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### Course: Numbers & Operations - The Real & Complex Number Systems 211-217>Unit 7

Lesson 4: Dividing whole numbers by unit fractions

# Dividing a whole number by a unit fraction

In this video, we'll learn how to divide a whole number by a fraction. We'll watch as three whole units are divided into sections, each being one-fourth of a whole. Then see practice problems counting these sections to understand the result of the division.

## Want to join the conversation?

• One thing I don't understand, when we divide 3 by 1, we get a result of 3, but when we divide 3 by 1/4 we a get a number higher than 3, I'm kind of confused, can someone explain?
• When we divide 3 by 1, we are trying to find how many 1's there are in 3. In this case, there are 3 ones in 3. The same goes when we divide by fractions, when we divide 3 by 1/4, we are trying to find how many 1/4's there are in 3. There are 4 quarters in 1, so there must be 3 times as many quarters in 3 than there are in one. 4 times 3 is 12, so there are 12 1/4's in 3. Another way to think about this is to use logic. 3 divided by 1 is 3. 3 divided by 2 is 1.5. So we can see that the answer gets smaller as the divisor gets larger, therefore, the answer must get larger as the divisor gets smaller. Hope this helps!
• So, do you basically do the whole number times the denominator of the unit fraction to get your answer?
• Why can't I vote for you? I don't even know why we are vote?
• all you need to do is just multiply the whole number by the denominator
• Yes, but I would like to point out that if the number has a numerator that is not one, you need to do it the way Mr. Sal shows you. :)
(1 vote)
• It is easy 3 divided 1/4 is just doing 4x3
• I have found that if you do the whole number times the denominator you can usually get the correct answer, but I've only done it on simpler problems. Does this process always work?
• Yes, when dividing a whole number by a unit fraction, multiplying the whole number by the unit fraction's denominator always works!
This is because, for any numbers a and b with b nonzero, we have

a divided by (1/b) = a times (b/1) = (a/1) times (b/1) = ab/1 = ab.

Have a blessed, wonderful day!
• how would you divide a whole number by a fraction when it's not 1/2, 1/3,1/4
for example 2 / 5/6. In a different module on proportions, the answer they give is a mixed numeral, but I can only get a fraction: 5/12
• when my teacher did the box way i noticed that you can just multiply the whole numbers and the denomanator
• When dividing fractions like 1/9 divide by 4, you only need to do 1/ 9 x 4 = 1/36
• This is essentially correct. Revise the last equation to say 1/(9 x 4) = 1/36, to make it clear that 9 and 4 are multiplied first.

Have a blessed, wonderful day!
• The easier way is to say the number divided the numerator and that answer times the denominator.
• at , he said i am going to hand draw it so its not going to
be perfect, look how perfect that IS!

## Video transcript

- Lets think about what three divided by one fourth is equal to. Pause this video and see if you can figure it out on your own. And I'll give you a hint, take three wholes and divide it into pieces or sections that are each one fourth of a whole and then think about how many sections you have. Alright now lets work through this together. Now let me draw three wholes. And so lets say this is... I'm gonna hand draw it, so its not gonna be perfect. But lets say that is one whole right over there. This is two wholes right over there. And then I have my third whole just like that. And now I'm going to divide it into pieces or sections that are each one fourth of a whole. So this first whole is four pieces that are each one fourth each, of four fourths. And then I have another four fourths right over here. And then I have another four fourths right over here. Another way to think about it, I took the three wholes, and I divided it into fourths. So if you divide it into fourths how many pieces am I going to have? Well this is pretty straight forward, you have one two three four five six seven eight nine ten 11 12 pieces. And I didn't even have to count that, each whole is gonna be four fourths. So three wholes is going to be three times four fourths, or 12 pieces or 12 sections. So that is going to be equal to 12. Another way to think about it is if you take three and you divide it into equal sections that are each a fourth you are going to have 12 equal sections.