Calculating Percent Increase in 3 Easy Steps

Calculating Percent Increase in 3 Easy Steps

Being able to calculate percent increase is an incredibly significant and useful math skill that can be applied in the classroom, on exams, and—most importantly—in the real world. While many students often perceive calculating percent increase as a difficult skill to master, it can actually be extremely easy.

(Looking for a Percent Increase Calculator to make a super fast calculation: Click here to access our free Percent Increase Calculator)

 The following free Calculating Percent Increase step-by-step lesson guide will teach you how to calculate percent increase using a simple and effective three-step process. As long as you can remember the three steps and learn to apply them, you will be able to quickly and accurately calculate percent to correctly solve math problems.

Before you learn about calculating percent increase using our three-step process, let’s do a quick recap of some key vocabulary terms and definitions related to percents.

Looking to learn how to calculate percent decrease or percent change? Use the links below to download our free step-by-step guides:

• How to calculate the percent decrease between two numbers

• How to calculate the percent change between two numbers

Percent Definition

In math, a percent refers to parts per one hundred and the mathematical symbol for percent is %.

For example, 40% means 40 per 100. In the diagram below, 40% of the box is shaded in blue.

In other words, percent is a ratio of some value out of one hundred.

For example, 20% means 20 out of every 100. With this definition in mind, if 20% of 200 students have a test tomorrow, then 40 total students have a test tomorrow.

Percent Increase Definition

Now that you understand percent, what does percent increase mean?

 In math, the percent increase between two numbers is the difference between the final number and the starting number. Percent increase is always expressed as a percentage of the first number.

 Keep in mind that percent increase will always be represented as a percentage and will include a % symbol.

For example, if you had $60 dollars at the start of the week and $90 at the end of the week and wanted to find the percent increase, the final number would be 90 and the starting number would be 60.

Identifying the starting number and the final number is relatively simple and it is key for solving percent increase problems.

Calculating Percent Increase

Now you are ready to learn to calculate percent increase using our easy three-step process.

Let’s take a close look at the previous scenario:

Calculating Percent Increase Example #1

For the first example, let’s find the percent increase for the following scenario:

If your total savings of $60 at the start of the week has grown to $90 by the end of the week, what is the percent increase?

Here is where our three-step process comes in:

Step 1: Find the difference of the values by subtracting the starting value from the final value.

In this case, the final value minus the starting value can be calculated as follows:

90 – 60 = 30

 So, the difference of the two values would be 30 in this example. Note that, when calculating percent increase, you will always be subtracting the smaller value from the larger value.

Step 2: Divide the difference by the starting number.

The next step is to take the difference (30 in this example) and divide it by the starting number (60 in this example) as follows:

30/60 = 0.50

Always express your answer as a decimal (doing this will make your life much easier when you get to step three).

Step 3: Multiply by 100

The final step is to multiply the decimal result from step two by one hundred and express the final result as a percent.

0.50 x 100 = 50

 Final Answer: 50% Increase

That’s all there is to it! By using the three steps, you can conclude that there was a 50% increase in how much money you had from the start of the week to the end of the week.

Confused? That’s totally fine. Let’s take a look at another example where we will calculate percent increase using the three-step process.

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Looking for a free Percent Increase Calculator?

If you need a faster way to calculate the percent increase between two numbers, check out our free Percent Increase Calculator tool, which lets you input the starting and final values to get an instant answer!

▶ Click here to access our free Percent Increase Calculator for students

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Calculating Percent Increase Example #2

In 2021, it cost $48 for Jacob to fill up his car’s gas tank. In 2022, it cost Jacob $64 to fill up his car’s gas tank. What was the percent increase in the cost fill up Jacob’s gas tank from 2021 to 2022?

To solve this problem, note that the starting value is 48 and the final value is 64.

Step 1: Find the difference of the values by subtracting the starting value from the final value.

In this example, the final value minus the starting value can be calculated as follows:

64– 48 = 16

Step 2: Divide the difference by the starting number.

For step two, take the difference (16 in this example) and divide it by the starting number (48 in this example) as follows:

16/48 = 0.3333333

Notice that the result is a repeating decimal, which is ok. You can round the result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 0.33

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percent. So…

0.33 x 100 = 33

 Final Answer: 33% Increase

We’re all finished! We have concluded that there was a 33% increase in the cost of filling Jacob’s gas tank from 2021 to 2022.

Hopefully, you are feeling better about calculating percent increase using the three-step method. But, if you could still use a little more practice, let’s take a look at one last example.

