Rates with fractions

Google Classroom

Problem

Ben drinks tea at an incredible rate. He drinks $3\dfrac12$3, start fraction, 1, divided by, 2, end fraction liters of tea every $\dfrac23$start fraction, 2, divided by, 3, end fraction of an hour. Ben drinks tea at a constant rate.

How many liters of tea does he drink in one hour?

 liters

Hint #11 / 7

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

Hint #22 / 7

$\phantom{=}\dfrac{~~~3\dfrac12 \text{ liters}~~~}{\dfrac23 \text{ hours}}$empty space, start fraction, space, space, space, 3, start fraction, 1, divided by, 2, end fraction, start text, space, l, i, t, e, r, s, end text, space, space, space, divided by, start fraction, 2, divided by, 3, end fraction, start text, space, h, o, u, r, s, end text, end fraction

Hint #33 / 7

$= 3 \dfrac{1}2 \div \dfrac23\qquad$equals, 3, start fraction, 1, divided by, 2, end fraction, divided by, start fraction, 2, divided by, 3, end fraction 

[Hide explanation]

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

Hint #44 / 7

$= \dfrac{7}2 \div \dfrac23\qquad$equals, start fraction, 7, divided by, 2, end fraction, divided by, start fraction, 2, divided by, 3, end fraction 

[Hide explanation]

Here's how we converted the mixed number to an improper fraction:

$\phantom{=}3 \dfrac{1}2$empty space, 3, start fraction, 1, divided by, 2, end fraction

$= \dfrac{2}{2} + \dfrac{2}{2} +\dfrac{2}{2} +\dfrac{1}{2}$equals, start fraction, 2, divided by, 2, end fraction, plus, start fraction, 2, divided by, 2, end fraction, plus, start fraction, 2, divided by, 2, end fraction, plus, start fraction, 1, divided by, 2, end fraction

$= \dfrac{7}{2}$equals, start fraction, 7, divided by, 2, end fraction

Hint #55 / 7

$= \dfrac{7}{2} \cdot \dfrac32\qquad$equals, start fraction, 7, divided by, 2, end fraction, dot, start fraction, 3, divided by, 2, end fraction 

[Hide explanation]

We changed dividing by $\dfrac23$start fraction, 2, divided by, 3, end fraction to multiplying by $\dfrac32$start fraction, 3, divided by, 2, end fraction because dividing by a fraction is the same as multiplying by its reciprocal.

Hint #66 / 7

$=\dfrac{21}{4}$equals, start fraction, 21, divided by, 4, end fraction liters per hour $\qquad$ 

[Hide explanation]

Here's how we multiplied the fractions:

$\phantom{=}\dfrac{7}{2} \cdot \dfrac32$empty space, start fraction, 7, divided by, 2, end fraction, dot, start fraction, 3, divided by, 2, end fraction

$=\dfrac{7 \cdot 3}{2 \cdot 2}$equals, start fraction, 7, dot, 3, divided by, 2, dot, 2, end fraction

$=\dfrac{21}{4}$equals, start fraction, 21, divided by, 4, end fraction

Hint #77 / 7

In one hour, Ben drinks $\dfrac{21}{4}$start fraction, 21, divided by, 4, end fraction liters of tea.