Friday, July 19, 2024

How To Find Rate In Math

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Examples Using Interest Rate Formula

Unit Rates | Solving Unit Rate Problems

Example 1: If Sam lends $5000 to his friend and received $6000 after a year. Using the interest rate formula, find at what interest rate did Sam lends the amount to his friend?


Simple intrest =$6000- $5000= $1000

Time=1 year

Interest Rate = /

Interest Rate = /

Interest Rate = 20%

Therefore, Sam will take a 20% interest rate from his friend in a year.

Example 2: James borrowed $600 from the bank at some rate per annum and that amount becomes double in 2 years. Calculate the rate at which James borrowed the money.


Simple interest =$1200- $600= $600

Time = 2 year

Interest Rate = /

Interest Rate = /

Interest Rate = 50%

Therefore, James borrowed the money at 50% rate.

Example 3: What is the interest rate on principal amount 12000 in 2 years, if the simple interest is 1200?


Using simple interest rate formula,

The interest rate of a given amount can be expressed as,

Interest Rate = /

Interest Rate = /

Interest Rate = 5%

Therefore, the interest rate is 5%

How To Used Unit Rate Calculator

The unit rate tool provided here is extremely simple and easy to use. Follow the steps given below to use this tool.

  • Step 1: Enter a numeric digit in the first input box i.e. below Quantity text.
  • Step 2: Enter the unit of the numerator i.e. under text.
  • Step 3: Enter the second numeric digit after the dotted line.
  • Step 4: Enter the unit of the denominator in the last input box
  • Step 5: Click on the Calculate button.

For example, if the numerator is given as 30 km and the denominator is given as 2.5 hours, the tool will divide them both and give the result as 12 km per hour.

How To Find The Average Rate Of Change

The average rate of change of a function corresponds to the slope of the line, which connects two endpoints of a given interval . Here is the average rate of change formula:

The average rate of change of the function has the change in y-values in the numerator and the change in x-values as the denominator. Well subtract the x and y-values of the second point from the x and y-values of the first point, then simplify.

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Nonlinear Rate Of Change

A nonlinear function, however, doesnt have a constant rate of change. It will have a different slope depending on what points you use in the average rate of change formula.

So, you can find the rate of change by forming a straight secant line segment that goes through two point, which well use in the average rate of change formula:

Image credit: Desmos

Rates Of Change Formula


To calculate the rate of change, we calculate the quotient between the changes in the quantities. This means,

Further to the derivation of this formula, we shall take the directions on a graph as a guide. Let us consider that changes are made in both the horizontal direction and the vertical direction .

In the horizontal direction, a change will imply


is the change in the horizontal direction ,

is the initial position on the x-axis,

is the final position on the x-axis.

Likewise, in the vertical direction, a change will imply,


is the change in the vertical direction ,

is the initial position on the y-axis,

is the final position on the y-axis.

Therefore, the rate of change formula becomes,

If the value of a quantity at the start recorded 5 units horizontally and 3 units vertically, thereafter, it recorded 8 units horizontally and 4 units vertically, what is the rate of change?


From the information given, we have

is 5,

Therefore the rate of change of a function formula would be,

The formula used in calculating the rate of change of a function is,


is the change in the horizontal direction ,

is the initial position on the x-axis,

is the final position on the x-axis,

is the change in the vertical direction ,

is the function of the initial position on the x-axis,

is the function of the final position on the x-axis.

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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.

What Is A Rate

A rate, like a ratio, is also a comparison between two numbers or measurements, but the two numbers in a rate have different units.

Some examples of rate include cost rates, per kg or 16,95 R/kg) and speed \).

When we calculate rate, we divide by the second value, so we are finding the amount per one unit.

Unit rates

For example, if we want a rate for \ for \ \ of flour, we write:

\ : \ \ = \ : \ \

= \/kg.

This rate is a unit rate.

