Quiz 1

Google Classroom

Problem

Robert climbed $775$775 steps in $12\dfrac12$12, start fraction, 1, divided by, 2, end fraction minutes.

How many steps did he average per minute?

 steps per minute

Hint #11 / 8

To find steps per minute, we divide total steps by minutes.

Hint #22 / 8

$\phantom{=}\dfrac{~~~775 \text{ steps}~~~}{12\dfrac12 \text{ minutes}}$empty space, start fraction, space, space, space, 775, start text, space, s, t, e, p, s, end text, space, space, space, divided by, 12, start fraction, 1, divided by, 2, end fraction, start text, space, m, i, n, u, t, e, s, end text, end fraction

Hint #33 / 8

$= 775 \div 12\dfrac12 \qquad$equals, 775, divided by, 12, start fraction, 1, divided by, 2, end fraction 

[Hide explanation]

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

Hint #44 / 8

$= 775 \div \dfrac{25}2 \qquad$equals, 775, divided by, start fraction, 25, divided by, 2, end fraction 

[Hide explanation]

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

$\phantom{=}12 \dfrac{1}2$empty space, 12, start fraction, 1, divided by, 2, end fraction

$= \dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac{2}{2} +\dfrac12$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, 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, 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, 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

$= \dfrac{25}{2}$equals, start fraction, 25, divided by, 2, end fraction

Hint #55 / 8

$= 775 \cdot \dfrac2{25} \qquad$equals, 775, dot, start fraction, 2, divided by, 25, end fraction 

[Hide explanation]

We changed dividing by $\dfrac{25}2$start fraction, 25, divided by, 2, end fraction to multiplying by $\dfrac2{25}$start fraction, 2, divided by, 25, end fraction because dividing by a fraction is the same as multiplying by its reciprocal.

Hint #66 / 8

$=\dfrac{1550}{25} \qquad$equals, start fraction, 1550, divided by, 25, end fraction 

[Hide explanation]

Here's how we multiplied the fractions:

$\phantom{=}775 \cdot \dfrac2{25}$empty space, 775, dot, start fraction, 2, divided by, 25, end fraction

$=\dfrac{775 \cdot 2}{1 \cdot 25}$equals, start fraction, 775, dot, 2, divided by, 1, dot, 25, end fraction

$=\dfrac{1550}{25}$equals, start fraction, 1550, divided by, 25, end fraction

Hint #77 / 8

$=62 \text{ steps per minute} \qquad$equals, 62, start text, space, s, t, e, p, s, space, p, e, r, space, m, i, n, u, t, e, end text 

[Hide explanation]

Here's how we simplified the fraction:

$\phantom{=}\dfrac{1550}{25}$empty space, start fraction, 1550, divided by, 25, end fraction

$= \dfrac{62 \cdot \cancel{25}}{1 \cdot \cancel{25}}$equals, start fraction, 62, dot, start cancel, 25, end cancel, divided by, 1, dot, start cancel, 25, end cancel, end fraction

$= 62$equals, 62

Hint #88 / 8

Robert averaged $62$62 steps per minute.