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Calculating Percent Increase Example #3

Last school year, 96 students tried out for the Varsity Baseball Team at Delta High School. This year, 212 students tried out. What was the percent increase in students who tried out for the Varsity Baseball Team?

 Just like the last two examples, you can solve this problem by following the three-step process:

Step 1: Find the difference of the values by subtracting the starting value from the final value.

 In this example, the final value minus the starting value can be calculated as follows:

212– 96 = 116

Step 2: Divide the difference by the starting number.

Did you notice that the result from step one is actually larger than the starting value? This occurrence is totally fine and will not prevent the three-step process from working. So, let’s continue with step two as follows:

Find the difference (116 in this example) and divide it by the starting number (96 in this example) as follows:

116/96 = 1.2083333

Just like in example 2, you can round the result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 1.21

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by 100 and express the final result as a percent. So…

1.21  x 100 = 121

Final Answer: 121% Increase

All done! Notice how, in this example, the percent increase is over 100%, which just means the ending value was more than double the starting number.

By now, you should be feeling confident in your ability to calculate percent increase using three-step process. However, if you would like some more practice, I recommend that you work through examples one through three again on your own.

Conclusion: Calculating Percent Increase

You can calculate percent increase given any two values by using the following 3-step method:

Step 1: Find the difference of the values by subtracting the starting value from the final value.

Step 2: Divide the difference by the starting number. Express result as a decimal.

Step 3: Multiply by 100. Express result as a %.

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What about Calculating Percent Decrease and Percent Change?

Learn how to calculate a percent decrease or a percent change between two numbers using our free step-by-step guides. Click the links below to get started.

⇥ Calculating Percent Decrease in 3 Easy Steps

⇥ Calculating Percent Change in 3 Easy Steps

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Don’t forget about our Free Percent Increase Calculator

Click here to get started using our free Percent Increase Calculator

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Are You Ready? 5 Free St Patricks Day Math Activities for Grades 3-8

Are you ready to channel your kids' enthusiasm for St. Patrick's Day into learning math?

Math puzzles give your kids an opportunity to think critically and deeply about mathematics, develop problem-solving strategies, and work through challenging problems.

And when math problems incorporate your kids' personal interests, their engagement will skyrocket!

So, go ahead and try these challenges and puzzles with your kids this month. These free and printable St. Patrick's Day math activities are perfect for warm-up and/or cool-down activities and are great for sparking mathematical discussions in your home or classroom. The puzzles are perfect for students in grades 3 through 8.

How to Download: You can download any of the puzzles by right-clicking on the image and saving it to your computer or by dragging-and-dropping it to your desktop.

1.) Find the value of the '?'

Use your math skills to find the value of each icon.

Top Hat = 3

Pot of Gold = 9

Teddy Bear = 5

Irish Flag = 4

? = 21

Hint: Start with the Teddy Bear.

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2.) Multiplication tables work like a Bingo board, where the value of each box represents the product of its corresponding row and column.

Rainbow = 0

Green Hat = 1

Leprechaun = 2

Heart = 4

Pot of Gold = 0

Shamrock = 5

Looking for more free math challenges like this one to share with your kids? click here

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3.) Multiplication Area Model

Area models help kids to think visually about multiplication, which is the approach that Mathematical Mindsets author Jo Boaler recommends most for improving math understanding.

Balloons = 10

Shoe = 6

Leprechaun = 60

Shamrock = 30

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Are you looking for more daily math challenges and puzzles to share with your kids?

My best-selling workbook 101 Math Challenges for Engaging Your Students is now available as a PDF download. You can get yours today by clicking here.

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4.) Which One Doesn't Belong? 

Remember that WODB? activities are meant to spark mathematical thinking and discussion and do not have a single correct answer.

Want to learn more about how to use WOBD? math activities with your kids? click here

Tip: Have your kids justify their thinking in writing!

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Are you looking for more daily WODB? math graphics?

You can now share 101 daily WODB warm-up activities for grades 1-9 with your kids with our PDF workbook!

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5.) Math Writing Prompt

Writing about math encourages creativity, exploration, and communicating one's thoughts and feelings, which leads to deep and meaningful understanding of difficult math concepts.

And Think/Notice/Wonder (TNW) writing activities are a great way to get your kids engaged in math writing every day.

