What Does 'of' Mean in Algebra?
2026-02-28 11:03 Diff
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Last updated on October 21, 2025

In algebra, ‘of’ refers to multiplication. It helps us find the part of a number in various contexts, such as fractions, percentages, and ratios. In this article, we will learn more about the use of ‘of’ in algebra and word problems.

What Does 'of' Mean in Algebra?

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The word ‘of’ in algebra is used in expressions involving fractions, ratios, and percentages. It is used to find a part of something. The word ‘of’ refers to multiplying numbers. The word ‘of’ in algebra indicates multiplication.


Example: \(\frac{1}{2}\) of 10.


\(\frac{1}{2}\) of 10 means multiplying \(\frac{1}{2}\) by 10.


\(\frac{1}{2}\) × 10 = 5.
 

Context of ‘of’ in Word Problems

In word problems, the word ‘of’ indicates that multiplication is required to find part of a quantity. It is used to find the part of a whole. 

Example 1: Emilin read \(\frac{3}{5}\) of a 20-page book. Calculate the total number of pages Emilin read. 


Here, the \(\frac{3}{5}\) of 20 refers to \(\frac{3}{5} × 20 = (3 × 20) ÷ 5 = 60 ÷ 5 = 12.\)

Example 2: Lilly has 60 chocolates, and she gave 1/3 of them to her friend. How many chocolates did Lilly give to her friend?
Lilly gave \(\frac{1}{3}\) of 60 chocolates to her friend, so \(\frac{1}{3} × 60 = 20. \frac{1}{3} × 60 = 60 ÷ 3 = 20\)


Therefore, Lilly gave 20 chocolates to her friend.
 

Example 3: A pizza was divided into 8 equal slices. Maria ate \(\frac{3}{8}\)of the pizza. How many slices did she eat?

\(\frac{3}{8}\) of 8 = \(\frac{3}{8} \times 8\) \(= \frac{3 \times 8}{8} \) \(= \frac{24}{8} = 3\)

Answer: Maria ate 3 slices.
 

Example 4: A toy costs $50. Sarah gets a discount of \(\frac{2}{5}\) of the price. How much money does she save?

\(\frac{2}{5} \) of \(50\) \(= \frac{2}{5} \times{50}\) \(= \frac{2 \times 50}{5} \) \(= \frac{100}{5} = 20\)

Sarah saves 20 dollars.
 

Example 5: A runner completed \(\frac{7}{10}\) of a 50 km marathon. How many kilometers did the runner complete?

\(\frac{7}{10}\) of 50 \(= \frac{7}{10} \times 50 = \) \(\frac{7 \times 50}{10} \) \(= \frac{350}{10} = 60 \)

John have 60 candies.
 

Real World Percentage Scenarios

Given below are some real world scenarios involving percentages that show how 'of' is used in algebra.
 

1. Shopping discounts

A jacket costs $80. The store offers a 25% discount. How much money do you save?
 

Explanation: 
“25% of 80” means:
\(\frac{25}{100} \times 80 = 20\)

you save 20 dollars

2. Exam Scores

Lisa scored 80% of 50 questions correctly in a math test. How many questions did she answer correctly?

Explanation: 
“80% of 50” means:
\(\frac{80}{100} \times 50 = 40\)

Lisa answered 40 questions correctly.

3. Salary Increase 

Raj’s salary is $2,000 per month. He received a 10% raise. How much is the raise?

Explanation:
“10% of 2000” means: 
\(\frac{10}{100} \times 2000 = 200\)
 

4. Population Growth

A town has 5,000 people. Its population increases by 6% this year. How many people were added?

Explanation: 
“6% of 5000” means:
\(\frac{6}{100} \times 5000 = 300\)

The town gained 300 people.

5. Sale of fruits

A basket contains 60 apples. 15% of them are rotten. How many apples are rotten?
 

Explanation:
“15% of 60” means:
\(\frac {15}{100} \times 60 = 9\)


9 apples are rotten.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.