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By Step Guide To Unit Rates And Rates

In math, a rate is a ratio that compares two different quantities that have different units. For example, if we say Jim types \ words in a minute, then his rate of typing is \ words per minute. The word per indicates that we are dealing with a rate. The word per can be replaced with the / symbol in problems.

Developing The Concept: Rates

Simple Interest Finding rate

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.

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Negative Rates Of Change

Negative rates of change occur when the quotient of the changes between both quantities gives a negative value. For this to occur, one of the changes must produce a negative change while the other must give a positive change. Beware that when both changes produce negative values, then the rate of change is positive and not negative!

Again, the steepness of the slope is dependent on which quantity experiences a greater change relative to the order quantity. This means that if the change in y-values is greater than that of the x-values, then the slope will be gentle. In contrast, when the change in x-values is greater than that of the y-values, then the slope would be steep.

Note that the direction of the arrow pointing downwards reveals that the rate of change is indeed negative. Take a quick check on these figures below to understand much better.

Calculate the rate of change between two coordinates and and determine

a. The type of rate of change.

b. Whether the slope is steep or gentle.


In order to sketch the graph, we plot the points in the coordinate plane.

Now, in order to calculate the rate of change, we apply the formula,

a. Since our rate of change is -4, thus, it has a negative rate of change.

b. We notice that the change towards the y-direction is greater than the change in the x-direction , therefore, the slope when plotted on a graph would be gentle as shown in the figure.

What Is The Difference Between Rate And Unit Rate

Rate is the ratio of two different quantities with different units, whereas unit rate expresses the number of units of the first quantity for one unit of the second quantity. In unit rate, the denominator is always of one unit. An example of unit rate is 50 miles per hour, which means 50 miles are covered in one hour, whereas, 1000 miles/10 hours, is an example of rate and not unit rate.

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Determine If You Have A Percent Increase Or A Percent Decrease

Compare your results to your initial data values. If you perform a calculation expecting a percentage increase and receive a negative number as a result, the percent change is actually a percentage decrease. In the same way, if you perform calculations for a percentage decrease and it results in a negative value, the percent change is actually a percentage increase. In the example comparing sales quarters, the solution produces a positive number after conducting calculations for a percentage increase, so the percent change is a 20% increase.

Related: How To Calculate Percentage, Percentage Change and Percentage Difference

Rates Of Change Examples

Constant Rate Of Change 7.4 A

There are practical applications of rates of change. A good application is in the determination of speed. An illustration below would elaborate better.

A car starts from rest and arrives at a point J which is 300m from where it started in 30 seconds. At the 100th second, it reaches a point F which is 500m from his starting point. Calculate the average speed of the car.


Below is a sketch of the journey of the car.

The average speed of the car is equivalent to the rate of change between the distance travelled by the car and the time it took.


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Average Growth Rate Over Time Example

You would use the average growth rate over time method to calculate the average annual growth rate for several years. For example, the preschool’s enrollment numbers for the past four years are…

You can use the average growth rate over time calculation method to find the average annual growth rate for the preschool. In this example, the present value is 489, the past value is 328 and the number of years is 4:

Growth rate after 2016: / 350 x 100 = 11.43%Growth rate after 2017: / 390 x 100 = 3.08%Growth rate after 2018: / 402 x 100 = 21.64%

Average growth rate over time = / 3 = 12.05% per year

Divide The Value Of Prevalence By The Population Size

Take the number of cases you’re evaluating and divide it by the value that represents the population size you’re determining prevalence in. For the example of flu in the office, you can divide the number of flu cases, 35, by the total number of people in the office, 200. The result for this calculation is .175.

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What Is A Unit Rate In Math

Your students have no doubt encountered rates and ratios before , but it may help them to review these concepts before solving problems that use them.

Standard: Understand the concept of a unit rate a/b associated with a ratio a:b with b 0.

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.

