Question

How do you solve `\frac { 2} { 5} \div \frac { 7} { 10} \cdot \frac { 2} { 3}`?

Answer 1

See a solution process below:

Explanation:

We can rewrite this expression as:

`(2/5)/(7/10) * 2/3`

We can then use this rule of dividing fractions to simplify the term on the left:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(2)/color(blue)(5))/(color(green)(7)/color(purple)(10)) * 2/3 => (color(red)(2) xx color(purple)(10))/(color(blue)(5) xx color(green)(7)) * 2/3 => (color(red)(2) xx cancel(color(purple)(10))2)/(cancel(color(blue)(5)) xx color(green)(7)) * 2/3 =>`

`4/7 * 2/3`

We can now multiply the numerators and denominators of the two remaining fractions:

`4/7 * 2/3 => (4 * 2)/(7 * 3) => 8/21`