What Does 'of' Mean in Algebra?

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.
 

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.
 

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.