How To Calculate Interest Rate

Solving Unit Rate Word Problems | Math with Mr. J

This article was co-authored by Bryan Hamby. Bryan Hamby is the owner of Auto Broker Club, a trusted auto brokerage in Los Angeles, California. He founded Auto Broker Club in 2014 out of a passion for cars and a unique talent for customizing the car dealership process to be on the buyers side. With 1,400+ deals closed, and a 90% customer retention rate, Bryans focus is to simplify the car buying experience through transparency, fair pricing, and world class customer service.There are 12 references cited in this article, which can be found at the bottom of the page. This article has been viewed 636,065 times.

If you know the amount of a loan and the amount of interest you would like to pay, you can calculate the largest interest rate you are willing to accept. You can also look at your interest payments in a year and see what your annual percentage rate was. Calculating interest rates is not only easy, it can save you a lot of money when making investment decisions.

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How Do You Solve For The Rate In The Compound Interest Formula

Problems that ask you to solve for the rate r in the compound interest formula require the use of roots or creative use of exponents. Lets look at an example.

Problem Suppose 5000 dollars is deposited in an account that earns compound interest that is done annually. If there is 7000 dollars in the account after 2 years, what is the annual interest rate?

Solution The easiest way to approach this problem is to use the compound interest formula,

This formula applies when interest is earned on an annual basis and the interest is earned once a year.

Lets look at the quantities in the problem statement:

  • 5000 dollars is deposited in an account > P = 5000
  • If there is 7000 dollars in the account after 2 years > A = 7000 and n = 2

Putting these values into the formula above gives us

We need to find the annual interest rate r. Since the r is hidden in the parentheses, we start by isolating the parentheses.

To get at the r, we need to remove the square on the parentheses.

Using a calculator to do the square root, we get r 0.183 or 18.3%.

Although most calculators have a square root key, when removing powers it is often useful to raise both sides to a power. For instance, we could remove the square by raising both sides to the ½ power.

When you raise a power to another power, you multiply the exponents 2 ½ = 1. The right side simply becomes 1 + r. Now we can solve for r:

To solve for r in this equation, we follow similar steps.

Applying Percentage Base And Rate Worksheets

This is a fantastic bundle which includes everything you need to know about Applying Percentage, Base, and Rate across 15+ in-depth pages. These are ready-to-use Common core aligned Grade 6 Math worksheets.Each ready to use worksheet collection includes 10 activities and an answer guide. Not teaching common core standards? Dont worry! All our worksheets are completely editable so can be tailored for your curriculum and target audience.

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What Is Unit Rate Definition

A unit rate is defined as a ratio that compares the first quantity to one unit of the second quantity. The two quantities being compared have different units. For example, if a person types 500 words in an hour, then it is expressed as 500 words per hour or 500 words/hour. Here, we can observe that the denominator is 1.

How To Find Unit Rate

ratios and proportions

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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What Is The Definition Of Rate In Math

Rate is usually defined as a ratio of two quantities with different units. Usually, the rate is written as a fraction, with the first quantity as the numerator and the second quantity as the denominator. 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.

When To Use The Average Rate Of Change Formula

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.

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How Do I Calculate A Rate

CVO website describing Mt RainierIn 1892, the terminus of Nisqually Glacier, on the southern side of Mt. Rainier in Washington, was located 40 meters above the current position of the Nisqually river bridge. In 1951, the terminus was located 790 m above the bridge. Calculate Nisqually Glacier’s rate of retreat from the bridge between 1892 and 1951.

  • Determine which changing variable is X and which is t.
  • This is one of the most important steps if the number you had gotten was 12,700 meters per year then the glacier would have retreated more than the height of the mountain in a single year – not likely. If you had gotten .0078 meters per year, that is less than a centimeter and that would not be measurable. As it turns out, in North America glaciers typically have been retreating at rates of 3-25 m per year. Since our rate falls somewhere in the middle, it’s probably reasonable.
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