what is 6/7 divided by 1/2
The correct answer and explanation is:
To solve 67÷12\frac{6}{7} \div \frac{1}{2}, follow these steps:
- Change the division to multiplication:
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 12\frac{1}{2} is 21\frac{2}{1}. So, the expression becomes: 67×21\frac{6}{7} \times \frac{2}{1} - Multiply the fractions:
Multiply the numerators (the top numbers) and the denominators (the bottom numbers): 6×27×1=127\frac{6 \times 2}{7 \times 1} = \frac{12}{7} - Simplify the fraction (if necessary):
In this case, 127\frac{12}{7} is already in its simplest form, as 12 and 7 have no common factors other than 1.
Thus, the answer is 127\frac{12}{7}.
Explanation:
When dividing fractions, the key operation is changing division into multiplication by using the reciprocal of the second fraction. The reciprocal of 12\frac{1}{2} is 21\frac{2}{1}, and multiplying 67\frac{6}{7} by 21\frac{2}{1} gives the result 127\frac{12}{7}. It’s important to remember that multiplication of fractions follows the rule of multiplying numerators and denominators directly, which simplifies the operation compared to other forms of division.
In cases where both the numerator and denominator have common factors, simplification can occur by dividing them by their greatest common divisor (GCD). However, for 127\frac{12}{7}, no further simplification is needed.