Rates with fractions

Google Classroom

Problem

Lucy is a dress maker. She sews $\dfrac47$start fraction, 4, divided by, 7, end fraction of a dress in $\dfrac34$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.

 dresses

Hint #11 / 7

The question is asking how much of the dress can she sew in one hour; we can answer this question by finding the unit rate, dresses per hour.

Hint #22 / 7

To find dresses per hour, we divide dresses by hours.

Hint #33 / 7

$\phantom{=}\dfrac{~~~ \dfrac47 \text{ dress}~~~}{\dfrac34 \text{ hour}}$empty space, start fraction, space, space, space, start fraction, 4, divided by, 7, end fraction, start text, space, d, r, e, s, s, end text, space, space, space, divided by, start fraction, 3, divided by, 4, end fraction, start text, space, h, o, u, r, end text, end fraction

Hint #44 / 7

$= \dfrac{4}7 \div \dfrac34\qquad$equals, start fraction, 4, divided by, 7, end fraction, divided by, start fraction, 3, divided by, 4, end fraction 

[Hide explanation]

We rewrote the complex fraction as a division problem because the fraction bar means "divided by".

Hint #55 / 7

$= \dfrac{4}{7} \cdot \dfrac43\qquad$equals, start fraction, 4, divided by, 7, end fraction, dot, start fraction, 4, divided by, 3, end fraction 

[Hide explanation]

We changed dividing by $\dfrac34$start fraction, 3, divided by, 4, end fraction to multiplying by $\dfrac43$start fraction, 4, divided by, 3, end fraction because dividing by a fraction is the same as multiplying by its reciprocal.

Hint #66 / 7

$=\dfrac{16}{21}\qquad$equals, start fraction, 16, divided by, 21, end fraction 

[Hide explanation]

Here's how we multiplied the fractions:

$\phantom{=}\dfrac{4}{7} \cdot \dfrac43$empty space, start fraction, 4, divided by, 7, end fraction, dot, start fraction, 4, divided by, 3, end fraction

$=\dfrac{4 \cdot 4}{7 \cdot 3}$equals, start fraction, 4, dot, 4, divided by, 7, dot, 3, end fraction

$=\dfrac{16}{21}$equals, start fraction, 16, divided by, 21, end fraction

Hint #77 / 7

In one hour, Lucy can sew $\dfrac{16}{21}$start fraction, 16, divided by, 21, end fraction dress.