# Divide Chocolates: Division & Fraction Homework for Kids

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• Physou
In summary, the conversation discusses the concept of division and multiplication using real-world examples such as dividing chocolates by boxes and the potential confusion of dividing things with different names. It is mentioned that in a third-grade math course, it may be simplified to only divide or multiply quantities with the same units, but in the real world, there is no problem with multiplying or dividing different units. The speaker also mentions that introducing division by fractions too early may be a mistake for most 8-year-old children. Additionally, they bring up the difficulty in distinguishing the active and passive voice in some languages when understanding division and multiplication. The conversation also touches on the concept of 1 chocolate per chocolate and how it can still be meaningful even without owning any chocolates. Lastly
Physou
I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or is it "forbidden" to divide things that don't have the same name, i.e. chocolate and box , as I read in an arithmetic course for kids ? Thank you !

Physou said:
I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or is it "forbidden" to divide things that don't have the same name, i.e. chocolate and box , as I read in an arithmetic course for kids ?
It might "forbidden" in a third-grade math course, to keep things simple, but in the real world, there is no problem with dividing or multiplying quantities that have different units. "Miles per hour" is a ratio (i.e., a quotient) that involves distance units and time units. To calculate your average speed when you drive 120 miles in 2 hours, you get ##\frac{120 \text{ miles }}{2 \text{ hours }} = 60 \frac{\text{ miles }}{ \text{ hour }}##, are as it's usually written, 60 mph.

The same goes for multiplication of different kinds of units. If you apply a force of 50 lb on a lever that is 2 ft long, you are applying a torque of 50 * 2 lb-ft, or 100 ft-lbs.

Physou
Thank you for your interest ! there seems to be indeed 2 ways and 2 different results : with the realistic way of chocolates divided by boxes we are closer to the idea of speed and other things with 2 dimensions; the "forbidden" way doesn't but seems more tempting to use, easier to understand by children : 6 chocolates divided by 1/2 ( not by a half box ) can be immediately seen as what that means : 12 halves as we cut the chocolates in 2, and we don't need to think of 6 chocolates in a half box and multiply by 2 half boxes and get 12 full chocolates. But all this is confusing : divided boxes, divided chocolates .. this is not so easy, even less for kids I presume !

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Physou said:
I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or is it "forbidden" to divide things that don't have the same name, i.e. chocolate and box , as I read in an arithmetic course for kids ? Thank you !
It is forbidden to add or subtract things that don't have the same name, usually when we multiply or divide we have things that are different. 12 chocolates per box is meaningful, 1 chocolate per chocolate, or 1 square chocolate is not.

1 chocolate per chocolate is not meaningful, but saying " 6 chocolates divided by halves give 12 halves but divided by 1/2 box give 12 chocolates " is correct ?

Physou said:
1 chocolate per chocolate is not meaningful, but saying " 6 chocolates divided by halves give 12 halves but divided by 1/2 box give 12 chocolates " is correct ?
I think these analogies are only useful for integers. I also think that introducing division by fractions too early is a mistake: 8 years old is too early for most kids.

Thank you for your insight; division by halves and thirds with a knife has gone ok, I will wait more time to introduce the divided box and the different meaning. Talking about analogies , in south east Asian agglutinative languages the active / passive voice is often not used in spoken practice, so that trying to distinguish " divide " and " divided by " with the help of the active / passive analogy from the real world is difficult with kids.

6 chocolate per half a box means 12 chocolates per box, I don't see anything wrong in dividing chocolates by boxes.

MrAnchovy said:
It is forbidden to add or subtract things that don't have the same name, usually when we multiply or divide we have things that are different. 12 chocolates per box is meaningful, 1 chocolate per chocolate, or 1 square chocolate is not.
You always have 1 chocolate per chocolate. If you do not own any chocolate, you also have 2 chocolate per chocolate you own.

1 square chocolate - well, if it is not round? ;)

## 1. How do I divide chocolates evenly among a group?

The best way to divide chocolates evenly among a group is to first count the number of chocolates you have and the number of people in the group. Then, use long division to divide the total number of chocolates by the number of people. The quotient will be the number of chocolates each person should receive.

## 2. Can I use fractions to divide chocolates?

Yes, you can definitely use fractions to divide chocolates. Fractions represent parts of a whole, so you can divide a certain number of chocolates into equal parts using fractions. For example, if you have 12 chocolates and want to divide them into thirds, each person would receive 4 chocolates (12 ÷ 3 = 4).

## 3. How do I divide chocolates using a number line?

To divide chocolates using a number line, first draw a number line and label the starting and ending points with the total number of chocolates. Then, divide the number line into equal parts based on the number of people you want to divide the chocolates among. The number of chocolates in each part will be the answer to your division problem.

## 4. How do I check if my division of chocolates is correct?

To check if your division of chocolates is correct, you can use multiplication. Multiply the number of chocolates each person received by the number of people and the result should be the total number of chocolates you started with. For example, if you divided 12 chocolates among 4 people, you should have 3 chocolates per person. 3 x 4 = 12, so your division is correct.

## 5. Can I use different methods to divide chocolates?

Yes, there are many different methods you can use to divide chocolates. Some other methods include using arrays, equal groups, and repeated subtraction. It's important to choose the method that is easiest for you and helps you understand the concept of division and fractions better.

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