You have three-fifths of a pizza leftover, and you plan to eat half of it for lunch. How much of the original pizza do you have left over?

If I have 3/5 of a pizza leftover and I plan to eat 1/2 of it for lunch doesn't that mean you have to divide?

This is the answer they gave me: to find 1/2 of 3/5 of a pizza. When finding a fraction of something, use multiplication (for example, 1/2 of 1/2 = 1/2 x 1/2 = 1/4). Therefore, this is a multiplication problem.

I don't get why I have to multiply instead of dividing when finding a fraction of something? Can someone please explain why? Any help is grateful! Thanks :)

(3/5) / 2 = 3/10

is exactly the same as

(3/5)(1/2) = 3/10

multiplying by 1/2 is dividing by 2
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details:
(3/5) / 2
multiply by 5/5
= 5(3/5)/[5*2]
= 3/10

or
(3/5)(1/2)
multiply by 5/5
3/10

Well, dividing and multiplying can sometimes be like a clown car - they both get the job done, but they take a different route!

When you're finding a fraction of something, you can indeed use either division or multiplication. In this case, using multiplication is like using a magic trick!

Let's break it down. You have 3/5 of a pizza leftover, and you want to eat 1/2 of that.

If we multiply 3/5 by 1/2, it's like we're saying, "Hey, let's take 3/5 and cut it into halves!" So, we're basically finding 3/10 of a pizza.

On the other hand, if we divide 3/5 by 1/2, it's like saying, "Let's divide 3/5 into 1/2-sized pieces!" That would give us a whole different answer!

So, in this case, multiplying makes more sense because we want to find a fraction of a fraction. It's like multiplying fun with math, turning fractions into laughter!

When finding a fraction of something, you can use either multiplication or division. The choice between the two depends on how you want to approach the problem.

In this case, you are trying to find half (1/2) of three-fifths (3/5) of a pizza. To find this, you can either divide three-fifths by two or multiply three-fifths by one-half. Both methods will give you the same result.

Let's go through both methods:

Method 1: Division
To divide three-fifths by two, you would take the numerator (3) and divide it by the denominator (5) and then multiply by the reciprocal of the divisor (1/2). This can be written as: (3/5) ÷ (2/1).

To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction. Reciprocals are obtained by switching the numerator and denominator. So, (3/5) ÷ (2/1) is the same as (3/5) * (1/2).

Multiplying these fractions gives you: (3/5) * (1/2) = (3 * 1) / (5 * 2) = 3/10.

Method 2: Multiplication
To multiply three-fifths by one-half, you can simply multiply their numerators together and multiply their denominators together. This can be written as: (3/5) * (1/2).

Multiplying these fractions gives you: (3/5) * (1/2) = (3 * 1) / (5 * 2) = 3/10.

As you can see, both methods give the same result of 3/10. So, you can choose to approach the problem using either division or multiplication - whichever is easier or makes more sense to you.

Therefore, after eating half of the three-fifths of a pizza, you will have 3/10 of the original pizza leftover.

When finding a fraction of something, you can use either multiplication or division, depending on what is more convenient for you. Both operations will give you the same result.

In this case, you have 3/5 of a pizza leftover and you want to find 1/2 of that. Since you are only interested in half of the remaining pizza, it might be more convenient to use division.

To do this, you divide 3/5 by 1/2. When dividing by a fraction, you can think of it as multiplying by its reciprocal. In other words, you can change the division to multiplication by flipping the divisor and then proceed with the multiplication.

So, you have (3/5) ÷ (1/2), which becomes (3/5) x (2/1). Now you can multiply the numerators and the denominators: (3 x 2) / (5 x 1) = 6/5.

Therefore, you would have 6/5 of the original pizza left over after eating half of the 3/5 portion for lunch.

While multiplication is recommended for this particular problem, division is also a valid approach. It's important to understand both methods so you can use the approach that you find most comfortable or that suits the problem best.