Question

topic: dividing fractions and mixed numbers
progress:
the movement of the progress bar may be uneven because questions can be worth more or less
divide: $dfrac{7}{12} div dfrac{2}{3}$
$dfrac{18}{7}$
$dfrac{7}{2}$
$dfrac{7}{18}$
$dfrac{7}{8}$

Explanation:

Step1: Recall fraction division rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{7}{12} \div \frac{2}{3} = \frac{7}{12} \times \frac{3}{2}$.

Step2: Multiply numerators and denominators

Multiply the numerators: $7 \times 3 = 21$. Multiply the denominators: $12 \times 2 = 24$. So we have $\frac{21}{24}$.

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 3. $\frac{21 \div 3}{24 \div 3} = \frac{7}{8}$. Wait, wait, no, wait. Wait, in Step 2, when we multiply $\frac{7}{12} \times \frac{3}{2}$, we can simplify before multiplying. The 3 in the numerator and 12 in the denominator have a common factor of 3. So 12 ÷ 3 = 4, 3 ÷ 3 = 1. So now we have $\frac{7}{4} \times \frac{1}{2} = \frac{7}{8}$? Wait, no, wait, original multiplication: $\frac{7}{12} \times \frac{3}{2}$. The 3 and 12: 12 is 3×4, so cancel 3, get $\frac{7}{4} \times \frac{1}{2} = \frac{7}{8}$? Wait, but let's check again. Wait, maybe I made a mistake. Wait, $\frac{7}{12} \times \frac{3}{2}$: numerator 7×3=21, denominator 12×2=24. 21 and 24 are both divisible by 3: 21÷3=7, 24÷3=8. So $\frac{7}{8}$. Wait, but looking at the options, the last option (assuming the last one is 7/8) is the correct one. Wait, let's re-express the steps correctly.

Correct Step1: Apply division rule

Fraction division: $a/b \div c/d = a/b \times d/c$. So $\frac{7}{12} \div \frac{2}{3} = \frac{7}{12} \times \frac{3}{2}$.

Correct Step2: Simplify before multiplying

The 3 in the numerator of the second fraction and 12 in the denominator of the first fraction have a GCD of 3. So divide 12 by 3 (get 4) and 3 by 3 (get 1). Now the expression is $\frac{7}{4} \times \frac{1}{2}$.

Correct Step3: Multiply

Multiply numerators: 7×1=7. Multiply denominators: 4×2=8. So the result is $\frac{7}{8}$.

Answer:

$\frac{7}{8}$ (assuming the last option is $\frac{7}{8}$; if the options are as follows: first $\frac{18}{7}$, second $\frac{7}{2}$, third $\frac{7}{18}$, fourth $\frac{7}{8}$, then the answer is the fourth option, e.g., D. $\frac{7}{8}$)