Want to learn more about how to use TNW math activities with your kids? click here

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How will you use these math puzzles with your kids? Share your thoughts and suggestions in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

Translating Words into Algebraic Expressions: Free Guide

Translating Words into Algebraic Expressions

Welcome to this complete guide to translating words into algebraic expressions (also known as algebraic translation), where you will learn how to identify and apply key information, in the form of words and phrases, to accurately translate a given set of words into an algebraic expression involving both numbers and variables.

Why is learning how to translate words into algebraic expressions a crucial skill that every math student must learn? Because it is often the case that math problems are expressed completely in words without any explicit use of numbers, expressions, or equations. In order to solve these types of math word problems, students have to be able to translate words into expressions or equations so they may model and solve such scenarios.

Are you ready to learn everything there is to know about algebraic translation?

The following free Translating Words into Algebraic Expressions lesson guide is a step-by-step tutorial that will teach you how to easily and accurately translate any given word phrase into a mat equation.

How can you translate written expressions into numerical form?

The key skill associated with algebraic translation is being able to rewrite mathematical situations expressed in words as a mathematical expression involving numbers, operations, and variables.

Before we get to actually translating words into algebraic expressions, let's lay some important groundwork!

Tip #1: Expressing Variables

For example, what if we wanted to translate the phrase the sum of seven and five into an expression. It would be pretty easy to translate this phrase into 7 + 5 and your job would be done.

But what if we changed the phrase to the sum of a number and five? How would our numerical expression change? Since a number could represent any value, we have to use a variable (since a variable can represent any value).

In this case, you could translate the sum of a number and five into x + 5 where x represents a number.

When using letters as variables in a math expression or equation, x is the most commonly chosen letter, but you can actually choose any letter to represent an unknown value.

Example A: Translate the phrase ten plus a number into an algebraic expression.

To complete this translation, we can break the given phrase down into three parts:

I: ten ➔ 10

II: plus ➔ +

III: a number ➔ x

Now, you can translate ten into 10, plus into an addition sign, and a number into a variable leaving you with:

ten plus a number ➔ 10 + x

Tip #2: More Than/Less Than

Now, let’s slightly change the words given in Example A as follows:

Example B: Translate the phrase ten more than a number into an algebraic expression.

You probably already know that more than is associated with addition so the sign is not going to change. But what about the order of the terms?

Think about it this way: we have a number (some unknown value) and this phrase represents ten more than whatever that value is. So, in this case, you will start with the variable first and then add ten to it as follows:

ten more than a number ➔ x+ 10

You would be correct to wonder whether or not the order of the terms matters in this example. Technically, it does not because addition is commutative. But what about subtraction, which is not commutative?

See Also: The Commutative Property: Everything You Need to Know

Example C: Translate the phrase six less than a number into an algebraic expression.

Notice again that we are seeing the word than.

You probably already know that less than is associated with subtraction so you already know what sign you will be using.

This phrase represents a value that is six units smaller than whatever our unknown value is. So, to find that number, we would have to take our variable and subtract six from it as follows:

six less than a number ➔ n-6

In cases like Example B and Example C, the second term comes first and the first term comes second (you have to switch the order).

So, we can conclude that than is a switch word, which means that the operator in the middle stays the same, but the first term and the last term are switched. Look out for this relationship when you see the phrase more than or less than in words.

Tip #3: Groupings and Parenthesis

Let’s move onto another example…

Example D: Translate the phrase the difference of three and a number into an algebraic expression.

Translating this phrase into an expression should be pretty straightforward.

Since difference means subtraction, we can easily perform the following algebraic translation:

the difference of three and a number ➔ 3 - p

Now, what if we changed this expression to the difference of three and twice a number plus one

Example D: Translate the phrase the difference of three and twice a number plus one into an algebraic expression.

So, now instead of 3 - p, we have to write the expression as 3 - the entire expression twice a number plus one, which we can call 2p + 1.

Note that you will have to use parenthesis to enclose the entire expression twice a number plus one as follows:

the difference of three and twice a number plus one ➔ 3 - (2p+1)

So, whenever you are performing algebraic translations, you can use parenthesis to separate independent groupings.

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Translate Algebraic Expressions Practice

Now that you understand some key elements of translating words into algebraic expressions, you are ready to practice on your own. Go ahead and translate the following words into algebraic expressions on your own and then check the answer key at the end of this post to see how you did!

Practice Problems: Translate each phrase into an algebraic expression.

