📄 7th Grade Math (Pre-Algebra): Percentages and Proportional Relationships Worksheet
📌 1. True / False
1. A percentage is a ratio that compares a number to 100.
2. If two ratios are proportional, their cross products are equal.
3. A discount is an increase in the original price of an item.
4. A sales tax is an amount added to the price of an item.
5. To find 25% of a number, you can multiply the number by 0.25.
✏️ 2. Fill in the Blanks
1. A is a ratio that compares a part to a whole, where the whole is 100.
2. Two quantities are in a relationship if their ratio is constant.
3. To convert a decimal to a percentage, you multiply the decimal by .
4. The is the amount of money paid for the use of borrowed money or money earned on an investment.
5. A is a decrease in the original price of an item.
🔗 3. Matching
« A comparison of two quantities by division.
« An equation stating that two ratios are equal.
« A rate in which the second quantity in the comparison is one unit.
« The amount by which a quantity increases, expressed as a percentage of the original amount.
« Interest calculated only on the principal amount.
✍️ 4. Short Answer Questions
1. Explain how to find the percent change between an original value and a new value.
💡 Suggested Answer: To find the percent change, first calculate the difference between the new value and the original value. Then, divide this difference by the original value. Finally, multiply the result by 100 to express it as a percentage.
2. What does it mean for two quantities to be directly proportional?
💡 Suggested Answer: Two quantities are directly proportional if they increase or decrease at the same rate, meaning their ratio remains constant. If one quantity doubles, the other quantity also doubles.
🎯 5. Multiple Choice
1. What is 15% of 80?
2. A shirt originally costs 40. It is on sale for 20% off. What is the sale price?
3. If 5 apples cost 2.50, how much do 12 apples cost, assuming the price is proportional?
📝 6. Open-Ended Questions
1. A store is having a 30% off sale on all items. If a bicycle originally costs 250, what is the sale price of the bicycle?
💡 Solution Steps:
First, calculate the amount of the discount:
Discount = 30% of 250
Discount = 0.30 \times 250 = 75
The discount is 75.
Next, subtract the discount from the original price to find the sale price:
Sale Price = Original Price - Discount
Sale Price = 250 - 75 = 175
The sale price of the bicycle is 175.
2. Sarah earned 35 in simple interest after 2 years on an investment of 500. What was the annual simple interest rate?
💡 Solution Steps:
The formula for simple interest is \( I = P \cdot r \cdot t \), where \( I \) is the interest, \( P \) is the principal, \( r \) is the annual interest rate, and \( t \) is the time in years.
We are given:
\( I = 35 \) USD
\( P = 500 \) USD
\( t = 2 \) years
Substitute these values into the formula:
\( 35 = 500 \cdot r \cdot 2 \)
\( 35 = 1000 \cdot r \)
To find \( r \), divide both sides by 1000:
\( r = \frac{35}{1000} \)
\( r = 0.035 \)
To express the rate as a percentage, multiply by 100:
\( r = 0.035 \times 100 = 3.5% \)
The annual simple interest rate was 3.5%.
3. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to use 5 cups of flour, how much sugar do you need to maintain the same proportion?
💡 Solution Steps:
Let \( F \) be the amount of flour and \( S \) be the amount of sugar. The given ratio is:
\[ \frac{F}{S} = \frac{2 \text{ cups flour}}{3 \text{ cups sugar}} \]
We want to find the amount of sugar (let's call it \( x \)) needed for 5 cups of flour. Set up a proportion:
\[ \frac{2}{3} = \frac{5}{x} \]
To solve for \( x \), cross-multiply:
\( 2 \cdot x = 3 \cdot 5 \)
\( 2x = 15 \)
Divide both sides by 2:
\( x = \frac{15}{2} \)
\( x = 7.5 \)
Therefore, you need 7.5 cups of sugar.
Name Surname: .................................. Date: .... / .... / 202...
Percentages and Proportional Relationships Worksheet
SCORE
A. True (T) / False (F)
( .... )
A percentage is a ratio that compares a number to 100.
( .... )
If two ratios are proportional, their cross products are equal.
( .... )
A discount is an increase in the original price of an item.
( .... )
A sales tax is an amount added to the price of an item.
( .... )
To find 25% of a number, you can multiply the number by 0.25.
B. Fill in the Blanks
1)
A .................... is a ratio that compares a part to a whole, where the whole is 100.
2)
Two quantities are in a .................... relationship if their ratio is constant.
3)
To convert a decimal to a percentage, you multiply the decimal by .....................
4)
The .................... is the amount of money paid for the use of borrowed money or money earned on an investment.
5)
A .................... is a decrease in the original price of an item.
C. Matching Concepts
( .... )
A comparison of two quantities by division.
- Simple Interest
( .... )
An equation stating that two ratios are equal.
- Ratio
( .... )
A rate in which the second quantity in the comparison is one unit.
- Percent Increase
( .... )
The amount by which a quantity increases, expressed as a percentage of the original amount.
- Unit Rate
( .... )
Interest calculated only on the principal amount.
- Proportion
D. Short Answer Questions
1)
Explain how to find the percent change between an original value and a new value.
2)
What does it mean for two quantities to be directly proportional?
E. Multiple Choice Questions
1)
What is 15% of 80?
A) 8B) 12C) 15D) 16
2)
A shirt originally costs 40. It is on sale for 20% off. What is the sale price?
A) 8B) 20C) 32D) 48
3)
If 5 apples cost 2.50, how much do 12 apples cost, assuming the price is proportional?
A) 4.00B) 5.00C) 6.00D) 7.50
F. Open-Ended Questions
1)
A store is having a 30% off sale on all items. If a bicycle originally costs 250, what is the sale price of the bicycle?
2)
Sarah earned 35 in simple interest after 2 years on an investment of 500. What was the annual simple interest rate?
3)
A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to use 5 cups of flour, how much sugar do you need to maintain the same proportion?