Wednesday, January 25, 2023

How To Do Unit Rate Math Problems

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Unit Rate Solved Examples

Unit Rates | Solving Unit Rate Problems

Now that we have learned about unit rates and how to calculate it, lets see some solved examples on it.

Solved Example 1: Find the rate. A dog walks 696 steps in 12 min. How many steps does a dog take in one minute?

Solution:

A dog walks 696 steps in 12 min.

Therefore, number of steps per minute = \

Number of steps per minute = 58 steps per minute.

Solved Example 2: Jayda takes 3 hours to deliver 189 newspapers on her paper route. What is the rate per hour at which she delivers the newspapers?

Solution:

Jayda takes 3 hours to deliver 189 newspapers.

Therefore, number of papers delivered per hour = \

Number of papers delivered per hour = 63 papers per hour.

Solved Example 3: Nierra earns Rs. 750 for 4 hours of tutoring. How much does Nierra earn for 1 hour of tutoring?

Solution:

Nierra earns Rs. 750 for 4 hours of tutoring.

Therefore, earnings in 1 hour = \

Earnings for 1 hour = 187.5 steps per minute.

If you are checking Unit Rate article, also check the related maths articles in the table below:

What Is A Unit Rate In Math

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example if you ran 70 yards in 10 seconds you ran on average 7 yards in 1 second. Both of the ratios 70 yards in 10 seconds and 7 yards in 1 second are rates but the 7 yards in 1 second is a unit rate.

How Do You Find The Rate In Simple Interest

Simple interest is calculated with the following formula: S.I.= P × R × T where P = Principal R = Rate of Interest in % per annum and T = The rate of interest is in percentage r% and is to be written as r/100. Principal: The principal is the amount that initially borrowed from the bank or invested. See also Do elephant seals eat penguins? Best answer 2022

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Rates In The Real World

Rate and unit rate are used to solve many real-world problems. Look at the following problem. Tonya works 60 hours every 3 weeks. At that rate, how many hours will she work in 12 weeks? The problem tells you that Tonya works at the rate of 60 hours every 3 weeks. To find the number of hours she will work in 12 weeks, write a ratio equal to 60/3 that has a second term of 12.

60/3 = ?/1260/3 = 240/12

Removing the units makes the calculation easier to see. However, it is important to remember the units when interpreting the new ratio.

Tonya will work 240 hours in 12 weeks.

You could also solve this problem by first finding the unit rate and multiplying it by 12.

60/3 = 20/120 × 12 = 240

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. A sign in a store says 3 Pens for $2.70. How much would 10 pens cost? To solve the problem, find the unit price of the pens, then multiply by 10.

$2.70 ÷ 3 pens = $0.90 per pen$0.90 × 10 pens = $9.00

Finding the cost of one unit enables you to find the cost of any number of units.

Examples Using Unit Rate Formula

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Example 1: A farmer harvests 15 acres per day and gets 150 bushels of wheat per acre. Calculate the number of bushels of wheat he needs to harvest in a day using the unit rate formula.

Solution:

Let a = quantity harvested and b = number of days

To find: Quantity per day

Bushels of wheat harvested per acre = 15 × 150

= 2250 Bushels

Using the unit rate formula: unit rate= a/b,

Bushels of wheat harvested per day = 2250 / 1

= 2250

Therefore, the wheat harvested per day = 2250 Bushels

Example 2: If a shop offers you 15 chocolates for $7.5, what does the unit cost be?

Solution:

Price of 15 chocolates = $7.5

To find: cost per chocolate

Let a = cost, b = number of chocolates

Using the unit rate formula: unit rate= a/b,

Per unit cost of chocolates = Cost of chocolates/ Number of chocolates

= $ 7.5/15

Therefore, the per-unit cost of chocolates = $0.5

Example 3: If a fruit shop offers a dozen blueberries for $24, calculate the unit rate.

Solution:

Price of 12 blueberries = $24

Let a = cost and b = dozen

To find: cost per dozen

Using the unit rate formula: unit rate= a/b,

Per unit cost of blueberries = Price of blueberries/Number of blueberries

= 24/12 = $2

Therefore, the per-unit cost of blueberries = $2

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Unit Rate Problems 6th Grade

Welcome to our Unit Rate Problems 6th Grade page. Here you will find our range of 6th Grade Unit Rate worksheetswhich will help your child apply and practice using unit rates in a range of different contexts.

Want to test yourself to see how well you have understood this skill?.

  • Try our NEWquick quiz at the bottom of this page.

