Rates with fractions

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Problem

A ferry traveled $\dfrac16$start fraction, 1, divided by, 6, end fraction of the distance between two ports in $\dfrac37$start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.

At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

 of the distance

Hint #11 / 7

The question is asking what fraction of the distance the ferry travels in one hour. We can answer this question by first finding the rate fraction of distance per hour.

Hint #22 / 7

To find fraction of distance per hour, we divide fraction of distance by hours.

Hint #33 / 7

$\phantom{=}\dfrac{~~~ \dfrac16 \text{ of distance}~~~}{\dfrac37 \text{ hour}}$empty space, start fraction, space, space, space, start fraction, 1, divided by, 6, end fraction, start text, space, o, f, space, d, i, s, t, a, n, c, e, end text, space, space, space, divided by, start fraction, 3, divided by, 7, end fraction, start text, space, h, o, u, r, end text, end fraction

Hint #44 / 7

$= \dfrac{1}6 \div \dfrac37\qquad$equals, start fraction, 1, divided by, 6, end fraction, divided by, start fraction, 3, divided by, 7, end fraction 

[Hide explanation]

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

Hint #55 / 7

$= \dfrac{1}{6} \cdot \dfrac73\qquad$equals, start fraction, 1, divided by, 6, end fraction, dot, start fraction, 7, divided by, 3, end fraction 

[Hide explanation]

We changed dividing by $\dfrac37$start fraction, 3, divided by, 7, end fraction to multiplying by $\dfrac73$start fraction, 7, divided by, 3, end fraction because dividing by a fraction is the same as multiplying by its reciprocal.

Hint #66 / 7

$=\dfrac{7}{18}\text{ of distance per hour}\qquad$equals, start fraction, 7, divided by, 18, end fraction, start text, space, o, f, space, d, i, s, t, a, n, c, e, space, p, e, r, space, h, o, u, r, end text 

[Hide explanation]

Here's how we multiplied the fractions:

$\phantom{=}\dfrac{1}{6} \cdot \dfrac73$empty space, start fraction, 1, divided by, 6, end fraction, dot, start fraction, 7, divided by, 3, end fraction

$=\dfrac{1 \cdot 7}{6 \cdot 3}$equals, start fraction, 1, dot, 7, divided by, 6, dot, 3, end fraction

$=\dfrac{7}{18}$equals, start fraction, 7, divided by, 18, end fraction

Hint #77 / 7

In one hour, the ferry travels $\dfrac{7}{18}$start fraction, 7, divided by, 18, end fraction of the distance between the two ports.