If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 6: Multiplying fractions word problems

# Multiplying fractions word problem: muffins

Sal solves a word problem by multiplying 2 fractions. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• To solve, can't you also do 3/4 divided by 2? 3/4*1/2=3/8, right? • Yes you can! Dividing by a number is the same as multiplying by its reciprocal. To find the reciprocal of a number we swap the numerator and denominator. Just be careful not to get confused when saying you divide a fraction by something. For example, you might accidentally do this:

``3/4 ÷ 23/(4÷2)3/2``

Which as you know isn't right!
• 1/2 means half?? right or wrong • 7/24x20/21x9/10= • how do you know whether you have to add, subtract, divide, or multiply?? Someone help please asap!! • In worded problems like this, the clue to add, subtract, divide, or multiply comes from a few words in the problem itself

If you see the words sum, altogether or increase in a worded problem, you probably have to do addition. If you see the words difference, decrease or less than, you probably have to do subtraction. If you see the words of, each or product, you probably have to multiply. If you see the words per, average or shared equally, you probably have to divide.

In this worded problem, we see the word "of". This means we have to multiply 1/2 by 3/4. If you do that, the answer is 3/8
• But my Math teacher told me to NEVER multiply the denominator • i don't get how to simply • in multiplying fractions do you always have to multiply the denominator all the time or just certain problems? • The central hotel just hired a new chef . This chef mkes a hot sauce dat uses 1 3/4 tablespoons of chilly powder he needs to increase d recipe by 3 1/2 times how many table spoons of chilly powder should be used? • A recipe for banana oat muffins calls for 3/4 of a cup of old-fashioned oats.

(\ /)
( . . ) < ( 🧁 )
( > <)

You are making 1/2 of the recipe. How much oats should you use?

(\ /)
( • • ) <( 1/2 of recipe)
( > <)

So if the whole recipe requires 3/4 of a cup and you're making half of the recipe, you want half of 3/4, right?

(\ /)
( - - ) <(...)
( > <)

You want half of the number of old-fashioned oats as the whole recipe.

(\ /)
( • • ) <( 1/2 of [x] 3/4 ! )
( > <)

So you want 1/2 of 3/4. So you just multiply 1/2 times 3/4, and this is equal to-- you multiply the numerators.

(\ /)
( . . ) <(1/2 x 3/4 =... )
( > <)

1 times 3 is 3. 2 times 4 is 8. And we're done!
You need 3/8 of a cup of old-fashioned oats.

(\ /)
( ^ ^ ) <(...3/8!)
( > <)

And let's visualize that a little bit, just so it makes a little bit more sense.
Let me draw what 3/4 looks like, or essentially how much oats you would need in a normal situation, or if you're doing the whole recipe.

So let me draw. Let's say this represents a whole cup, and if we put it into fourths-- let me divide it a little bit better.

So if we put it into fourths, 3/4 would represent three of these, so it would represent one, two, three. It would represent that many oats.

Now, you want half of this, right? Because you're going to make half of the recipe. So we can just split this in half.

Let me do this with a new color. So you would normally use this orange amount of oats, but we're going to do half the recipe, so you'd want half as many oats.

So you would want this many oats. Now, let's think about what that is relative to a whole cup.

Well, one way we can do it is to turn each of these four buckets, or these four pieces, or these four sections of a cup into eight sections of a cup. Let's see what happens when we do that.

So we're essentially turning each piece, each fourth, into two pieces. So let's divide each of them into two.

So this is the first piece.

We're going to divide it into two right there, so now it is two pieces. And then this is the second piece right here. We divide it into one piece and then two pieces.

This is the third piece, so we divide it into one, two pieces, and this is the fourth piece, or the fourth section, and we divide it into two sections.

Now, what is this as a fraction of the whole?

Well, we have eight pieces now, right? One, two, three, four, five, six, seven, eight, because we turned each of the four, we split them again into eight, so we have 8 as the denominator, and we took half of the 3/4, right?

Remember, 3/4 was in orange.

Let me make this very clear because this drawing can get confusing.
This was 3/4 right there. So that is 3/4.
This area in this purple color is 1/2 of the 3/4.

But let's think about it in terms of the eights.

How many of these sections of eight is it? Well, you have one section of eight here, two sections of eight there, three sections of eight, so it is 3/8.

So hopefully that makes some sense or gives you a more tangible feel for what it means when you take 1/2 of 3/4.

[I made this extra readable for you guys! I hope this helps just a slight bit.]  