1.) nine times a number

2.) the sum of a number and twelve

3.) twice a number decreased by eleven

4.) twenty less than a number

5.) half a number plus two

6.) the quotient of five and a number

7.) five times the difference of a number and one

8.) the sum of sixteen and three times a number minus four

Wait! Don’t scroll further until you’re ready to see the answer key.

Answer Key:

1.) nine times a number ➔ 9x

2.) the sum of a number and twelve ➔ n + 12

3.) twice a number decreased by eleven ➔ 2y - 11

4.) twenty less than a number ➔ m - 20

5.) half a number plus two ➔ (x/2) + 2

6.) the quotient of five and a number ➔ 5 ÷ p

7.) five times the difference of a number and one ➔ 5(x-1)

8.) the sum of sixteen and three times a number minus four ➔ 16 + (3y - 4)

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How to Translate Algebraic Expressions Video

Are you looking for more help with translating algebraic expressions? Check out our free step-by-step video lesson below:

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Associative Property of Multiplication Explained in 3 Easy Steps

Associative Property of Multiplication Definition

In math, the associative property of multiplication is a rule which states that the groupings of values or variables being multiplied together does not affect the product or outcome.

The associative property of multiplication can help you to model and solve simple and complex multiplication problems. This rule is a fundamental law in mathematics and applies to any multiplication problem.

The following guide to understanding and applying the associative property of multiplication will share a step-by-step tutorial as well as a free associative property of multiplication worksheet.

Let’s start off by looking at a few examples…

Associative Property of Multiplication Example

Take a look at the equation above:

(a x b) x c = a (b x c)

Notice that the terms (a, b, and c) are in the same order, but grouped differently. On the left side of the equals sign, a and b are in parenthesis. On the right side of the equal side, b and c are in parenthesis. And, according to the order of operations, you must perform operations inside of parenthesis first.

So, according to the associative property of multiplication, the left side of the equal sign and the right side of the equal sign will always equal the same value, no matter what values a, b, and c represent.

Now, let’s go ahead and explore why the associative property proves this equation to be true by substituting numerical values in for a, b, and c:

a=8, b=4, c=2

Step One: Follow the order of operations by performing multiplication inside of the parenthesis first.

In this example, perform (8 x 4) on the left side of the equation and (4 x 2) on the right side of the equation as follows:

(8 x 4 ) x 2 = 8 x (4 x 2)

32 x 2 = 8 x 8

Step Two: After working out the products inside of the parenthesis, the next step is to multiply the next line of the equation. In this case, 32 x 2 on the left side, and 8 x 8 on the right side.

32 x 2 = 8 x 8

64 = 64

Step Three: Verify your answer.

Remember that, according to the associative property of multiplication definition, the groupings of values or variables being multiplied together does not affect the product or outcome. Therefore, the left side of the equation and the right side of the equation should equal the same value.

In this example, the associative property holds true since both sides of the equation are equal to 64.

See Also: Check Out This Awesome Mean, Median, and Mode Activity

Associative Property of Multiplication Example Recap:

(8 x 4 ) x 2 = 8 x (4 x 2)

32 x 2 = 8 x 8

64 = 64 ✓

What About Division?

Now that you understand the associative property of multiplication, let’s see if the inverse of multiplication—division—is also associative.

What if we reused the associative property of multiplication example from before, but changed the multiplication signs to division signs?

Just like the last example, a=8, b=4, and c=2, the order of the terms is the same on both sides of the equal sign, but the terms are grouped differently. And also notice that the operation is no longer multiplication, but division.

Step One: Follow the order of operations by performing division inside of the parenthesis first.

In this example, perform (8 ÷ 4) on the left side of the equation and (4 ÷ 2) on the right side of the equation as follows:

(8 ÷ 4 ) ÷ 2 = 8 ÷ (4 ÷ 2)

2 ÷ 2 = 8 ÷ 2

Step Two: After working out the quotients inside of the parenthesis, the next step is to divide the next line of the equation. In this case, 2 ÷ 2 on the left side, and 8 ÷ 8 on the right side.

2 ÷ 2 = 8 ÷ 2

1 ≠ 4

Step Three: Verify your answer.

Remember that, the associative property states that different groupings of the terms in an equation should not change the result. In the first example, we proved that the associative property works for multiplication since both sides of the equation equaled the same number (64=64).

However, in the division example, we see that the left side of the equation and the right side of the equation result in different values. In this case, 1 and 4, which are obviously nit equal.

Therefore, in this example, the associative property does not hold true for division since both sides of the equation are not equal.