How To Calculate Unit Rate

wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 17 people, some anonymous, worked to edit and improve it over time. This article has been viewed 155,373 times.

Unit rate is a comparison of any two separate but related measurements when the second of these measurements is reduced to a value of one. Calculating the unit rate in any set of circumstances will require the use of division.

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Chocolate Chip Cookie Recipe

You want to use Adesinas World Famous Chocolate Chip Cookie Recipe to make some cookies. You need 11/2 cups of sugar for every 2/5 cup of chocolate chips. You have 10 cups of chocolate chips to use. If you want to use all of the chips, how much sugar do you need? First, find how much sugar you need for 1 cup of chips. The ratio of sugar to chips is 11/2 to 2/5. To find the unit rate, divide 11/2 by 2/5. 3/2 ÷ 2/5 = 1/2 × 5/2 = 15/4 = 33/4. The unit rate is 33/4 cups of sugar per 1 cup of chips. To use all 10 cups of chocolate chips, multiply 33/4 by 10 to find the amount of sugar you need. 10 × 33/4 = 10 × 15/4 = 150/4 = 371/2. You need 371/2 cups of sugar. Try this one for yourself. For a cake recipe you need 2 1/4 cups of milk. If you have 15 cups of milk and want to use it all to make cakes, how many cups of flour do you need?

Unit Rates In A Graph Walkthrough Video

Solving Unit Rate Word Problems | Math with Mr. J

This short video walkthrough shows several problems from our Unit Rates in a Graph Worksheet 6:1 being solved and has been produced by theWest Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

Take a look at some more of our worksheets similar to these.

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Definition Of Unit Rate In Mathematics

Unit rate is a very important factor in Mathematics. A unit rate means a comparison between 2 units and the superiority and difference between both of them. The accurate unit rate definition includes all the crucial factors about the two units, which are compared with each other in the first place.

There exist a lot of unit rate real-life examples that can define the same in the best possible ways. However, the definition and meanings of this rate can be separate in real-life & Mathematics. Therefore, this definition should be properly taken into consideration by those who want to solve their unit rate problems and become an expert in finding the unit rate value in the first place.

To define unit rate in Mathematics is to compare two units with each other and find whether which unit is superior to the other and which unit needs more detailed analysis in itself for sure. Therefore, to find the appropriate meaning of unit rate, you should relate it with the subject or context in which you want to find the definition, and this will directly take you to the most valid and easy definition of unit rate in the first place and that too undoubtedly.

How To Find Unit Rate

The process of breaking down the cost to a smaller unit reveals the unit rate of the product. This is helpful to make informed decisions at the store, as the volumes of product in various packaging are often different. By comparing unit rates, savvy customers are able to make price comparisons based on common units of the product regardless of packaging and advertised sale prices.

Lets break down the soda cost per bottle further to determine the cost per ounce. If one 20 ounce bottle costs roughly $0.75, then dividing that cost by 20 ounces reveals the cost per ounce.

\\

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.

The important thing to remember when analyzing unit rates is that the units must be the same. Lets consider another example to illustrate this point.

Suppose you are on a road trip in Wyoming and on the first day you covered 300 miles in 4 hours of mostly highway driving. You can quickly determine your average rate of speed as miles per hour with the following calculation:

\ \

\ \

\

\

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Benefits Of Using Unit Rate In Mathematics:

There exist a lot of different benefits of using Unit Rate in Mathematics, and some of them can be listed as below:

Identifies and Compares Variation in Equations: As we all know that different equations have different frameworks, and all of them should be equally considered so that the result of the Mathematical problem becomes positive and approachable. This is made possible to a much quicker extent with the help of unit rate. A unit rate can measure the approximation of similarity as well as the difference between 2 units and can result in making them successful for the people solving these problems or equations for sure.

The Calculations Become Less Risky & Tough: The toughness of approximation and detection is greatly reduced with the help of unit rate, and this is the most important benefit of this rating in the first place.

The riskiness of all these calculations is primarily reduced, and the extent is quite enlarged with the help of unit rate, and that is why Mathematics has a lot for unit rate and its usage in the initial place and that too undoubtedly.

Ratios And Proportional Relationships

Solving word problems with ratios

6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship.Expectations for unit rates in this grade are limited to non-complex fractions.For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.””We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

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What Is Unit Rate Formula

A unit rate that has the denominator as 1, compares a quantity to the other, which is its unit of measure. If a person runs three miles in 30 minutes, he runs at a rate of one mile every 10 minutes. The rate of miles per minute gives the distance traveled per unit of time. Unit rate is always expressed as the quantity of 1.

