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Lesson 2: Relate fraction division to fraction multiplication

# Multiplication and division relationship for fractions

We learn how multiplication and division are related, even when we're dealing with fractions. Watch how dividing by a number is the same as multiplying by its reciprocal. Then watch Sal practice expressing these relationships using both division and multiplication.

## Want to join the conversation?

• So couldn't 42 = 7 / 1/6 be written as 42 x 7 = 1/6 instead of 42 x 1/6 = 7?
• There is this to consider.
"Example one":
2x3 = 6 and 3x2 = 6
This is not true for the order in division.
15/3 = 5 however 3/15 = 1/5 or 0.2 they both yield a smaller number however the one with a larger number for its denominator yields a significantly smaller number when compared to the one with a larger numerator.

When dividing fractions this has to be taken into consideration.

"Example two":
4 x 1/16 = 1/4 or 0.25
1/16 x 4 = 1/4 or 0.25

4 divided by 1/16 = 64
1/16 divided by 4 = 1/64 or 0.015625

"Example three":
A whole number divided by a fraction yields a larger "whole" number.

A fraction divided by a whole number yields an even "smaller fraction."
Example three simplified:
number/fraction = number or "n/f=n"
fraction/number = fraction or "f/n=f"

There needs to be a video called "The differences between multiplying and dividing fractions".

After wracking my brain on this for six hours I had to break this apart and figure out the underlying system so that it's possible to get the right answer every time.
• What's the reason of doing 42*1/6=7? Can't I write as 42*7=1/6? Unfortunately, This is very common in Khan Academy videos. There isn't enough explanation in details.
• So is your question 42*1/6=7 = 42*1/6=7?
because 42*1/6=42/6 and fraction is basically division so 42÷6=7 that makes sense and 42*7=294 so did I answer your question?
• I don't understand this video
• Sal is trying to explain that like whole numbers, you have a "family" of numbers, or that the numbers should equal each other like as an example 5*6=30,so 30/6=5. Hope that helped!(* times. / divide)
• Bro why show the hard way then the easier way?
• i dont no
• I am trying to understand this for 6 hours now , i give up, i think i am retarded. I just cannot figure out which by which you have to multiply to get the right answer. It seems like every time its a different component that has to be divaded or multiplied.
• You have to multiply the bottom number/denominator with the whole number and then just stick a 1/ before product. Let’s say, 1/3 divided by 4. The bottom number would be 3, and 4 is a whole number. 4x3=12 So now we put 1/ before 12, which means the answer is 1/12
• This is so confusing
• they show too much divison and fration
• I need more explanation . I don't understand which number I should use to divide. 5.NF.B7
• You have to multiply the bottom number/denominator with the whole number and then just stick a 1/ before product. Let’s say, 1/3 divided by 4. The bottom number would be 3, and 4 is a whole number. 4x3=12 So now we put 1/ before 12, which means the answer is 1/12
• me to I need help to understand it's kind of confusing to me
• Let me try to explain this,

``1/4 ÷ 2 = 1/8``

If you now think of these numbers as,
1/4 - Total of a chocolate bar left
2 - number of groups/breaks you want to make
1/8 - Fraction of chocolate that goes into the each group

Now you can re-write this in any meaningful order,

1.
``Fraction of chocolate bar in each group = Total of chocolate bar ÷ number of groupThis is,1/8 = 1/4 ÷ 2``

2.
``Total of chocolate bar = Fraction of chocolate bar in each group × number of groups This is,1/4 = 1/8 × 2``

3.
``number of groups = Total of chocolate bar ÷ Fraction of chocolate bar in each groupThis is,2 = 1/4 ÷ 1/8``