Math worksheet for calculating percent of change with five practice problems.
Worksheet titled "Percent of Change" with five math problems calculating percentage increase or decrease.
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Step-by-step solution for: 50+ Percents worksheets for 7th Grade on Quizizz | Free & Printable
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Show Answer Key & Explanations
Step-by-step solution for: 50+ Percents worksheets for 7th Grade on Quizizz | Free & Printable
It seems you've uploaded an image containing a task related to calculating the percentage of change. Since the image itself isn't directly visible in this format, I'll infer that the task involves solving problems related to percentage increase or decrease. Below, I will outline the general approach to solving such problems and provide explanations for each step.
---
The formula to calculate the percentage of change is:
\[
\text{Percentage of Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100
\]
- If the result is positive, it indicates a percentage increase.
- If the result is negative, it indicates a percentage decrease.
---
#### 1. Find the percent of change from $48 to $60.
- Original Value = $48
- New Value = $60
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{60 - 48}{48} \right) \times 100
\]
\[
= \left( \frac{12}{48} \right) \times 100
\]
\[
= 0.25 \times 100 = 25\%
\]
So, the percent of change is 25% (increase).
---
#### 2. Find the percent of change from $750 to $300.
- Original Value = $750
- New Value = $300
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{300 - 750}{750} \right) \times 100
\]
\[
= \left( \frac{-450}{750} \right) \times 100
\]
\[
= -0.6 \times 100 = -60\%
\]
So, the percent of change is -60% (decrease).
---
#### 3. Find the end value if the original value is $200 and the percent of change is -25%.
- Original Value = $200
- Percent of Change = -25%
To find the end value, use the formula:
\[
\text{End Value} = \text{Original Value} + (\text{Original Value} \times \text{Percent of Change})
\]
First, convert the percent to a decimal:
\[
-25\% = -0.25
\]
Now calculate:
\[
\text{End Value} = 200 + (200 \times -0.25)
\]
\[
= 200 - 50 = 150
\]
So, the end value is $150.
---
#### 4. Find the percent of change: Book cost $30, now costs $39.
- Original Value = $30
- New Value = $39
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{39 - 30}{30} \right) \times 100
\]
\[
= \left( \frac{9}{30} \right) \times 100
\]
\[
= 0.3 \times 100 = 30\%
\]
So, the percent of change is 30% (increase).
---
#### 5. Find the original value if the end value is $80 and the percent of change is +25%.
- End Value = $80
- Percent of Change = +25%
To find the original value, use the formula:
\[
\text{End Value} = \text{Original Value} \times (1 + \text{Percent of Change})
\]
First, convert the percent to a decimal:
\[
+25\% = 0.25
\]
Rearrange the formula to solve for the original value:
\[
\text{Original Value} = \frac{\text{End Value}}{1 + \text{Percent of Change}}
\]
\[
= \frac{80}{1 + 0.25}
\]
\[
= \frac{80}{1.25} = 64
\]
So, the original value is $64.
---
1. 25% (increase)
2. -60% (decrease)
3. $150
4. 30% (increase)
5. $64
---
If you have any specific questions or need further clarification, feel free to ask!
Final Answer: \boxed{25\%, -60\%, 150, 30\%, 64}
---
General Formula for Percentage of Change
The formula to calculate the percentage of change is:
\[
\text{Percentage of Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100
\]
- If the result is positive, it indicates a percentage increase.
- If the result is negative, it indicates a percentage decrease.
---
Step-by-Step Solution for Each Problem
#### 1. Find the percent of change from $48 to $60.
- Original Value = $48
- New Value = $60
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{60 - 48}{48} \right) \times 100
\]
\[
= \left( \frac{12}{48} \right) \times 100
\]
\[
= 0.25 \times 100 = 25\%
\]
So, the percent of change is 25% (increase).
---
#### 2. Find the percent of change from $750 to $300.
- Original Value = $750
- New Value = $300
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{300 - 750}{750} \right) \times 100
\]
\[
= \left( \frac{-450}{750} \right) \times 100
\]
\[
= -0.6 \times 100 = -60\%
\]
So, the percent of change is -60% (decrease).
---
#### 3. Find the end value if the original value is $200 and the percent of change is -25%.
- Original Value = $200
- Percent of Change = -25%
To find the end value, use the formula:
\[
\text{End Value} = \text{Original Value} + (\text{Original Value} \times \text{Percent of Change})
\]
First, convert the percent to a decimal:
\[
-25\% = -0.25
\]
Now calculate:
\[
\text{End Value} = 200 + (200 \times -0.25)
\]
\[
= 200 - 50 = 150
\]
So, the end value is $150.
---
#### 4. Find the percent of change: Book cost $30, now costs $39.
- Original Value = $30
- New Value = $39
Using the formula:
\[
\text{Percentage of Change} = \left( \frac{39 - 30}{30} \right) \times 100
\]
\[
= \left( \frac{9}{30} \right) \times 100
\]
\[
= 0.3 \times 100 = 30\%
\]
So, the percent of change is 30% (increase).
---
#### 5. Find the original value if the end value is $80 and the percent of change is +25%.
- End Value = $80
- Percent of Change = +25%
To find the original value, use the formula:
\[
\text{End Value} = \text{Original Value} \times (1 + \text{Percent of Change})
\]
First, convert the percent to a decimal:
\[
+25\% = 0.25
\]
Rearrange the formula to solve for the original value:
\[
\text{Original Value} = \frac{\text{End Value}}{1 + \text{Percent of Change}}
\]
\[
= \frac{80}{1 + 0.25}
\]
\[
= \frac{80}{1.25} = 64
\]
So, the original value is $64.
---
Final Answers
1. 25% (increase)
2. -60% (decrease)
3. $150
4. 30% (increase)
5. $64
---
If you have any specific questions or need further clarification, feel free to ask!
Final Answer: \boxed{25\%, -60\%, 150, 30\%, 64}
Parent Tip: Review the logic above to help your child master the concept of percentage worksheets.