"Of" Means "Times" (x) in Math

My Uncle John visited our home frequently. He always loved mathematics. On more than one occasion, he would ask me to quickly give him an answer to this question, "What is one half of seven-eighths?" I was a child at that time, and it seemed logical to me that one half of seven-eighths should be 3 and a half eighths. Of course, I was wrong, but he wouldn't give me the correct answer...he just wanted me to think about it. Apparently I did think long and hard about it since I still use his example when I teach math. Students need to become familiar with key words in math.

Fractions
"Of" means "times"-or multiply-in math; therefore, the way to solve Uncle John's problem is to substitute the multiplication sign for the word of. Students should be able to make the connection using trigger words in math.
1/2 of 7/8 means 1/2 x 7/8.
The process in multiplying fractions is to multiply the numerators (top numbers in the fractions) and then multiply the denominators (bottom numbers in the fractions).
Multiply numerators: 1 x 7 = 7
Multiply denominators: 2 x 8 = 16
Hey, Uncle John...now I get it...1/2 x 7/8 is 7/16.

Try this problem:
What is 2/3 of 4/5?
Change it to 2/3 x 4/5.
Multiply numerators: 2 x 4 = 8
Multiply denominators: 3 x 5 = 15
2/3 of 4/5 is 8/15.

What is ¾ of 12?
Change it to 3/4 x 12/1.
Multiply numerators: 3 x 12 = 36
Multiply denominators: 4 x 1 = 4
¾ of 12 is 36/4 or 9.

Percents
Note: to change a percent into a decimal, move the decimal point two places to the left.
Example: 25% = .25

What is 60% of 80?
Remember that of means times.
60% of 80 means 60% times 80.
.60 x 80 = 48
60% of 80 is 48.

I never did forget Uncle John's example problem. He was teaching me math vocabulary words way back then. He drilled the fact into my head that "of" means "times" in math. I, in turn, drilled it into my students' heads.
Uncle John would've been a great teacher.

When teaching math vocabulary to students, emphasize the fact that they can substitute the multiplication sign for the word of. My students referred to this idea many times. Little word tricks in math can mean the difference between frustration and success.

Other math articles by this author:
Teaching Math: Shortcut for Comparing Fraction
Have Fun Teaching Squares and Square Roots