Question

1. $\frac{3}{4} div \frac{1}{7} =$
2. $\frac{6}{8} div \frac{3}{9} =$
3. $\frac{3}{7} div \frac{5}{12} =$

Explanation:

26.

Step1: Recall fraction division rule

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{3}{4} \div \frac{1}{7}$ becomes $\frac{3}{4} \times \frac{7}{1}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $3 \times 7 = 21$. Multiply the denominators: $4 \times 1 = 4$. So the result is $\frac{21}{4}$.

Step1: Apply fraction division rule

For $\frac{6}{8} \div \frac{3}{9}$, we take the reciprocal of $\frac{3}{9}$ which is $\frac{9}{3}$ and multiply with $\frac{6}{8}$. So it's $\frac{6}{8} \times \frac{9}{3}$.

Step2: Simplify and multiply

Simplify $\frac{9}{3}=3$ and $\frac{6}{8}=\frac{3}{4}$. Now multiply $\frac{3}{4} \times 3=\frac{9}{4}$ (or we can multiply directly: $6\times9 = 54$, $8\times3 = 24$, then simplify $\frac{54}{24}=\frac{9}{4}$).

Step1: Use fraction division method

For $\frac{3}{7} \div \frac{5}{12}$, the reciprocal of $\frac{5}{12}$ is $\frac{12}{5}$. So we have $\frac{3}{7} \times \frac{12}{5}$.

Step2: Multiply numerators and denominators

Multiply numerators: $3\times12 = 36$. Multiply denominators: $7\times5 = 35$. So the result is $\frac{36}{35}$.

Answer:

$\frac{21}{4}$ (or $5\frac{1}{4}$)

27.