# 5.6 Ratios and rate  (Page 4/10)

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Find the unit rate: $423$ miles to $18$ gallons of gas.

23.5 mpg

Find the unit rate: $406$ miles to $14.5$ gallons of gas.

28 mpg

## Find unit price

Sometimes we buy common household items ‘in bulk’, where several items are packaged together and sold for one price. To compare the prices of different sized packages, we need to find the unit price. To find the unit price, divide the total price by the number of items. A unit price    is a unit rate for one item.

## Unit price

A unit price    is a unit rate that gives the price of one item.

The grocery store charges $\text{3.99}$ for a case of $24$ bottles of water. What is the unit price?

## Solution

What are we asked to find? We are asked to find the unit price, which is the price per bottle.

 Write as a rate. $\frac{3.99}{\text{24 bottles}}$ Divide to find the unit price. $\frac{0.16625}{\text{1 bottle}}$ Round the result to the nearest penny. $\frac{0.17}{\text{1 bottle}}$

The unit price is approximately $\text{0.17}$ per bottle. Each bottle costs about $\text{0.17}.$

Find the unit price. Round your answer to the nearest cent if necessary.

$\text{24-pack}$ of juice boxes for $\text{6.99}$

$0.29/box Find the unit price. Round your answer to the nearest cent if necessary. $\text{24-pack}$ of bottles of ice tea for $\text{12.72}$$0.53/bottle

Unit prices are very useful if you comparison shop. The better buy is the item with the lower unit price. Most grocery stores list the unit price of each item on the shelves.

Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at $\text{14.99}$ for $64$ loads of laundry and the same brand of powder detergent is priced at $\text{15.99}$ for $80$ loads.

Which is the better buy, the liquid or the powder detergent?

## Solution

To compare the prices, we first find the unit price for each type of detergent.

 Liquid Powder Write as a rate. $\frac{\text{14.99}}{\text{64 loads}}$ $\frac{\text{15.99}}{\text{80 loads}}$ Find the unit price. $\frac{\text{0.234…}}{\text{1 load}}$ $\frac{\text{0.199…}}{\text{1 load}}$ Round to the nearest cent. $\begin{array}{c}\text{0.23/load}\hfill \\ \text{(23 cents per load.)}\hfill \end{array}$ $\begin{array}{c}\text{0.20/load}\hfill \\ \text{(20 cents per load)}\hfill \end{array}$

Now we compare the unit prices. The unit price of the liquid detergent is about $\text{0.23}$ per load and the unit price of the powder detergent is about $\text{0.20}$ per load. The powder is the better buy.

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand A Storage Bags, $\text{4.59}$ for $40$ count, or Brand B Storage Bags, $\text{3.99}$ for $30$ count

Brand A costs $0.12 per bag. Brand B costs$0.13 per bag. Brand A is the better buy.

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand C Chicken Noodle Soup, $\text{1.89}$ for $26$ ounces, or Brand D Chicken Noodle Soup, $\text{0.95}$ for $10.75$ ounces

Brand C costs $0.07 per ounce. Brand D costs$0.09 per ounce. Brand C is the better buy.

Notice in [link] that we rounded the unit price to the nearest cent. Sometimes we may need to carry the division to one more place to see the difference between the unit prices.

## Translate phrases to expressions with fractions

Have you noticed that the examples in this section used the comparison words ratio of, to, per, in, for, on , and from ? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
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what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
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what is nanomaterials​ and their applications of sensors.
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How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?