Associative Property of Division Example Recap:

(8 ÷ 4 ) ÷ 2 = 8 ÷ (4 ÷ 2)

2 ÷ 2 = 8 ÷ 2

1 ≠ 4 ✕

Conclusion: Associative Property Math Facts

The previous example has shown us that the associative property works for multiplication, but it does not work for division.

Therefore, as long as all of the terms are being multiplied (not divided), the groupings of values or variables being multiplied together does not affect the product or outcome.

So, (a x b) x c = a x (b x c) for any real number values represented by a, b, and c.

Key idea: The associative property of multiplication can be applied when the terms are in the SAME ORDER, but GROUPED DIFFERENTLY.

The Associative Property of Multiplication Video

Are you looking for a more in-depth and visual explanation of the associative property of multiplication? Check out our free YouTube video using the link below:

Tags: associative property of multiplication, associative property example, associative property of multiplication example, associative property of multiplication definition, associative property in math, associative law of multiplication, the associative property of multiplication

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Have thoughts? Share your thoughts in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

More Free Math Resources You Will Love:

Number Bonds Explained: Free Worksheets Included

What is a Number Bond?

Number Bond Definition

What is a number bond? A number bond is a simple visual math aid that is used to show a given number can be represented as the sum of two numbers.

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Number Bond Example: 5

Let’s take a closer look at the number 5. You know that the number 5 can be thought of as the sum of 4 and 1, the sum of 3 and 2, or the sum of 5 and 0. In terms of number bonds, these different ways of expressing the number 5 as the composite sum of two numbers can be visually represented using number bonds as follows:

And, since addition is commutative, meaning that the order of the terms does not matter (e.g. 2+3=5 and 3+2=5), you can also express the above number bonds in reverse order as follows:

Looking to learn more about the commutative math property? Click here to access our free step-by-step guide

Now that you understand what number bonds are and what they represent, it’s time to explore why they are such a useful tool for helping your students to develop strong number sense and fluency with performing operations on numbers.

For starters, the visual nature of number bonds is an excellent way to help students to conceptualize numbers and how they can be expressed as a composite sum of two numbers. By understanding this composite nature of numbers, students are better equipped to perform mental math quickly and accurately and perform advanced operations.

 For example, imagine a student becoming familiar with the following number bonds for 10:

With this understanding, a student could easily and accurately solve an expanded addition problem by combining terms that equal 10 as follows:

Number Bond Example: Number Bonds to 10

Now that you understand the value of having your students practice and understand number bonds, you can start by focusing on number bonds to 10. The diagram below shows the number bonds to 10.

Free Number Bonds Worksheet

 Are you looking for free printable number bonds worksheets (with answer keys included) that will give your students plenty of practice with completing number bonds to 10? If so, use the links below to download your free pdf number bonds worksheet.

➔ Click here to download your free Number Bonds worksheet

Subtraction Number Bonds

Everything related to number bonds that we have covered so far have related to the fact that number bonds represent how a number can be expressed as the sum of two other numbers. But what about subtraction? We know that addition and subtraction share an inverse relationship. This inverse relationship can be explored via number bonds (note that this is an advanced step that should not be explored until your students have completely mastered the number bonds to 10 and possibly beyond.

Number Bond Example 03: Subtraction

For example, how could a student use her understanding of number bonds to solve the problem 10 - ___ = 7?

In this example, the student knows that one of the number bonds for 10 includes the number 7 and that the other number is 3 (because 7+3=10).

With this understanding in mind, it is a logical conclusion that 10 – 3 = 7 meaning that the missing number is 3.

This answer may seem extremely simple to find and you may even think that the use of a number bond is not even necessary. However, if we rewrite this problem as:

10 – X = 7 where x=3

We can see how understanding number bonds can apply to more advanced problems including high school level algebra.

Observe the diagram below that represents this application of subtraction number bonds:

Conclusion

Number bonds are simple visual tools that are used to show how a number can be represented as a composite sum of two other numbers. A number bond includes a whole number with two branches stemming from the number and leading to the two other numbers whose sum is equal to the original whole number. Number bonds are a valuable visual tool for helping students to practice and develop number sense, which is a critical foundational math skill that students will need to be successful at higher level of mathematics.

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Tags:  number bond, number bonds to 10, number bond example, number bonds worksheet, number bonds to 10 worksheet, number bonds to 5, number bonds kindergarten, subtraction number bonds, complete the number bond

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Share your thoughts in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

More Free Math Resources You Will Love: