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Home / 7th Grade / 7th Grade Math (Pre-Algebra) / Percentages and Proportional Relationships / Practice Questions
🎓 7th Grade 📚 7th Grade Math (Pre-Algebra)

💡 7th Grade Math (Pre-Algebra): Percentages and Proportional Relationships Practice Questions

1
Solved Example
Easy Level
💡 Understanding Percentages: What is 35% of 120?
This is a foundational skill for working with percentages.
Solution & Explanation
  • 👉 Step 1: Convert the percentage to a decimal.
    To convert a percentage to a decimal, divide it by 100.
    \[ 35% = \frac{35}{100} = 0.35 \]
  • 👉 Step 2: Multiply the decimal by the given number.
    Now, multiply 0.35 by 120.
    \[ 0.35 \times 120 = 42 \]
  • ✅ Answer: 35% of 120 is 42.
2
Solved Example
Medium Level
📌 Finding the Whole: If 18 is 40% of a number, what is the number?
This question requires you to find the original amount when a part and its percentage are known.
Solution & Explanation
  • 👉 Step 1: Set up a proportion.
    We know that "part is to whole as percent is to 100". Let the unknown number be \(x\).
    \[ \frac{18}{x} = \frac{40}{100} \]
  • 👉 Step 2: Cross-multiply.
    Multiply the numerator of the first fraction by the denominator of the second, and vice versa.
    \[ 18 \times 100 = 40 \times x \] \[ 1800 = 40x \]
  • 👉 Step 3: Solve for \(x\).
    Divide both sides by 40.
    \[ x = \frac{1800}{40} \] \[ x = 45 \]
  • ✅ Answer: The number is 45.
3
Solved Example
Medium Level
📊 Calculating Percentage: What percentage of 75 is 15?
This helps you determine what portion of a whole a given number represents.
Solution & Explanation
  • 👉 Step 1: Set up a proportion.
    Let the unknown percentage be \(P\). We want to find what percent 15 is of 75.
    \[ \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \] \[ \frac{15}{75} = \frac{P}{100} \]
  • 👉 Step 2: Cross-multiply.
    \[ 15 \times 100 = 75 \times P \] \[ 1500 = 75P \]
  • 👉 Step 3: Solve for \(P\).
    Divide both sides by 75.
    \[ P = \frac{1500}{75} \] \[ P = 20 \]
  • ✅ Answer: 15 is 20% of 75.
4
Solved Example
Real World Example
🛒 Shopping Discounts: A jacket originally costs 80. It is on sale for 25% off. What is the sale price of the jacket?
Understanding discounts is a practical life skill!
Solution & Explanation
  • 👉 Step 1: Calculate the discount amount.
    Find 25% of the original price, 80.
    \[ \text{Discount} = 25% \times \80 \] \[ \text{Discount} = 0.25 \times \80 = \20 \]
  • 👉 Step 2: Subtract the discount from the original price.
    Original price - Discount = Sale price
    \[ \80 - \20 = \60 \]
  • ✅ Answer: The sale price of the jacket is 60.
5
Solved Example
Real World Example
💰 Simple Interest: Sarah deposited 600 into a savings account that earns 3% simple interest per year. How much interest will she earn in one year?
This shows how percentages are used in personal finance.
Solution & Explanation
  • 👉 Step 1: Identify the principal, rate, and time.
    Principal (P) = 600
    Rate (R) = 3% = 0.03
    Time (T) = 1 year
  • 👉 Step 2: Use the simple interest formula.
    The formula for simple interest is \(I = P \times R \times T\).
    \[ I = \600 \times 0.03 \times 1 \] \[ I = \18 \]
  • ✅ Answer: Sarah will earn 18 in interest in one year.
6
Solved Example
Medium Level
📈 Percentage Change: A toy's price increased by 10% last month. If its original price was 20, and then it decreased by 10% this month, what is its current price?
Be careful! A 10% increase followed by a 10% decrease does not always result in the original price.
Solution & Explanation
  • 👉 Step 1: Calculate the price after the 10% increase.
    Increase amount = 10% of 20 = \(0.10 \times \20 = \2\)
    Price after increase = Original price + Increase amount = \(\20 + \2 = \22\)
  • 👉 Step 2: Calculate the price after the 10% decrease.
    The decrease is 10% of the new price (22), not the original price.
    Decrease amount = 10% of 22 = \(0.10 \times \22 = \2.20\)
    Current price = Price after increase - Decrease amount = \(\22 - \2.20 = \19.80\)
  • ✅ Answer: The current price of the toy is 19.80.
7
Solved Example
Medium Level
🍎 Proportional Reasoning with Survey Data: In a survey of 200 students, 45% said their favorite fruit was apples. How many students chose apples? If 30 students chose bananas, what percentage of students chose bananas?
This combines finding a part from a percentage and finding a percentage from a part.
Solution & Explanation
  • 👉 Part 1: How many students chose apples?
    • Step 1a: Convert the percentage to a decimal.
      \[ 45% = 0.45 \]
    • Step 1b: Multiply the decimal by the total number of students.
      \[ 0.45 \times 200 = 90 \]
    • So, 90 students chose apples.
  • 👉 Part 2: What percentage of students chose bananas?
    • Step 2a: Set up a proportion.
      Let \(P\) be the percentage of students who chose bananas.
      \[ \frac{\text{number of students for bananas}}{\text{total number of students}} = \frac{P}{100} \] \[ \frac{30}{200} = \frac{P}{100} \]
    • Step 2b: Cross-multiply and solve for \(P\).
      \[ 30 \times 100 = 200 \times P \] \[ 3000 = 200P \] \[ P = \frac{3000}{200} \] \[ P = 15 \]
    • So, 15% of students chose bananas.
  • ✅ Answer: 90 students chose apples, and 15% of students chose bananas.
8
Solved Example
Real World Example
🍽️ Restaurant Bill with Tip: Emily's family had dinner at a restaurant, and the bill came to 50. They want to leave a 15% tip. What is the total cost of the dinner, including the tip?
Calculating tips is a common real-world application of percentages.
Solution & Explanation
  • 👉 Step 1: Calculate the tip amount.
    Find 15% of the bill amount, 50.
    \[ \text{Tip} = 15% \times \50 \] \[ \text{Tip} = 0.15 \times \50 = \7.50 \]
  • 👉 Step 2: Add the tip to the original bill.
    Total cost = Bill + Tip
    \[ \50 + \7.50 = \57.50 \]
  • ✅ Answer: The total cost of the dinner, including the tip, is 57.50.

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