators together and the denominators together: [
\frac{3 \times 3}{8 \times 2} = \frac{9}{16}
]
So, ( \frac{3}{8} \div \frac{2}{3} = \frac{9}{16} ).
Explanation
Dividing fractions can often confuse students, but understanding the concept of reciprocal multiplication simplifies the process significantly. When dividing fractions, you are essentially asking how many times the divisor (the fraction you are dividing by) fits into the dividend (the fraction you are dividing). By flipping the second fraction and changing the division into multiplication, you make the operation more manageable.
The multiplication of two fractions involves straightforward operations where the numerator (top number) is multiplied together, and the same goes for the denominators (bottom numbers). In this example, the numerators ( 3 ) and ( 3 ) yield ( 9 ), while the denominators ( 8 ) and ( 2 ) yield ( 16 ).
This method ensures that you maintain the integrity of the fractions while performing the operation, yielding a simplified result. The final answer, ( \frac{9}{16} ), is in its simplest form and provides a clear understanding of how fractions interact through division.