Division of fractions by fractions

$2/5 \div 1/10 = ?$

1. Show $2/5$ on the figure by drawing five equal parts, and then shade the two parts as shown in the following diagram:

2. $2/5 \div 1/10$ is the same as to say how many $1/10$ are there in $2/5$. Divide all parts of the diagram to obtain 10 equal parts as shown in the following diagram:

3. In step 2, the diagram shows that there are four $2/5$ in $1/10$.

By comparing the equations $2/5 \div 1/10 = 4$ and $2/5 \times 10/1 = 4$, you will note that the dividend does not change, but the division sign changes to multiplication sign and the denominator of the divisor becomes the numerator while its numerator becomes the denominator.

Therefore, $2/5 \div 1/10 = 4$.

Based on the above results, the following formula is obtained:

$a/b \div c/d = a/b \times d/c$

$1/3 \div 1/9 = ?$

Using the formula $a/b \div c/d = a/b \times d/c$, $1/3 \div 1/9 = 1/3 \times 9/1 = 9/3 = 3$.

Therefore, $1/3 \div 1/9 = 3$.

$65/100 \div 1/25 = ?$

Using the formula $a/b \div c/d = a/b \times d/c$, $65/100 \div 1/25 = 65/100 \times 25/1 = 65/4 = 16\frac{1}{4}$.

Therefore, $65/100 \div 1/25 = 16\frac{1}{4}$.

$125/1000 \div 6/50 = ?$

Using the formula $a/b \div c/d = a/b \times d/c$, $125/1000 \div 6/50 = 125/1000 \times 50/6 = 25/4 \times 1/6 = 25/24 = 1\frac{1}{24}$.

Therefore, $125/1000 \div 6/50 = 1\frac{1}{24}$.

$1500/605\,500 \div 5/27 = ?$

Using the formula $a/b \div c/d = a/b \times d/c$, $1500/605\,500 \div 5/27 = 1500/605\,500 \times 27/5 = 81/6055$.

Therefore, $1500/605\,500 \div 5/27 = 81/6055$