9/10 divided by 3/5 in simplest form

9/10 divided by 3/5 in simplest form

The Correct Answer and Explanation is:

To divide two fractions, we follow these steps:

Step 1: Flip the second fraction (the divisor)

When dividing fractions, instead of dividing, we multiply the first fraction by the reciprocal (the flipped version) of the second fraction. In this case, the second fraction is ( \frac{3}{5} ). The reciprocal of ( \frac{3}{5} ) is ( \frac{5}{3} ).

Step 2: Multiply the fractions

Now, we multiply the first fraction by the reciprocal of the second fraction:
[
\frac{9}{10} \div \frac{3}{5} = \frac{9}{10} \times \frac{5}{3}
]

Step 3: Multiply the numerators and denominators

To multiply fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
[
\frac{9}{10} \times \frac{5}{3} = \frac{9 \times 5}{10 \times 3} = \frac{45}{30}
]

Step 4: Simplify the fraction

The result is ( \frac{45}{30} ). Now, simplify the fraction by finding the greatest common divisor (GCD) of 45 and 30. The GCD of 45 and 30 is 15. Divide both the numerator and denominator by 15:
[
\frac{45}{30} = \frac{45 \div 15}{30 \div 15} = \frac{3}{2}
]

Final Answer:

The simplified result of ( \frac{9}{10} \div \frac{3}{5} ) is ( \frac{3}{2} ).

Explanation:

When dividing fractions, remember the key principle: multiply by the reciprocal. This means instead of dividing ( \frac{9}{10} ) by ( \frac{3}{5} ), we multiply ( \frac{9}{10} ) by ( \frac{5}{3} ). The multiplication is straightforward, as we just multiply the numerators and denominators. After multiplying, we simplify the fraction by finding the GCD and dividing both the numerator and denominator by this number. In this case, the GCD of 45 and 30 is 15, leading to the final simplified fraction of ( \frac{3}{2} ).