25/2 divided by 2/3
Understand the Problem
The question is asking for the result of dividing the fraction 25/2 by the fraction 2/3. This involves performing a division of fractions which can be solved by multiplying the first fraction by the reciprocal of the second fraction.
Answer
The result is $\frac{75}{4}$ or $18 \frac{3}{4}$.
Answer for screen readers
The answer is $\frac{75}{4}$ or $18 \frac{3}{4}$.
Steps to Solve
- Identify the fractions to divide
We have two fractions: $\frac{25}{2}$ and $\frac{2}{3}$. We need to divide these two fractions.
- Convert division to multiplication by the reciprocal
Dividing by a fraction is the same as multiplying by its reciprocal. So we rewrite the expression: $$ \frac{25}{2} \div \frac{2}{3} = \frac{25}{2} \times \frac{3}{2} $$
- Multiply the numerators and the denominators
Now, we multiply the numerators together and the denominators together: $$ \frac{25 \times 3}{2 \times 2} $$
- Calculate the products
Calculating the products, we have:
Numerator: $25 \times 3 = 75$
Denominator: $2 \times 2 = 4$
- Write the final fraction
So we rewrite the result: $$ \frac{75}{4} $$
- Convert to mixed number (if necessary)
Finally, we can convert this improper fraction to a mixed number:
$$ 75 \div 4 = 18 \quad \text{remainder } 3 $$
This gives us $18 \frac{3}{4}$.
The answer is $\frac{75}{4}$ or $18 \frac{3}{4}$.
More Information
When dividing fractions, remember that it can always be converted to multiplication by using the reciprocal of the second fraction. This technique is very useful for simplifying calculations.
Tips
- Forgetting to take the reciprocal of the second fraction before multiplying. Always remember that dividing by a fraction means multiplying by its reciprocal.
- Not simplifying the final fraction or mixed number. It's important to present the answer clearly.
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