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5 6 Ratios and Rate Prealgebra 2e

As you can see, breaking down costs to the smallest unit reveals the cost savings of the sale. Of course, saving a few cents per ounce of soda may not be the deciding factor of your purchase. Other factors come into play when consumers are shopping, like brand loyalty and personal preference. However, comparing unit costs provides an objective way of making consumer choices based on the price. Let’s consider the treasure trove of rates that may be in your grocery cart the next time you go shopping.

1. In the following exercises, write each ratio as a fraction.
2. You do not have to write out every step when you multiply the numerator and denominator by powers of ten.
3. Notice in Example 5.67 that we rounded the unit price to the nearest cent.
4. This is a unit rate; it gives the distance traveled per one hour.
5. Including Luisa, there are a total of 22 people, 10 of whom are women.

Unit rate can be defined as the ratio between two measurements with the second term fixed at 1 unit. Finding the cost of one unit enables you to find the cost of any number of units. Removing the units makes the calculation easier to see. However, it is important to remember the units when interpreting the new ratio. For example, the expression between 20kg of sugar and 14 kg of wheat is an example of a ratio.

Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . Write the ratio of 114to238114to238 as a fraction. These 5th grade ratio worksheets are a great way to introduce this concept. In the context of simple interest, rate is defined as the percentage of the money that is paid by a borrower to a lender on a per annum basis.

Examples Using Unit Rate Formula

When rates are simplified, the units remain in the numerator and denominator. We know that to simplify a fraction, we divide out common factors. Similarly in a ratio of measurements, we divide out the common unit. We want to know the ratio of Hector’s total cholesterol to his HDL cholesterol. Remember that to divide mixed numbers, you first rewrite them as improper fractions.

Grades

If the measurements are not in the same units, we must first convert them to the same units. Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information. Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information. To find the unit price of an item, simply divide the amount of money by the number of items (or the number of litres, kilograms, etc.). Franklin can jog approximately 2,000 meters in 4 minutes.

How to Calculate and Compare Unit Prices at the Store

It would take 1 person 70 days to build the wall. As a unit price is a ratio that compares the number of people decreases, the time taken will increase. So 1 person would take 36 days to complete the job.

Applications of Ratios

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. Let us consider an example of a car that is traveling at a speed of 150 miles in 3 hours. This can be expressed as 150 miles divided by 3 hours which is equal to 150 miles/3 hours or 50 miles/hour.

In the example above, it’s “apples per day.” This ensures that the rate is accurately represented and can be easily compared with other rates. A unit rate is a rate that compares the first quantity to one unit of the second quantity, expressed as a ratio. A unit rate tells us how many units of the first quantity relate to just one unit of the second quantity. Only C is a unit rate because the 2000 lizards are expressed as a quantity per 1 year. Neither A nor B are unit rates because A is expressed a quantity per 6 months and B is expressed as quantity per 3 cages. Have you noticed that the examples in this section used the comparison words ratio of, to, per, in, for, on, and from?