Today's Topic

Topic: Percentages and Ratios
Difficulty: beginner
Category: Daily English / Mathematics

Key Vocabulary

Important words and phrases for this topic

• percent: A symbol (%) representing one part in every hundred.

  • Example: "Twenty percent (20%) of students passed the exam."

• percentage: A number or ratio expressed as a fraction of 100.

  • Example: "The percentage of correct answers was 85%."

• ratio: A relationship between two numbers showing how many times one value contains another.

  • Example: "The ratio of boys to girls is 3:2, meaning there are 3 boys for every 2 girls."

• proportion: A part, share, or number considered in relation to a whole.

  • Example: "A large proportion of the budget goes to salaries."

• convert: To change from one form, system, or unit to another.

  • Example: "To convert 50% to a decimal, divide by 100 to get 0.5."

Examples & Application

Provide practical examples or application scenarios

Example 1: Sales and Discounts

"This item is on sale with a 25 percent discount (25% off). The original price was $100, so you save $25."

Example 2: Statistics

"According to the survey, 60 percent of respondents (60%) prefer online shopping. The ratio of online to in-store shoppers is 3:2."

Example 3: Cooking and Recipes

"The proportion of flour to sugar in this recipe is 2:1, which means you need twice as much flour as sugar."

Practice Activities

Practice today's topic through various methods, focusing on practical application and speaking

Speaking Practice

Read aloud and practice saying the following sentences, focusing on pronunciation and fluency

• "To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100."

• "The ratio of 3 to 4 can be written as 3:4 or as a fraction three fourths."

• "If 50 percent of students are female, that means half of the students are female, which is a ratio of 1:1."

• "The proportion of water to rice in this recipe is crucial for perfect results."

Role Play Scenarios

Simulate real situations and practice using today's learning in conversation

Scenario: Shopping at a department store during a sale

Customer: "Excuse me, what's the discount on this jacket?"
Sales Associate: "It's 30 percent off today."

Customer: "So if it's originally $80, how much would I save?"
Sales Associate: "You'd save $24, making the final price $56."

Customer: "Great! And what percentage of your inventory is on sale?"
Sales Associate: "About 40 percent of our items have discounts. The ratio of sale items to regular price items is roughly 2:3."

Practice Notes

Record your discoveries, difficulties, or interesting observations during practice

Pronunciation Tips:

• "percent" - stress on second syllable: per-CENT
• "percentage" - stress on second syllable: per-CENT-age
• "ratio" - stress on first syllable: RAY-shee-oh or RAY-shoh
• "proportion" - stress on second syllable: pro-POR-shun

Common Expressions:

• Reading percentages: 50% = "fifty percent"
• Reading ratios: 3:2 = "three to two" or "a ratio of three to two"
• Fractions to percentages: 1/4 = 25%, 1/2 = 50%, 3/4 = 75%
• Decimal to percentage: 0.75 = 75%

Conversion Relationships:

• Percentage to decimal: 25% = 0.25 (divide by 100)
• Decimal to percentage: 0.8 = 80% (multiply by 100)
• Fraction to percentage: 3/5 = 60% (divide and multiply by 100)
• Ratio to percentage: 3:5 means 3/8 = 37.5% and 5/8 = 62.5% of the total

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Daily Reflection

Key Takeaway: Today I documented English terms related to percentages and ratios, which are commonly used in daily life contexts like shopping, statistics, and cooking, as well as in technical documentation and algorithm problems.