Percent of Change | Percent Increase and Decrease | Math with Mr. J
Summary
TLDRIn 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
📚 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.
Mindmap
Keywords
💡Percent of Change
💡Amount of Change
💡Decrease
💡Increase
💡Old Number
💡New Number
💡Division
💡Multiplication
💡Negative
💡Positive
💡Decimal
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
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