25/3 divided by 3/4
The Correct Answer and Explanation is :
To solve ( \frac{25}{3} \div \frac{3}{4} ), we need to follow the rules of dividing fractions.
Step 1: Flip the second fraction and change the division to multiplication.
The rule for dividing fractions is to multiply the first fraction by the reciprocal (the flipped version) of the second fraction. The reciprocal of ( \frac{3}{4} ) is ( \frac{4}{3} ).
So, the expression becomes:
[
\frac{25}{3} \div \frac{3}{4} = \frac{25}{3} \times \frac{4}{3}
]
Step 2: Multiply the fractions.
Now, we multiply the numerators (top numbers) and the denominators (bottom numbers) separately:
[
\frac{25}{3} \times \frac{4}{3} = \frac{25 \times 4}{3 \times 3} = \frac{100}{9}
]
So, ( \frac{25}{3} \div \frac{3}{4} = \frac{100}{9} ).
Step 3: Simplify the fraction.
The fraction ( \frac{100}{9} ) cannot be simplified further, as 100 and 9 do not have any common factors other than 1.
Thus, the answer is ( \frac{100}{9} ), or approximately 11.11 when expressed as a decimal.
Explanation:
When dividing fractions, it’s important to remember that the operation is not the same as dividing whole numbers. Instead of dividing by a fraction, we multiply by its reciprocal. In this case, flipping ( \frac{3}{4} ) to ( \frac{4}{3} ) and then multiplying by it simplifies the division process. After multiplying, we check if the fraction can be simplified. If the numerator and denominator share common factors, we can reduce the fraction. Here, since 100 and 9 don’t share any common factors, the fraction remains in its simplest form.
So, the result of ( \frac{25}{3} \div \frac{3}{4} ) is ( \frac{100}{9} ).