Rates with fractions

Google Classroom

Problem

Charlie reads quickly. He reads $1\dfrac37$1, start fraction, 3, divided by, 7, end fraction pages every $\dfrac23$start fraction, 2, divided by, 3, end fraction minutes. Charlie reads at a constant rate.

How many pages does he read per minute?

 pages per minute

Hint #11 / 8

To find pages per minute, we divide pages by minutes.

Hint #22 / 8

$\phantom{=}\dfrac{~~~1 \dfrac37 \text{ pages}~~~}{\dfrac23 \text{ minute}}$empty space, start fraction, space, space, space, 1, start fraction, 3, divided by, 7, end fraction, start text, space, p, a, g, e, s, end text, space, space, space, divided by, start fraction, 2, divided by, 3, end fraction, start text, space, m, i, n, u, t, e, end text, end fraction

Hint #33 / 8

$= 1 \dfrac{3}7 \div \dfrac23\qquad$equals, 1, start fraction, 3, divided by, 7, 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 / 8

$= \dfrac{10}7 \div \dfrac23\qquad$equals, start fraction, 10, divided by, 7, 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:

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

$= \dfrac{7}{7} + \dfrac{3}{7}$equals, start fraction, 7, divided by, 7, end fraction, plus, start fraction, 3, divided by, 7, end fraction

$= \dfrac{10}{7}$equals, start fraction, 10, divided by, 7, end fraction

Hint #55 / 8

$= \dfrac{10}{7} \cdot \dfrac32\qquad$equals, start fraction, 10, divided by, 7, 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 / 8

$=\dfrac{30}{14}\qquad$equals, start fraction, 30, divided by, 14, end fraction 

[Hide explanation]

Here's how we multiplied the fractions:

$\phantom{=}\dfrac{10}{7} \cdot \dfrac32$empty space, start fraction, 10, divided by, 7, end fraction, dot, start fraction, 3, divided by, 2, end fraction

$=\dfrac{10 \cdot 3}{7 \cdot 2}$equals, start fraction, 10, dot, 3, divided by, 7, dot, 2, end fraction

$=\dfrac{30}{14}$equals, start fraction, 30, divided by, 14, end fraction

Hint #77 / 8

$=\dfrac{15}{7}$equals, start fraction, 15, divided by, 7, end fraction pages per minute $\qquad$

[Hide explanation]

Here's how we simplified the fraction:

$\phantom{=}\dfrac{30}{14}$empty space, start fraction, 30, divided by, 14, end fraction

$= \dfrac{15 \cdot \cancel{2}}{7 \cdot \cancel{2}}$equals, start fraction, 15, dot, start cancel, 2, end cancel, divided by, 7, dot, start cancel, 2, end cancel, end fraction

$= \dfrac{15}{7}$equals, start fraction, 15, divided by, 7, end fraction

Hint #88 / 8

Charlie reads $\dfrac{15}{7}$start fraction, 15, divided by, 7, end fraction pages per minute.