What does "of" mean in math?

Question

Ok, Im feeling a little dumb here, I should definately know this, I am drawing a blank here. I have a question stating:

A survey has found that 7/10 of the people in a city own pets. Of those who own pets, 2/3 have dogs. What fraction of those surveyed own dogs?

Answer 1

"of" means multiplication and is mainly used with fractions.

Example: "1/2 of 6" means (1/2) times 6, which is equal to 3.

Answer 2

Let's say that the town has 300 people. The survey found that 7/10ths of the 300 people own pets. That is (7/10) 300 = 210 people. The "of" means "That fraction of", or "That part of", indicating "Those that own the pets", which is necessarily a SMALLER number than 300.

Okay, the survey went on to say that OF THOSE that own pets, 2/3 have dogs. Well, but we know that 210 people own pets, which was meant by "of those" that own pets. Okay, so we do the multiplication again, (2/3) 210 = 140 people that own dogs.

Look at the process here:

300 people
(7/10) 300 = 210 people with pets
(2/3) (7/10) 300 = (2/3) 210 = 140 people with pets that are dogs.

You can draw 3 successive circles, one inside the other. The largest has 300 people, the next one smaller has 210 people, and the smallest 140. The word "of" means "being a part of", so that the smallest circle is "of" the next larger, which in turn is "of" the largest.

By golly I hope you got it now.

Answer 3

"of" means multiplication and is mainly used with fractions.

Example: "1/2 of 6" means (1/2) times 6, which is equal to 3.

when you want to convert word problems to equation, "of" means multiplication.
Let's say that the town has 300 people. The survey found that 7/10ths of the 300 people own pets. That is (7/10) 300 = 210 people. The "of" means "That fraction of", or "That part of", indicating "Those that own the pets", which is necessarily a SMALLER number than 300.

Okay, the survey went on to say that OF THOSE that own pets, 2/3 have dogs. Well, but we know that 210 people own pets, which was meant by "of those" that own pets. Okay, so we do the multiplication again, (2/3) 210 = 140 people that own dogs.

Look at the process here:

300 people
(7/10) 300 = 210 people with pets
(2/3) (7/10) 300 = (2/3) 210 = 140 people with pets that are dogs.

You can draw 3 successive circles, one inside the other. The largest has 300 people, the next one smaller has 210 people, and the smallest 140. The word "of" means "being a part of", so that the smallest circle is "of" the next larger, which in turn is "of" the largest.


it means multiplication:
"7/10 of the people in a city own pets."
amount of people who own pets = 7/10 *(amount of total population)

and "of those who own pets, 2/3 have dogs."
amount of people who own dogs = 2/3 * (amount of people who own pets)

this means that
amount of people owning dogs = (2/3)*(7/10)*(amount of total population)
or simply put, 7/15 of total population.>>> (2/3)*(7/10) = 7/15

Answer 4

when you want to convert word problems to equation, "of" means multiplication.

Problem:
A survey has found that 7/10 of the people in a city own pets. Of those who own pets, 2/3 have dogs. What fraction of those surveyed own dogs?

let x be the no. of people in a city who owns pet.

so "7/10 of the people..." means (7/10)x or 7x/10

of those who own pets, 2/3 have dogs.

therefore:

2/3 of (7x/10) or (2/3)(7x/10) = 14x/30

= 0.4667x

or simply 46.67% of the people in that city have dog.

Answer 5

What's the complication?

2/3 of pet owners own dogs.
7/10 are pet owners

Multiply them together

Answer 6

it means multiplication:
"7/10 of the people in a city own pets."
amount of people who own pets = 7/10 *(amount of total population)

and "of those who own pets, 2/3 have dogs."
amount of people who own dogs = 2/3 * (amount of people who own pets)

this means that
amount of people owning dogs = (2/3)*(7/10)*(amount of total population)
or simply put, 7/15 of total population.>>> (2/3)*(7/10) = 7/15

Answer 7

Of means to multiply in math.

Answer 8

means you multiply and deals with fractions, percentages

Answer 9

it usually means to multiply in math