<h3><u>Question:</u></h3>
Mitch lost 10/3 pounds in 5/7 in a week. Which complex fraction, when simplified, will compute the unit rate of pounds per week?
A)10/3 over 5/7
B)10/3 over 7/5
C)3/10 over 5/7
D)5/7 over 10/3
<h3><u>Answer:</u></h3>
Option A
The unit rate of pounds per week is 10/3 over 5/7
<h3><u>Solution:</u></h3>
Given that,
Mitch lost
pounds in
of a week
We have to compute the unit rate of pounds per week
Unit rate means that number of pounds lost in 1 week
From given information,
![\text{Weight lost in } \frac{5}{7} \text{ of a week } = \frac{10}{3} \text{ pounds }](https://tex.z-dn.net/?f=%5Ctext%7BWeight%20lost%20in%20%7D%20%5Cfrac%7B5%7D%7B7%7D%20%5Ctext%7B%20of%20a%20week%20%7D%20%3D%20%5Cfrac%7B10%7D%7B3%7D%20%5Ctext%7B%20pounds%20%7D)
So to find the number of pounds lost in 1 week, divide the total pounds lost (10/3) by the time in weeks (5/7)
![\text{Number of pounds lost in 1 week } = \frac{\text{pounds lost in} \frac{5}{7} \text{ week }}{\frac{5}{7} \text{ week }}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20pounds%20lost%20in%201%20week%20%7D%20%3D%20%5Cfrac%7B%5Ctext%7Bpounds%20lost%20in%7D%20%5Cfrac%7B5%7D%7B7%7D%20%5Ctext%7B%20week%20%7D%7D%7B%5Cfrac%7B5%7D%7B7%7D%20%5Ctext%7B%20week%20%7D%7D)
![\text{Number of pounds lost in 1 week } = \frac{\frac{10}{3}}{\frac{5}{7}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20pounds%20lost%20in%201%20week%20%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B10%7D%7B3%7D%7D%7B%5Cfrac%7B5%7D%7B7%7D%7D)
Thus unit unit is 10/3 over 5/7
Multiply the length and width for a rectangle like the one shown.
5.3(2.6) = 13.78 square yards.
Answer:
Gold, Orange, White, Blue
Step-by-step explanation:
7/8 gallons in 1/2 hour
Looking for gallons per hour, or
![\frac{gallons}{hour}](https://tex.z-dn.net/?f=%5Cfrac%7Bgallons%7D%7Bhour%7D)
.
So, this is basically a division problem of 7/8 divided by 1/2. Dividing by a fraction is the same as multiplying by that fraction's reciprocal.
![\frac{7/8}{1/2}\frac{gallons}{hour}](https://tex.z-dn.net/?f=%5Cfrac%7B7%2F8%7D%7B1%2F2%7D%5Cfrac%7Bgallons%7D%7Bhour%7D)
![\frac{\frac{7}{8}}{\frac{1}{2}} = \frac{7}{8} * \frac{2}{1} = \frac {7}{8} * 2 = \frac{14}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B7%7D%7B8%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%3D%20%5Cfrac%7B7%7D%7B8%7D%20%2A%20%5Cfrac%7B2%7D%7B1%7D%20%3D%20%5Cfrac%20%7B7%7D%7B8%7D%20%2A%202%20%3D%20%5Cfrac%7B14%7D%7B8%7D)
Now we simplify by a factor of 2:
![\frac{14}{8} = \frac{7}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B8%7D%20%3D%20%5Cfrac%7B7%7D%7B4%7D)
And here we are! There are 7/4 gallons leaking per hour. This is the same as 1.75 gallons per hour. Hope this helps! :)