Percent of Change | Percent Increase and Decrease | Math with Mr. J

Summary

In this educational video, Mr. J teaches the concept of percent of change using two examples. The formula involves subtracting the old number from the new, dividing by the old number, and multiplying by 100 to get the percentage change. The video demonstrates a decrease from 50 to 34, resulting in a -32% change, and an increase from 10 to 22, yielding a 120% increase. The lesson emphasizes the importance of using the original number as the base for calculating the percentage change and interpreting the results as either an increase or decrease based on the sign of the result.

Takeaways

• 🔢 Calculate percent of change by taking the difference between the new and old numbers.
• 📉 For a decrease, subtract the old number from the new number to find the change, then divide by the old number and multiply by 100.
• 📈 For an increase, follow the same process but the result will be a positive percentage.
• ⚠️ Always divide by the original number to find the percentage change relative to the starting point.
• 👉 A negative result indicates a decrease, while a positive result indicates an increase.
• 📌 Moving the decimal point two places to the right converts the decimal to a percentage.
• 📋 The script provides two examples: one with a decrease from 50 to 34 and one with an increase from 10 to 22.
• 📐 The first example results in a -32% change, indicating a decrease.
• 📈 The second example results in a 120% change, indicating an increase.
• ✅ The script emphasizes checking the sign of the result to determine if there was an increase or decrease.

Q & A

What is the formula for calculating the percent of change?

The percent of change is calculated by taking the amount of change (new number minus old number), dividing by the old number, and multiplying by 100 to convert it to a percent.

How do you interpret a negative percent of change?

A negative percent of change indicates a decrease in value. It shows that the new number is lower than the old number.

In the first example, why is the result negative 32 percent?

The result is negative 32 percent because the value decreased from 50 to 34, and the negative sign shows the direction of change as a decrease.

What are two ways to express a percent of change that is a decrease?

You can express a decrease as either a negative percent (e.g., -32%) or as a positive percent followed by the word 'decrease' (e.g., 32% decrease).

What does it mean when the percent of change is positive?

A positive percent of change indicates an increase in value. It shows that the new number is higher than the old number.

In the second example, how is the percent increase calculated?

The percent increase is calculated by taking the new number (22) minus the old number (10), which gives 12. Then, 12 is divided by the old number (10) to get 1.2, which is multiplied by 100 to get a 120 percent increase.

How do you know if a percent of change represents an increase or a decrease?

A positive percent represents an increase, and a negative percent represents a decrease. You can also confirm by comparing the old and new numbers.

Why is it important to divide by the old or original number when calculating percent of change?

Dividing by the old or original number is important because it gives the percentage change relative to the starting point, showing how much the original value has changed.

What is the percent of change from 10 to 22 in the second example?

The percent of change from 10 to 22 is 120 percent, indicating an increase.

What does it mean if the result of the percent of change calculation is zero?

If the result is zero, it means there has been no change in value between the old and new numbers.

Outlines

00:00

📚 Calculating Percent of Change

This video segment introduces the concept of calculating the percent of change in mathematics. The presenter, Mr. J, explains that to find the percent of change, one must first determine the amount of change by subtracting the old number from the new number. This difference is then divided by the old number and multiplied by 100 to convert it into a percentage. The segment uses two examples to illustrate the process: a decrease from 50 to 34, which results in a -32% change, and an increase from 10 to 22, leading to a 120% increase. The presenter emphasizes the importance of using the old number as the reference for the percentage change and notes that a negative result indicates a decrease, while a positive result indicates an increase.

Keywords

💡Percent of Change

Percent of change is a mathematical concept used to express the difference between two values as a percentage. It is calculated by taking the difference between the new and old values, dividing by the old value, and then multiplying by 100. In the video, this concept is central to understanding how to quantify changes in values, whether they are increases or decreases. For instance, when the value decreases from 50 to 34, the percent of change is calculated as (34-50)/50 * 100, resulting in a negative 32 percent, indicating a decrease.

💡Amount of Change

The amount of change refers to the difference between the new and old values. It is the first step in calculating the percent of change and is obtained by subtracting the old number from the new number. In the script, the amount of change is highlighted when transitioning from a value of 50 to 34, resulting in a decrease of 16, which is then used to find the percent of change.

💡Decrease

A decrease indicates a reduction in value. In the context of the video, a decrease is shown when the new value is lower than the old value. The term is used to describe the situation where the value goes from 50 to 34, resulting in a negative percent of change, which signifies a reduction.

💡Increase

An increase implies a rise in value. The video explains how to identify an increase by looking at the sign of the percent of change. When the new value is higher than the old value, such as moving from 10 to 22, the percent of change is positive, indicating an increase.

