Question

Lucy is a dress maker. She sews 4 7 7 4 ​ start fraction, 4, divided by, 7, end fraction of a dress in 3 4 4 3 ​ start fraction, 3, divided by, 4, end fraction hour. Lucy sews at a constant rate. At this rate, how many dresses does Lucy sew in one hour? Include fractions of dresses if applicable.

Answer 1

`(16)/(21)` of a dress

Explanation:

For illustration

If in 3 hours, I sew 6 clothes

In 1 hour, I would sew (6/3) clothes.

Using the same analogy:

In
`(3)/(4)` hours, Lucy sews
`(4)/(7)` of a dress.

In 1 hour, Lucy will sew
`((4)/(7) / (3)/(4))` dresses

To simplify
`(4)/(7) / (3)/(4)` , We change the division sign to multiplication by taking the inverse of the fraction after the division sign.i.e.
`(3)/(4)`

`(4)/(7) / (3)/(4)=(4)/(7) X (4)/(3)=(16)/(21)`

In 1 hour, Lucy sews
`(16)/(21)` of a dress.