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April Padilla
April Padilla

A Complete Guide to Percent Increase and Decrease for Algebra 1 Common Core Students



Percent Increase and Decrease Common Core Algebra 1 Homework Answers




If you are looking for some help with your algebra homework on percent increase and decrease, you have come to the right place. In this article, we will explain what percent increase and decrease are, how to calculate them, how to use them in real-world problems, and how to check your answers. We will also provide some tips and tricks for solving percent increase and decrease problems, as well as some resources for more practice and homework help.




Percent Increase And Decrease Common Core Algebra 1 Homework Answers


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What are percent increase and decrease?




Percent increase and decrease are ways of expressing how much a quantity changes in relation to its original value. They are often used to compare changes in prices, populations, sales, grades, etc.


Percent increase means that the new value is greater than the original value, so the quantity has increased or grown. For example, if a shirt costs $20 and then goes on sale for $25, the price has increased by 25%.


Percent decrease means that the new value is less than the original value, so the quantity has decreased or shrunk. For example, if a town has 1000 people and then loses 200 people, the population has decreased by 20%.


How to calculate percent increase and decrease?




To calculate percent increase and decrease, we need to know two values: the original value and the new value. The original value is usually denoted by O and the new value by N. Then we can use the following formulas:


Percent increase = (N - O) / O * 100%


Percent decrease = (O - N) / O * 100%


The formulas are similar, except that we subtract N from O for percent decrease and O from N for percent increase. This is because we want to find the difference between the two values and divide it by the original value. Then we multiply by 100% to convert the decimal into a percentage.


Let's see some examples of how to use these formulas.


Example 1: Finding the percent increase of a price




Suppose a pair of jeans costs $40 and then goes on sale for $50. What is the percent increase of the price?


To find the percent increase, we need to plug in the values into the formula:


Percent increase = (N - O) / O * 100%


O = 40 (original price)


N = 50 (new price)


Percent increase = (50 - 40) / 40 * 100%


Percent increase = 10 / 40 * 100%


Percent increase = 0.25 * 100%


Percent increase = 25%


The answer is 25%. This means that the price of the jeans has increased by 25% from its original value.


Example 2: Finding the percent decrease of a population




Suppose a city has a population of 5000 people and then loses 1000 people due to migration. What is the percent decrease of the population?


To find the percent decrease, we need to plug in the values into the formula:


Percent decrease = (O - N) / O * 100%


O = 5000 (original population)


N = 4000 (new population)


Percent decrease = (5000 - 4000) / 5000 * 100%


Percent decrease = 1000 / 5000 * 100%


Percent decrease = 0.2 * 100%


Percent decrease = 20%


The answer is 20%. This means that the population of the city has decreased by 20% from its original value.


How to use percent increase and decrease in real-world problems?




Sometimes we are given a percent increase or decrease and we need to find either the original value or the new value. For example, we may want to know how much something costs after a discount or how much something was worth before an appreciation.


To solve these problems, we can use another formula that relates the original value, the new value, and the percent change:


N = O * (1 + P/100)


This formula works for both percent increase and decrease. The only difference is that P is positive for percent increase and negative for percent decrease. The formula means that we multiply the original value by a factor that represents the percent change. For example, if P is 25%, then (1 + P/100) is equal to (1 + 0.25), which is equal to 1.25. This means that we multiply the original value by 1.25 to get the new value.


We can use this formula to find either N or O if we know one of them and P. Let's see some examples of how to use this formula.


Example 3: Finding the final amount after a percent increase




Suppose you invest $1000 in a bank account that pays an annual interest rate of 5%. How much money will you have after one year?


To find the final amount, we need to plug in the values into the formula:


N = O * (1 + P/100)


O = $1000 (original amount)


P = +5% (percent increase)


N = ? (final amount)


N = $1000 * (1 + (+5)/100)


N = $1000 * (1 + 0.05)


N = $1000 * (1.05)


N = $1050


The answer is $1050. This means that you will have $1050 after one year of investing $1000 at an interest rate of 5%. Continuing the article. Example 4: Finding the original amount before a percent decrease




Suppose a car loses 15% of its value every year due to depreciation. If the car is worth $8500 after one year, what was its original value?


To find the original amount, we need to plug in the values into the formula:


N = O * (1 + P/100)


N = $8500 (new amount)


P = -15% (percent decrease)


O = ? (original amount)


We can rearrange the formula to solve for O by dividing both sides by (1 + P/100):


O = N / (1 + P/100)


O = $8500 / (1 + (-15)/100)


O = $8500 / (1 - 0.15)


O = $8500 / 0.85


O = $10000


The answer is $10000. This means that the car was worth $10000 before it lost 15% of its value.


How to check your answers using inverse operations?




One way to check your answers for percent increase and decrease problems is to use inverse operations. This means that you do the opposite of what you did to find the answer and see if you get back to the original values.


