# 4 1 Ratios and Rate Introductory Algebra

A unit rate or unit price is a rate that describes the rate or price for one unit of measure. A rate is a ratio that compares two different quantities of different units, such as miles per hour or dollars per ounce. The word per gives a clue that we are dealing with a rate. The word per can be further replaced by the symbol “/” in problems. A unit rate is about comparing a quantity to its unit of measure and can be calculated using the unit rate formula.

One real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person’s overall health. A ratio of less than to 1 is considered good. Since the price given is for 3 boxes, divide both the numerator and the denominator by 3 to get the price of 1 box, the unit price. For example, an employer wants to rent 6 buses to transport a group of 300 people on a company outing. The rate to describe the relationship can be written using words, using a colon, or as a fraction; and you must include the units.

If 100 miles are traveled in one hour, then we express it as 100 miles per hour. The word ‘per’ or the symbol ‘/’ is used to denote rate. For example, if we say that a car travels at a speed of 100 miles per hour, then it means in one hour it covers 100 miles. This way of comparing two different units expressed as a single ratio is termed as ‘Rate’.

This requires us to divide $36 by 4, which equals $9. We do not actually calculate rate; rate is a ratio between two things that have different units of measure. For example, if we know that a pack of 3 Romaine Hearts costs $2.99, then the rate is $2.99/pack of Romaine Hearts. Let’s consider the treasure trove of rates that may be in your grocery cart the next time you go shopping. In the examples listed here, the rate that you agree to pay is simply the cost related to the quantity of the product. In this section, we will use the fraction notation.

## What is the Definition of Rate?

The best buy is the item that has the lowest cost per ounce of juice. That is, we need to buy the carton, either concentrated or ready to serve, that has the lowest unit rate in terms of cost per ounce. The container with the lowest cost per unit is the best buy. That is, the jar of jelly that has the lowest unit rate in terms of cost per ounce is the best deal. The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.

- Similarly, customers would not buy the product if the value of the product is less than the price.
- For example, if we are given the rate $4.50/5 gallons of milk, we can divide 4.50 by 5 to find the unit price, which is dollars per one gallon of milk.
- In unit rate, the denominator is always of one unit.
- Clearly, this is comparing “apples to oranges” in the sense that the underlying units are not the same.
- If we have a pound of deli meat and the cost is $9.99, our rate would then be $9.99 per pound.

A ratio of less than 55 to 11 is considered good. We will often work with ratios of decimals, especially when we have ratios involving money. However, if we need to compare 5 meters to 60 centimeters, we will have to convert the quantities to a common unit and then make the comparison. Therefore, the 24-ounce jar has the lowest unit rate, and is hence the best buy because it has the lowest cost per ounce of $0.129.

When two quantities of different units are compared and expressed as a ratio, it is known as a rate. For example, the ratio of the distance covered by a car in miles to the time taken in hours. Miles and hours are two different https://1investing.in/ units here. Anyla’s trip compares quantities with different units (blocks and minutes) so it is a rate and can be written . This fraction can be simplified by dividing both the numerator and the denominator by 2.

## Unit Cost

Clearly, this is comparing “apples to oranges” in the sense that the underlying units are not the same. A conversion of either miles to kilometers or kilometers to miles must be made to make a fair comparison of average speed. The important thing to remember when analyzing unit rates is that the units must be the same.

Since rates compare two quantities measured in different units of measurement they must include their units. Hence, customers should compute the unit price to know what is paying for a single item rather than looking at the total quantity of product he is purchasing. The unit price is a measurement used to represent the price of a particular good or service to be exchanged with customers or consumers for money.

## Rate Definition

This fraction means that the rate of buses to people is 6 to 300 or, simplified, 1 bus for every 50 people. A poll at Forrester University found that 4,000 out of 6,000 students are unmarried. Find the ratio of unmarried to married students. A ratio is simplified if it is equivalent to a fraction that has been simplified.

## Definition of Rate

Express the fraction with 1 in the denominator by dividing both the numerator and the denominator by 3. Write a rate to represent the cost per number of pounds. If 4,000 students out of 6,000 are unmarried, then 2,000 must be married. The ratio of unmarried to married students can be represented as 4,000 to 2,000, or simply 2 to 1.

For example, when we say that we are driving at a speed of 6868 miles per hour we mean that we travel 6868 miles in 11 hour. We would write this rate as 6868 miles/hour (read 6868 miles per hour). The common abbreviation for this is 6868 mph. Note that when no number is written before a unit, it is assumed to be 1.1. A rate compares the values of two different quantities. In a unit rate, however, one quantity is compared to 1 unit of the other quantity.

That is, we can compare 1 meter to 5 meters and identify which one is larger. D) The 2-pound bag has a lower price of $1.89/2 pounds. Write a rate to represent the cost per ounce for Brand B. Write a rate to represent the cost per ounce for Brand A. Express the fraction with 1 in the denominator to find the number of passengers in one subway car. Rewrite each fraction with a common denominator, 66.

## Unit Rates

A rate is a ratio that compares two different quantities that have different units of measure. A rate is a comparison that provides information such as dollars per hour, feet per second, miles per hour, and dollars per quart, for example. The word “per” usually indicates you are dealing with a rate. Rates can be written using words, using a colon, or as a fraction. It is important that you know which quantities are being compared. In math, a rate is a ratio that compares two different quantities which have different units.

Often, we are asked to determine which of two given items is a “better buy”. In such cases, the unit price of each item is found and then, their unit prices are compared. The item with the smaller unit price is considered as the “better buy”.

We can express the rate by reducing them to the lowest form possible. For example, if a person takes 30 steps in 20 seconds, then the rate at which they walk is 30 steps/20 seconds or 3 steps/2 seconds. The unit price of an item is the cost per unit of the item. We divide the price of certain number of units of an item by the number of units to find the unit price of that item. In order to express $36 for one movie ticket as a unit rate, we need to determine the cost for one movie ticket.