In math, the word of usually means multiply. “Half of 10” means 12 × 10, which is 5. “25% of 80” means 0.25 × 80, which is 20. And “3 groups of 4” means 3 × 4, which is 12.
But “of” does not always mean multiply. In “the sum of 5 and 3”, the word that tells you what to do is sum, so you add. In “6 out of 8”, you make a fraction. This lesson shows you when “of” means multiply and how to spot the times it doesn’t.
Multiplication is a fast way to add equal groups. When you say “3 groups of 4”, you mean 4 + 4 + 4. That is the same as 3 × 4 = 12.
So the word “of” is how we say multiply out loud. “5 packs of 6 juice boxes” is 5 × 6 = 30 juice boxes, and “2 dozen eggs” is 2 groups of 12, or 2 × 12 = 24 eggs.
When “of” sits between two amounts, like “a groups of b”, “a fraction of a number” or “a percent of a number”, replace “of” with ×.
A box holds 4 rows of 9 chocolates. How many chocolates are in the box?
36 chocolates. 4 rows of 9 means 4 × 9 = 36.
To find a fraction of a number, multiply the fraction by the number. For example, 12 of 10 is 12 × 10 = 5. Taking half of something gives the same answer as multiplying it by 12.
When the top number of the fraction is not 1, you can do it in two easy steps: divide by the bottom number, then multiply by the top number.
34 of 20 is 15.
“Of” works the same way with two fractions. 12 of 13 is 12 × 13 = 16: half of one third is one sixth. To learn more, see multiplying fractions.
What is 23 of 18?
12. One third of 18 is 18 ÷ 3 = 6, so two thirds is 2 × 6 = 12.
A percent is a fraction out of 100, so “of” means multiply here too. First change the percent to a decimal or a fraction, then multiply.
The tip is $6.
To change a percent to a decimal, divide by 100: 15% = 0.15, 8% = 0.08 and 120% = 1.2. You can also use a fraction: 25% = 14, so 25% of 80 = 14 × 80 = 20.
For more practice, see finding a percentage.
What is 10% of 350?
35. 10% = 0.1, and 0.1 × 350 = 35.
When the number is unknown, use a letter for it and still replace “of” with ×. In algebra, we usually leave out the × sign and write the number in front of the letter.
See writing an algebraic expression for more phrases like these.
Write “one fourth of a number x, plus 7” as an expression.
14x + 7, or x4 + 7. “One fourth of x” is 14 × x, then add 7.
“Of” means multiply only when it joins two amounts. In many phrases, “of” is just part of a bigger phrase, and another word tells you the operation.
Reading “the sum of 5 and 3” as 5 × 3 = 15. The word “of” does not tell you the operation here; the word “sum” does. The answer is 5 + 3 = 8.
“What percent of 40 is 10?” still has a multiplication hidden inside: ? × 40 = 10. To find the missing number, you undo the multiplication by dividing. So when you are looking for the percent or the fraction, you divide.
Words such as “of”, “each” and “in all” are useful clues, but read the whole sentence before you choose an operation. See key words in math word problems for more of these traps.
A student got 18 out of 20 questions right. What percent is that?
90%. “18 out of 20” is the fraction 1820 = 18 ÷ 20 = 0.9, which is 90%.
In word problems, “of” often comes with a fraction or a percent of a total: “25 of the 30 students walk to school” means 25 × 30 = 12 students walk.
Watch for “of the rest” or “of what was left”. These phrases tell you to take the fraction of a new amount, not of the starting amount.
Ana has $22.50 left.
Taking 12 of the starting $60 instead of 12 of the $45 that was left. “Of the rest” always means of the new amount.
A class has 28 students. 37 of them have a pet. How many students have a pet?
12 students. One seventh of 28 is 28 ÷ 7 = 4, so three sevenths is 3 × 4 = 12.
Now check what you learned. Every answer is explained, and each time you play you get new questions.
Quiz complete!