English • Second Level

Expressions with Numbers and Percentages
Quantifiers and Expressions of Quantity

Rules & Exercises
📊 Expressions with Numbers and Percentages
Quantifiers and Numerical Expressions
Numbers with Nouns
• Five books
• Two hundred students
• Three thousand dollars
• Quantifier + noun
Percentages
• Twenty percent
• Half of the students
• Three quarters
• Fraction expressions
Numbers Five students passed Percentages Twenty percent passed Fractions Half of them passed Percentages Three-quarters passed
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Definition: Numerical expressions provide specific quantities and percentages express proportional quantities in English.
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Number formation: Use numerals or written words, followed by the appropriate noun form.
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Percentage rules: Use "percent" after numbers or fractional expressions for proportional quantities.
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Application: Essential for expressing precise quantities in statistics and data.
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Tip: Use "percent" after numbers for percentages
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Caution: Don't use "a/an" with numbers and nouns
Shortcut: Percent = per hundred (parts out of 100)
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Method: Practice converting between fractions and percentages
Exercise 1
Complete: "_____ students passed the exam."
Exercise 2
Complete: "_____ of the population voted."
Exercise 3
Complete: "The survey showed _____ percent agreement."
Exercise 4
Complete: "She has read _____ books this year."
Exercise 5
Complete: "_____ of the respondents agreed."
Exercise 6
Complete: "The company invested _____ million dollars."
Exercise 7
Complete: "_____ hours of work completed."
Exercise 8
Complete: "_____ of the tasks remain unfinished."
Exercise 9
Complete: "They sold _____ items during the sale."
Exercise 10
Complete: "_____ of the world's population lives in cities."
Solutions: Exercises 1 to 5
1 Students Passed Exam
Definition:

Number expressions: Use numerals or written numbers directly with countable nouns without articles.

Method of Solution:
  1. Identify if the context requires a specific number or percentage
  2. Determine if the noun is countable or uncountable
  3. Select the appropriate numerical expression format
  4. Ensure proper agreement between number and noun
Original: "_____ students passed the exam."
Solution: "Twenty-five students passed the exam."
Step 1: Identify the noun type

"Students" is a countable noun that can take numerical expressions.

Step 2: Determine the appropriate expression

The context suggests a specific number of students passed.

Step 3: Apply the rule

For countable nouns, use numbers directly: "twenty-five students".

Step 4: Verify the meaning

The sentence now specifies exactly how many students passed.

Final Answer:

The correct sentence is: "Twenty-five students passed the exam."

Rules Applied:

Countable noun rule: Use numbers directly with countable nouns

No article needed: Numbers don't require articles when modifying nouns

Hyphenation: Compound numbers from twenty-one to ninety-nine use hyphens

2 Population Voted
Definition:

Fractional expressions: Use fractions to express parts of a whole, followed by "of" and the noun.

Original: "_____ of the population voted."
Solution: "Three-quarters of the population voted."
Step 1: Identify the structure needed

The sentence requires a fractional expression with "of" construction.

Step 2: Determine the appropriate fraction

Common fractions for expressing proportions: half, quarter, third, etc.

Step 3: Apply the rule

For proportional expressions, use fractions: "three-quarters of".

Step 4: Verify the meaning

The sentence now indicates what proportion of the population voted.

Final Answer:

The correct sentence is: "Three-quarters of the population voted."

Rules Applied:

Fractional rule: Use fractions followed by "of" for proportional expressions

Hyphenation: Fractions are hyphenated: three-quarters, one-third

Of construction: Always use "of" after fractions

3 Survey Agreement
Definition:

Percentage expressions: Use numbers followed by "percent" to express parts per hundred.

Original: "The survey showed _____ percent agreement."
Solution: "The survey showed seventy-five percent agreement."
Step 1: Identify the required expression type

The sentence specifically mentions "percent", requiring a numerical percentage.

Step 2: Determine the appropriate percentage

Survey results often show percentages like 75% for high agreement.

Step 3: Apply the rule

For percentage expressions, use number + "percent": "seventy-five percent".

Step 4: Verify the meaning

The sentence now specifies the exact percentage of agreement found in the survey.

Final Answer:

The correct sentence is: "The survey showed seventy-five percent agreement."

Rules Applied:

Percent rule: Always use "percent" after numbers for percentage expressions

No "of": "Percent" doesn't require "of" when directly modifying nouns

Spelling: "Percent" is one word

4 Books Read This Year
Definition:

Number expressions: Use numerals or written numbers directly with countable nouns.

Original: "She has read _____ books this year."
Solution: "She has read twelve books this year."
Step 1: Identify the noun type

"Books" is a countable noun that can take numerical expressions.

Step 2: Determine the appropriate expression

The context suggests a specific number of books read.

Step 3: Apply the rule

For countable nouns, use numbers directly: "twelve books".

Step 4: Verify the meaning

The sentence now specifies exactly how many books were read.

Final Answer:

The correct sentence is: "She has read twelve books this year."

