The numbers or measurements being compared are sometimes called the terms of the ratio. For example, if a store sells 6 red shirts and 8 green shirts, the ratio of red to green shirts is 6 to 8.
A rate is a special ratio in which the two terms are in different units. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces. But notice that this time, a new unit is created: cents per hour. Rates are used by people every day, such as when they work 40 hours per week or earn interest every year at a bank. When rates are expressed as a quantity of 1, such as 2 feet per second that is, per 1 second or 5 miles per hour that is, per 1 hour , they can be defined as unit rates.
You can write any rate as a unit rate by reducing the fraction so it has a 1 as the denominator or second term. As a unit rate example, you can show that the unit rate of students for every 3 buses is 40 students per bus. Rate and unit rate are used to solve many real-world problems. Look at the following problem. At that rate, how many hours will she work in 12 weeks? Removing the units makes the calculation easier to see.
However, it is important to remember the units when interpreting the new ratio. When you find equal ratios, it is important to remember that if you multiply or divide one term of a ratio by a number, then you need to multiply or divide the other term by that same number. Let's take a look at a problem that involves unit price. How much would 10 pens cost? Your students have no doubt encountered rates and ratios before have they seen a speed limit sign?
Prerequisite Skills and Concepts: Students should have a basic understanding of ratios, how to write them, and an ability to simplify a ratio. Students should also have an ability to work with fractions and find equivalent fractions. Now that students know how to find a unit rate, they will learn how to find an equivalent ratio using unit rates.
Finding equivalent ratios uses the same thought process as finding equivalent fractions. Standard: Use ratio and rate reasoning to find equivalent ratios and solve real-world problems 6. Looking for more free math lessons and activities for elementary school students? The key differences between the two terms are listed below. In general, we can write down the formula for rate as the ratio between two quantities with various units.
Putting this in the ratio format, we get,. Let us take an example to understand this better. Ben rode his bike for 2 hours and traveled 24 miles.
To calculate the speed at which he rode, let us use the formula for rate. Here, the speed is the rate. Unit rate is also a comparison between two quantities that have different units except for the fact that the quantity in the denominator is always one. The rate "miles per minute" gives the distance traveled per unit of time.
In order to calculate the unit rate, we divide the denominator with the numerator in such a way that the denominator becomes 1. In other words, the denominator is always 1 in a unit rate. Example 1: A printer prints 60 pages of an e-book in 30 seconds.
Find the unit rate of the number of pages printed per second. To find the unit rate, we divide the total number of pages printed by the total number of seconds. Example 2: Fred is fond of baking and he bakes wonderful cakes. He bakes 32 cakes in 8 hours. Can you find his rate of baking cakes per hour? To compare the ratio between the flashlights and the batteries we divide the set of flashlights with the set of batteries. All these describe the ratio in different forms of fractions.
The ratio can consequently be expressed as fractions or as a decimal. A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. For the rectangle that follows, express the ratio of length to width as a fraction reduced to lowest terms. Express the ratio of length to width as a fraction reduced to lowest terms.
An automobile travels miles on 12 gallons of gasoline. Express the ratio distance traveled to gas consumption as a fraction reduced to lowest terms. Write a short sentence explaining the physical significance of your solution. Include units in your description. Thus, the rate is 56 miles to 3 gallons of gasoline. In plain-speak, this means that the automobile travels 56 miles on 3 gallons of gasoline.
Lanny travels kilometers on 14 liters of gasoline. When making comparisons, it is helpful to have a rate in a form where the denominator is 1. Such rates are given a special name. To do so, divide. Push the decimal in the divisor to the far right, then move the decimal an equal number of places in the dividend.
As we are dealing with dollars and cents, we will round our answer to the nearest hundredth. Because the test digit is greater than or equal to 5, we add 1 to the rounding digit and truncate; i. Frannie works 5. What is her hourly salary rate?
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