7/12 divided by 3/4
Understand the Problem
The question is asking us to divide the fraction 7/12 by the fraction 3/4. To solve it, we will multiply 7/12 by the reciprocal of 3/4, which is 4/3.
Answer
$\frac{7}{9}$
Answer for screen readers
The final answer is $\frac{7}{9}$.
Steps to Solve
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Identify the reciprocal of the fraction To divide by a fraction, we can multiply by its reciprocal. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.
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Set up the multiplication Now we can set up the multiplication of the fractions: $$ \frac{7}{12} \times \frac{4}{3} $$
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Multiply the numerators Multiply the numerators (top numbers) of the fractions: $$ 7 \times 4 = 28 $$
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Multiply the denominators Multiply the denominators (bottom numbers) of the fractions: $$ 12 \times 3 = 36 $$
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Combine the results Now combine the results from the multiplication of the numerators and denominators: $$ \frac{28}{36} $$
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Simplify the fraction To simplify the fraction, find the greatest common divisor (GCD) of 28 and 36, which is 4. Divide both the numerator and the denominator by 4: $$ \frac{28 \div 4}{36 \div 4} = \frac{7}{9} $$
The final answer is $\frac{7}{9}$.
More Information
Dividing fractions can be made easier by using the concept of reciprocals. The final result tells us how many parts of $\frac{3}{4}$ fit into $\frac{7}{12}$. The final fraction $\frac{7}{9}$ is a simplified form, which is often preferable in math.
Tips
- Forgetting to use the reciprocal: Some may try to directly divide which can lead to incorrect results. Always remember to multiply by the reciprocal.
- Not simplifying the fraction: Students sometimes forget to simplify the result if possible. Always check if the resulting fraction can be simplified.
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