Rules Applied:

Countable noun rule: Use numbers directly with countable nouns

No article needed: Numbers don't require articles when modifying nouns

Time context: "This year" indicates a specific timeframe for the action

5 Respondents Agreed
Definition:

Percentage expressions: Use percentages with "of" construction to express parts of a group.

Original: "_____ of the respondents agreed."
Solution: "Sixty percent of the respondents agreed."
Step 1: Identify the structure needed

The sentence requires a percentage followed by "of" and the noun group.

Step 2: Determine the appropriate percentage

Survey results often show percentages like 60% for moderate agreement.

Step 3: Apply the rule

For group percentages, use number + "percent of": "sixty percent of".

Step 4: Verify the meaning

The sentence now indicates what percentage of respondents agreed.

Final Answer:

The correct sentence is: "Sixty percent of the respondents agreed."

Rules Applied:

Percent with "of": Use "percent of" when referring to parts of a group

Group context: "Respondents" indicates a specific group being measured

Spelling: "Percent" is one word

Solutions: Exercises 6 to 10
6 Company Investment
Definition:

Large number expressions: Use numbers with magnitude words (million, billion) for large quantities.

Original: "The company invested _____ million dollars."
Solution: "The company invested five million dollars."
Step 1: Identify the magnitude needed

The sentence involves a company investment, which is typically expressed in millions.

Step 2: Determine the appropriate number

Corporate investments often involve round numbers like five million.

Step 3: Apply the rule

For large amounts, use number + magnitude word: "five million dollars".

Step 4: Verify the meaning

The sentence now specifies the exact amount of the investment.

Final Answer:

The correct sentence is: "The company invested five million dollars."

Rules Applied:

Magnitude rule: Use number + magnitude words for large quantities

No hyphens: Don't hyphenate numbers with magnitude words

Capitalization: Don't capitalize magnitude words unless at sentence start

7 Hours of Work
Definition:

Time expressions: Use numbers directly with time units without articles.

Original: "_____ hours of work completed."
Solution: "Eighty hours of work completed."
Step 1: Identify the unit of measurement

"Hours" is a unit of time that can take numerical expressions.

Step 2: Determine the appropriate number

Work completion might involve a significant amount like eighty hours.

Step 3: Apply the rule

For time units, use numbers directly: "eighty hours".

Step 4: Verify the meaning

The sentence now specifies the amount of work completed in hours.

Final Answer:

The correct sentence is: "Eighty hours of work completed."

Rules Applied:

Time unit rule: Use numbers directly with time units

No article needed: Numbers don't require articles with time units

Plural form: Use plural for numbers greater than one

8 Tasks Remain Unfinished
Definition:

Fractional expressions: Use fractions to express parts of a whole, followed by "of" and the noun.

Original: "_____ of the tasks remain unfinished."
Solution: "One-third of the tasks remain unfinished."
Step 1: Identify the structure needed

The sentence requires a fractional expression with "of" construction.

Step 2: Determine the appropriate fraction

Common fractions for expressing proportions: half, third, quarter, etc.

Step 3: Apply the rule

For proportional expressions, use fractions: "one-third of".

Step 4: Verify the meaning

The sentence now indicates what proportion of tasks remain unfinished.

Final Answer:

The correct sentence is: "One-third of the tasks remain unfinished."

Rules Applied:

Fractional rule: Use fractions followed by "of" for proportional expressions

Hyphenation: Fractions are hyphenated: one-third, two-thirds

Of construction: Always use "of" after fractions

9 Items Sold During Sale
Definition:

Number expressions: Use numerals or written numbers directly with countable nouns.

Original: "They sold _____ items during the sale."
Solution: "They sold three hundred items during the sale."
Step 1: Identify the noun type

"Items" is a countable noun that can take numerical expressions.

Step 2: Determine the appropriate expression

Sales often involve hundreds of items sold.

Step 3: Apply the rule

For large numbers, use "number + hundred/thousand": "three hundred".

Step 4: Verify the meaning

The sentence now specifies exactly how many items were sold.

Final Answer:

The correct sentence is: "They sold three hundred items during the sale."

Rules Applied:

Large number rule: Use number + hundred/thousand for large quantities

No hyphens: Don't hyphenate numbers with magnitude words

Plural form: Use plural for numbers greater than one

10 World Population in Cities
Definition:

Global percentage expressions: Use percentages with "of" construction for worldwide statistics.

Original: "_____ of the world's population lives in cities."
Solution: "More than half of the world's population lives in cities."
Step 1: Identify the scale needed

The sentence discusses world population, requiring a significant proportion.

Step 2: Determine the appropriate expression

Urbanization statistics often show more than half live in cities.

Step 3: Apply the rule

For global proportions, use expressions like "more than half of".

Step 4: Verify the meaning

The sentence now indicates the global urbanization statistic.

Final Answer:

The correct sentence is: "More than half of the world's population lives in cities."

Rules Applied:

Global statistics: Use "more than half" for significant worldwide proportions

Of construction: Always use "of" after fractions when modifying groups

Comparison: "More than" adds precision to fractional expressions

Expressions with numbers and percentages Quantifiers and Expressions of Quantity