For example, if you multiplied by a factor to find the new amount, you can divide by the same factor to find the original amount. If you divided by a factor to find the original amount, you can multiply by the same factor to find the new amount.


Let's see some examples of how to use inverse operations to check your answers.


Example 5: Checking the answer for example 3




In example 3, we found that the final amount after investing $1000 at an interest rate of 5% for one year was $1050. To check this answer, we can use inverse operations:


We multiplied the original amount ($1000) by a factor of 1.05 to get the final amount ($1050).


To check this, we can divide the final amount ($1050) by the same factor of 1.05 and see if we get back to the original amount ($1000).


$1050 / 1.05 = $1000


This is correct, so we can be confident that our answer is correct.


Example 6: Checking the answer for example 4




In example 4, we found that the original value of a car that was worth $8500 after losing 15% of its value was $10000. To check this answer, we can use inverse operations:


We divided the new amount ($8500) by a factor of 0.85 to get the original amount ($10000).


To check this, we can multiply the original amount ($10000) by the same factor of 0.85 and see if we get back to the new amount ($8500).


$10000 * 0.85 = $8500


This is correct, so we can be confident that our answer is correct. Continuing the article. How to practice percent increase and decrease problems?




Now that you have learned how to calculate and use percent increase and decrease, you may want to practice some more problems to master this skill. Here are some tips and tricks for solving percent increase and decrease problems, as well as some resources for more practice and homework help.


Tips and tricks for solving percent increase and decrease problems





  • Remember the formulas for percent increase and decrease: Percent increase = (N - O) / O * 100% and Percent decrease = (O - N) / O * 100%, where O is the original value and N is the new value.



  • Remember the formula for finding the original value or the new value given the percent change: N = O * (1 + P/100), where O is the original value, N is the new value, and P is the percent change (positive for increase and negative for decrease).



  • Use a calculator to do the calculations, but make sure you enter them correctly. For example, to enter 1 + P/100, you need to use parentheses: 1 + (P/100).



  • Convert percentages to decimals by dividing by 100 before multiplying or dividing by them. For example, to multiply by 25%, divide 25 by 100 and get 0.25, then multiply by 0.25.



  • Check your answers using inverse operations. For example, if you multiplied by a factor to find the new value, divide by the same factor to find the original value. If you divided by a factor to find the original value, multiply by the same factor to find the new value.



  • Use tape diagrams or tables to visualize the problem and organize the information. For example, you can use a tape diagram to show how a quantity changes from its original value to its new value after a percent increase or decrease.



Resources for more practice and homework help




If you need more practice or homework help with percent increase and decrease problems, you can use some of these online resources:



  • Math is Fun Percentage Calculator: This calculator can help you find the percent of a number, the percentage change between two numbers, or any other percentage problem.



  • Khan Academy Percent Word Problems: This website has videos and exercises on how to solve different types of percent word problems, including percent increase and decrease.



  • Math Worksheets 4 Kids Percent Increase and Decrease Worksheets: This website has printable worksheets on percent increase and decrease problems with different levels of difficulty.



  • Quizlet Algebra 1 Common Core Solutions: This website has step-by-step solutions and answers to algebra 1 common core textbook problems, including percent increase and decrease problems.



We hope this article has helped you understand how to solve percent increase and decrease problems. Remember to practice often and use the tips and tricks we shared. Good luck with your algebra homework!


Conclusion




In this article, we have learned how to:



  • Calculate percent increase and decrease using formulas.



  • Use percent increase and decrease in real-world problems.



  • Check our answers using inverse operations.



  • Practice percent increase and decrease problems using tips and tricks.



  • Find more resources for homework help.



Percent increase and decrease are important concepts in algebra that can help us compare changes in quantities over time. By mastering these skills, we can solve many types of problems involving percentages.


Frequently Asked Questions





  • What is the difference between percent increase and percent decrease?



Percent increase means that the new value is greater than the original value, so the quantity has increased or grown. Percent decrease means that the new value is less than the original value, so the quantity has decreased or shrunk.


  • What are the formulas for percent increase and decrease?



The formulas for percent increase and decrease are: Percent increase = (N - O) / O * 100% and Percent decrease = (O - N) / O * 100%, where O is the original value and N is the new value.


  • How do I find the original value or the new value given the percent change?



You can use this formula: N = O * (1 + P/100), where O is the original value, N is the new value, and P is the percent change (positive for increase and negative for decrease).


  • How do I check my answers for percent increase and decrease problems?



You can check your answers using inverse operations. For example, if you multiplied by a factor to find the new value, divide by the same factor to find the original value. If you divided by a factor to find the original value, multiply by the same factor to find the new value.


  • Where can I find more practice and homework help for percent increase and decrease problems?



You can use some of these online resources: Math is Fun Percentage Calculator, Khan Academy Percent Word Problems, Math Worksheets 4 Kids Percent Increase and Decrease Worksheets, Quizlet Algebra 1 Common Core Solutions.



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