💡Old Number

The old number, also known as the original or starting value, is the initial value from which changes are measured. The video emphasizes the importance of dividing by the old number when calculating percent of change to determine how much the value has changed relative to the starting point.

💡New Number

The new number is the value after a change has occurred. It is used in the calculation of the amount of change by being subtracted from the old number. In the video, the new number is crucial for determining whether there has been an increase or decrease from the old number.

💡Division

Division is a mathematical operation used in the calculation of percent of change to find out how many percent units the change represents of the old number. The video demonstrates division by showing how to divide the amount of change by the old number to get the decimal form of the percent change.

💡Multiplication

Multiplication is used in the video to convert the decimal form of the percent change into a percentage. By multiplying the result of the division by 100, the change is expressed as a percentage, making it easier to understand and compare.

💡Negative

A negative value in the context of percent of change indicates a decrease from the original value. The video uses the term 'negative' to describe the result of the calculation when the new value is less than the old value, as seen when the value decreases from 50 to 34.

💡Positive

A positive value signifies an increase in the context of percent of change. The video explains that a positive percent of change, such as the one calculated when the value increases from 10 to 22, indicates that the new value is greater than the old value.

💡Decimal

Decimals are used in the video to represent the intermediate step in converting the division result into a percentage. After dividing the amount of change by the old number, the result is multiplied by 100 to shift the decimal point two places to the right, resulting in a percentage.

Highlights

Introduction to calculating percent of change.

Formula for percent change: (New number - Old number) / Old number * 100.

Example 1: Calculating percent decrease from 50 to 34.

The importance of using the old number as the divisor.

Result of example 1: A 32% decrease.

Expressing percent change as both positive and negative.

Example 2: Calculating percent increase from 10 to 22.

Method to convert decimal to percentage by moving the decimal point.

Result of example 2: A 120% increase.

Understanding the difference between positive and negative percent changes.

Double-checking the direction of change with the problem context.

The significance of the negative sign indicating a decrease.

The significance of the positive sign indicating an increase.

Summary of percent change calculations for both examples.

Closing remarks and thanks for watching.

Transcripts

[Music]

welcome to math with mr j

[Music]

in this video i'm going to cover percent

of change

and we have two examples that we're

going to go through together

in order to get this down now when we

calculate percent of change

we take the amount of change so the new

number

minus the old number and divide by the

old number

we then multiply that by 100 to convert

that

to a percent so let's jump into number

one

where we have 50 to 34 so we start with

a 50

and now we have a 34. so we had a

decrease there so keep that in mind

as we go through our problem so the

first thing we need to do

is calculate the amount of change so the

new number

minus the old number will give us that

so the new number

is 34 minus the old number of 50.

so 34 minus 50 gives us

a negative 16. now that negative

is important because it shows us that we

have a decrease

divide that by the old or original

number of 50

and then multiply by 100 to convert that

to a percent it's very important to

always

divide by the old or original number

because that's the number that

changed so we want the percentage change

relative to the number we started with

we're looking at the percent

that that number changed all right so

negative 16

divided by 50 is going to give us a

negative 32 hundredths

and then multiply that by 100 again to

convert that decimal

to a percent so we can multiply that

decimal by 100

by moving the decimal twice to the right

so

1 2 and we end up with a

negative 32 percent

so we can express that answer in two

ways

just like what we wrote negative 32

percent

and that negative shows us that we had a

decrease so this would be one way

or we can write 32 percent

and then the word decrease

to show that we had a decrease so 32

percent decrease

or negative 32 now both of those

represent that percent of

change between the 50 and 34. they

represent that decrease

now remember whenever you see a negative

that represents

a decrease let's move on to number two

where we have 10 to 22

so we can see that we have an increase

there we started with a 10

and now we have a 22. so let's plug our

numbers in

and see exactly what the percent of

change is so the new number

is 22 subtract the old to get the amount

of change

so we're going to get 22 minus 10 is 12.

divide by the old or original number of

10

and then multiply by 100 to convert that

to a percent

12 divided by 10 is going to give us one

and two-tenths and then we multiply by

100

to convert it to a percent so let's move

the decimal twice to the right 1

2 and we can fill that gap with a 0

there so we end up with

120 and that

is positive so we know it's an increase

so we had a 120 percent

increase now remember we can always tell

if we have an increase or decrease

based on positive and negative a

positive

represents an increase a negative

represents a decrease and we can always

double check with the problem

so for example number one we started

with a 50

and now we have a 34. so we decreased in

value

so that's going to be a percentage

decrease

number two we started with a 10 and now

we have 22

so we increased in value and that's

going to be

a percentage increase so i hope that

helped

thanks so much for watching until next

time

peace