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.

Course: 6th grade (Illustrative Mathematics)>Unit 4

Lesson 3: Lesson 11: Using an algorithm to divide fractions

Dividing fractions review

Review the basics of dividing fractions, and try some practice problems.

Dividing fractions

Dividing fractions is the same as multiplying by the reciprocal (inverse).
For example:
$\frac{3}{4}÷\frac{2}{3}$$=\frac{3}{4}×\frac{3}{2}$
Once we have a multiplication problem, we multiply the numerators then multiply the denominators.
Example 1: Fractions
$\frac{3}{2}÷\frac{8}{3}=?$
The reciprocal of $\frac{8}{3}$ is $\frac{3}{8}$.
Therefore:
$\frac{3}{2}÷\frac{8}{3}=\frac{3}{2}×\frac{3}{8}$
$\phantom{\frac{3}{2}×\frac{3}{8}}=\frac{3×3}{2×8}$
$\phantom{\frac{3}{2}×\frac{3}{8}}=\frac{9}{16}$
Example 2: Mixed numbers
$3\frac{1}{2}÷1\frac{1}{4}=$
Let's start by converting the mixed numbers to fractions.
$\phantom{=}3\frac{1}{2}÷1\frac{1}{4}$
$=\frac{7}{2}÷\frac{5}{4}$
$=\frac{7}{1}\cdot \frac{2}{5}$

Practice

Problem 1
$\frac{3}{5}÷\frac{1}{9}=?$

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

• 3/5 divided by 1/9 = 5 3/5 but the thing is it is wrong.
Can someone explain the equition better. Thanks
• because you need to keep it as a improper fraction. Your mixed number is correct though.
• why do you get more points if you get some answers wrong?
• Because you're learning. As I like to say, "Failure gives way to knowledge" and when you fail, it gives you another chance to succeed. Don't fail on purpose, though. If you already know something, get it right. And don't fail exams. That's a bad idea, I've found out.
• Thanks for the review but I don’t understand
• It's very complicated to explain but just go with what it says. But the way I explain is "Keep Change Flip(KFC)". So, you keep the first fraction the same, you change the division sign to a multiplication sign, and then you flip the second fraction upside down sort of. Instead of Kentucky Fried Chicken its Kentucky Chicken Friends.(It's corny I know[Also note that I'm not a teacher])
• i cant even get the right answer
• Here's how you divide fractions. First you have to know how to multiply fractions which i'm going to skip knowing that khan academy teaches that first in 5th grade I believe. Anyways next in division you basically do the same thing but instead you flip the fraction the the right side. As shown in the equation below
2/3 divided by 4/5 turns into 2/3 * 5/4
If you don't understand you should probably re watch the khan academy video!
Little tip! you can also cross divide for example in this equation (you might want to write the equation down to better visualize it
3/4 * 8/6 In this equation 3 and 6 are diagonal to each other on the paper right? that means you can cross divide which is so much fun and can free yourself from simplifying at the end if you do it right! so 6 is divisable by 3 right? and they are opposite places in fractions. so when you cross divide you divide both numbers with something that makes both numbers smaller but both stay as whole numbers! so in this equation 3/4 * 8/6 turns into 1/4 * 8/2! you can simplify more with the 4 and 8 to get 1/1 * 2/2! to get 1 as your answer yay
• Why do I have to do this?
• Cause Sal said so
• I used keep change flip it was easy but i wish it gave it a little challenge so i could learn more all at 1 time who agrees
• I agree with you
• i dont understand when you add a 2 in front of the 2/3 as in 2 2/3. if i was to say 3/4 divided by 3 5/6 i dont understand it when you give a whole in front of the fraction
• When you see a fraction written with a number on its own in front, such as 3 5/6, it is a mixed fraction.

What it means is that you have 3 wholes, and 5/6 of a whole. So in other words, you can read it as 3 + 5/6.

If you wanted to divide 3/4 by 3 5/6 you would convert it into an improper fraction (a fraction where the top number, called the numerator, is larger than the bottom number, called the denominator) and then perform the division.

To illustrate this:

3/4 ÷ 3 5/6 = 3/4 ÷ 23/6 (23/6 comes from 3 * 6 + 5)
= 3/4 × 6/23 (6/23 because division of fractions is multiplying by the fraction flipped over, or in maths-speak, the reciprocal of the fraction)
= 18/92
= 9/46 (simplified fraction)
• Why would simplifying be involved in 4/5 to make 2/5, or 7/2 to make 7/1?