Percent Applications

Grade 6 · ratios · 105 practice problems · read aloud

🔊 Listen to this explanation

Percent Applications with Ratios

🧠 What is it and Why is it Useful?

A percent is a ratio that compares a number to 100. The word "percent" means "per hundred." We use percentages every day to understand things like discounts, test scores, and sales tax. It helps us compare different amounts easily!

📝 Step-by-Step Guide

To solve a problem where you find the percent of a number:

  1. Identify the Parts: Find the percent and the whole amount.
  2. Convert the Percent: Change the percent to a decimal by moving the decimal point two places to the left (e.g., 25% becomes 0.25).
  3. Multiply: Multiply the decimal by the whole amount.
  4. State the Answer: Don't forget the units or what the number represents!

🔍 Visual Examples

Example 1: Finding a Tip

Your restaurant bill is $40. You want to leave a 15% tip. How much money is the tip?

  1. Percent: 15%, Whole: $40
  2. Convert 15% to a decimal: 15% → 0.15
  3. Multiply: 0.15 × $40 = $6
  4. Answer: The tip is $6.

Example 2: Calculating a Test Score

You answered 42 questions correctly out of a total of 50. What is your score as a percent?

  1. Write the ratio: 42/50
  2. Convert the fraction to a decimal: 42 ÷ 50 = 0.84
  3. Convert the decimal to a percent: 0.84 × 100 = 84%
  4. Answer: Your score is 84%.

🚨 Common Mistakes to Avoid

  • Forgetting to convert the percent to a decimal before multiplying. (Multiplying by 25 is very different from multiplying by 0.25!).
  • Misplacing the decimal point when converting. Remember, it's always a two-place move to the left for percent to decimal.
  • Confusing "of" with multiplication. In math, finding "20% of 80" means you multiply 0.20 by 80.

💡 Tips & Tricks

  • Think of "%" as meaning "/100": 25% is just 25/100.
  • Use mental math for easy percents:
    • 50% = Half (÷ 2)
    • 25% = One-quarter (÷ 4)
    • 10% = One-tenth (÷ 10)
  • Check if your answer makes sense: 15% of 100 should be a small number (15), not a huge one!

🎯 Practice Suggestions

  • Practice with real-life scenarios: calculate discounts on video games, figure out sales tax on a toy, or find what percent of your classmates have pets.
  • Use online quiz games that focus on percent calculations.
  • Create flashcards with different percent problems on one side and the step-by-step solution on the back.

Practice problems

6 of the 105, worked through step by step — try them before opening the answer.

1 25% of 1200 = ?

Hint: Remember that percentage means 'per hundred.' Think about how to find a fraction of a whole number.

Show the answer

Answer: 300

  1. Understand the problem. We are asked to find 25% of 1200. "Percent" means "per hundred," so 25% means 25 per 100.
  2. Convert 25% to a decimal. To convert a percentage to a decimal, divide by 100. 25% = 25 / 100 = 0.25
  3. Multiply the decimal by the number. We now calculate 0.25 times 1200. 0.25 × 1200 = ?
  4. Break the multiplication into parts. 0.25 is the same as 1/4. So, 25% of 1200 = (1/4) × 1200.
  5. Perform the multiplication. (1/4) × 1200 = 1200 / 4 1200 ÷ 4 = 300
  6. State the final answer. 25% of 1200 = 300

2 Liam buys a used car for $3,500. He must pay a 7% sales tax on the purchase. How much does Liam pay in total?

Hint: First, find the amount of tax by calculating the percentage of the purchase price. Then, add that tax to the original price to find the total cost.

Show the answer

Answer: 3745

  1. Calculate the sales tax amount. 7% of $3,500 = 0.07 × 3,500 = $245.
  2. Add the tax to the original price to find the total. $3,500 + $245 = $3,745. The total amount Liam pays is $3,745.

3 Mason buys a new video game console for $372. The sales tax rate is 7%. How much does Mason pay in total, including tax?

Hint: Think about what 'percent' means: 7% is 7 out of 100. You need to find 7% of the price, then add it to the original price.

Show the answer

Answer: $398.04

  1. Find the amount of tax. 7% of $372 = 0.07 × 372 = $26.04.
  2. Add the tax to the original price. $372 + $26.04 = $398.04. Mason pays $398.04 in total.

4 A store offers a 30% discount on a $250 item, then charges 8% sales tax on the discounted price. What is the final price?

Hint: First calculate the discount amount, then subtract it from the original price to find the sale price. Next, calculate the tax on the sale price and add it to get the final amount.

Show the answer

Answer: 189

  1. Find the discount amount. The original price is $250, and the discount is 30%. Discount amount = 30% of 250 = (30/100) * 250 = 0.30 * 250 = 75.
  2. Subtract the discount from the original price to get the discounted price. Discounted price = 250 - 75 = 175.
  3. Calculate the sales tax on the discounted price. Sales tax rate is 8%. Tax amount = 8% of 175 = (8/100) * 175 = 0.08 * 175 = 14.
  4. Add the tax to the discounted price to get the final price. Final price = 175 + 14 = 189. So, the final price after discount and tax is $189.

Let's solve this step by step.

5 A store offers a 25% discount on a $120 item, then charges 8% sales tax on the discounted price. What is the final price?

Hint: First calculate the discount amount, then subtract it from the original price to find the sale price. Next, calculate the tax amount based on the sale price and add it to get the final cost.

Show the answer

Answer: 97.20

  1. Find the discount amount.** The original price is $120. Discount rate is 25%, so the discount amount is: Discount = 25% of 120 = (25/100) × 120 = 0.25 × 120 = 30. --- **
  2. Find the discounted price.** Discounted price = Original price − Discount = 120 − 30 = 90. --- **
  3. Calculate sales tax on the discounted price.** Sales tax rate = 8%. Tax amount = 8% of 90 = (8/100) × 90 = 0.08 × 90 = 7.20. --- **
  4. Find the final price.** Final price = Discounted price + Tax = 90 + 7.20 = 97.20. --- **Final answer:** 97.20

Let's go step-by-step. --- **

6 A store offers a 25% discount on a $240 item, then charges 8% sales tax on the discounted price. What is the final price?

Hint: First calculate the discount amount, then subtract it from the original price. Next, calculate the tax on the new price and add it to get the final amount.

Show the answer

Answer: 194.40

First, find the discount amount. The original price is $240 and the discount is 25%. 25% of 240 = 25/100 * 240 = 0.25 * 240 = 60. So, the discount amount is $60. Now subtract the discount from the original price: Discounted price = 240 - 60 = 180. Next, calculate the sales tax on the discounted price. Tax rate is 8%. 8% of 180 = 8/100 * 180 = 0.08 * 180 = 14.40. Add the tax to the discounted price: Final price = 180 + 14.40 = 194.40. Therefore, the final price after discount and tax is $194.40.

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