Let’s look into some real-time applications of unit rate.

  • Time rate: Distance per unit time, average speed , and interest rates
  • Cost Price: cost/pound, quantity per cost , or for comparing prices.
  • Other examples can be the literacy rate, the population, and other rates which provide specific data

The unit rate formula to calculate the rate for any two quantities say a and b can be given as,

Unit Rate = Ratio between two different quantities with different units

= a:b

= a/b

Examples Of How To Find Unit Rate Or Unit Price

Ryan purchased 3 apples for $1.80. What is the unit price, or the cost of one apple?

  • We want to know the price per apple unit so we set up a ratio with the number of apples in the denominator. The total price goes in the numerator. So the fraction is 1.80/3.
  • Complete the division: 1.80 ÷ 3 = .60. You can conclude that the per apple price unit rate is $0.60/1. Ryan paid a unit price of $0.60 per apple .

The pottery store can make 176 coffee mugs in an 8 hour day. How many mugs can they make in one hour?

  • We want to know the number of mugs made per hour unit so we set up a ratio with hours in the denominator. The total number of mugs made per day goes in the numerator. So the fraction is 176/8.
  • Complete the division: 176 ÷ 8 = 22. You can conclude that the per hour mug-making unit rate is 22/1. The pottery store makes 22 mugs per hour .

Kylie can run 12 laps in 30 minutes. How many laps does she run per minute?

  • We want to know the laps per minute unit so we set up a ratio with minutes in the denominator. The total laps goes in the numerator. So the fraction is 12/30.
  • Complete the division: 12 ÷ 30 = 0.4. You can conclude that the per minute lap unit rate is 0.4/1. Kylie can run 0.4 laps per minute .

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Developing The Concept: Rates

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

  • Say:Before we learned how to find a unit rate. Now we are going to learn how to use that unit rate to solve problems. Look at this problem.
  • Ask:What are we trying to find in this problem?We are trying to find out how long it takes Ebony to run 30 laps.
  • Ask:What information do we know that will help us solve this problem?We know that Ebony can run 18 laps in 12 minutes. We also know she is going to run at that same rate for 30 laps.
  • Ask:How far does Ebony run in one minute?Have students try to figure it out individually. Compare student solutions, and discuss why Ebony runs 1.5 laps in one minute.
  • Say:Let’s make a table to list the information we know.Make the following table but leave “Minutes” blank. Fill it in by soliciting class input.
    Laps

Calculate The Speed Of Go

Unit Rates, Ratios & Proportions – Word Problems

Lets say you drove a go-kart 6 miles in 30 minutes. This is a ratio of 6 miles to 30 minutes. You want to find out how much time it takes you to drive 1 mile. You can find equivalent ratios to figure this out. To find equivalent ratios, multiply or divide both the numerator and denominator in the ratio by the same number. If you divide both numbers in the ratio 30/6 by 3, you get the equivalent ratio 10/2. Divide 2 again to get the ratio 5/1. It takes 5 minutes to drive 1 mile, or you drive at a rate of 5 minutes per mile. This ratio is called the unit rate because it has 1 in the denominator. Try this one for yourself. What is the unit rate if you drove a go-kart 9 miles in 36 minutes?

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Examples For Defining The Unit Rate:

There also exist some Mathematical examples to state the unit rate definition, and these examples will also elaborate its involvement in 90% of the mathematical equations in the first place.

The examples of defining the unit rate can be:

  • Which unit is best from the below ones?

  • \ 3.50/2 litres of milk, or

  • \ 2.80/1.5 litre of milk.

If people compare both these units mathematically, then they will notice that the result of the first one is \ 1.75, and in the other case, the result will be \ 1.86.

When both these units are compared, the second one results as superior, and that is why between the comparison of these two units, the 2nd one becomes superior and better than the 1st one for sure.

Which unit is superior or the best?

  • 12 pencils for \ 9.00, or

  • Eighteen pencils for \ 6.70.

To find the superior or best unit among both of the above units, people will need to first know the proper unit rate math definition and then implement it in this example problem.

In finding the unit rate definition, the first factor totals up to \ 0.75, and the other sums up to \0.37. Among both of these units, according to the unit ratio definition, the first one results as superior to the 2nd unit.

Many more rate and unit rate examples can be listed in these series, and finding the appropriate unit rate is easily possible with these examples and by knowing the exact definition of unit rate in the first place.

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