Fractions

How to Divide Fractions (like ½ ÷ ¼) with Free Online Tutoring in Math

How to Divide Fractions (like ½ ÷ ¼)

Dividing  fractions, like ½ ÷ ¼, can be very confusing.  Why is the answer BIGGER than 1/2 and 1/4?  Shouldn’t the answer be smaller if you’re dividing?  When children are taught to illustrate a mathematical model, they can easily see why ½ ÷ ¼ gives you a bigger answer.  Unless children are taught to illustrate the division of the fractions, they often never fully understand what is happening with the fractions.  This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.

This is the final article  in a series of eleven that follow a cyclical learning approach.  Each article is a complete lesson on fractions that takes children step-by-step through the process of learning fractions.  By creating mathematical models, your child will gain a deeper and more concrete understanding of dividing fractions.  This deeper understanding will help to ensure a successful educational career. 

Articles within this series on Fractions:

  1. How to do fractions, Free Online Tutoring in Math for Understanding Fractions
  2. How to Add Fractions (like 4/7 + 3/7 )
  3. How to Subtract Fractions (like 8/9 – 4/9 )
  4. How to Add Fractions with Unlike Denominators (like 2/3 + 3/4 )
  5. How to Subtract Fractions with Unlike Denominators (like 2/3 – 1/4)
  6. How to Add Fractions that are Mixed Numbers (like 2 & 3/4 + 3 & 5/6 )
  7. How to Subtract Fractions that are Mixed Numbers (like 3 & 3/4 – 2 & 5/6)
  8. How to Multiply Fractions (like 2/3 x 5 )
  9. How to Divide Fractions (like 6 ÷ ¾ )
  10. How to Multiply Fractions (like 2/3 x 1/4)
  11. How to Divide Fractions (like ½ ÷ ¼)
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How to Divide Fractions
Online Tutoring in Math: Challenge
1
Watch Me
Terrance the Ticklish Mule

Terrance loves his alfalfa, but his owner keeps tickling his nose. His owner loves Terrance, but he can’t help tickling his favorite mule. Each day, Terrance eats 2/3 pounds of alfalfa. His owner divides the alfalfa into portions that are 2/7 pounds, how many portions will Terrance get to eat?

Hint: How many 2/7’s are in 2/3?

Watch this Free Tutoring for Math Video!

Press PLAY and Watch this Free Tutoring for Math Video below.  Then copy these strategies into your notes!

 

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Could your child benefit from a little One-On-One tutoring?

The problem below is called a “Work with Me” challenge.  This challenge encourages your child to work step-by-step along side me to solve this challenge.  All of the following challenges are called “On Your Own” challenges.  However, many of my students who struggle with fractions will do five or six of the “On Your Own” challenges as a “Work with Me” challenge.  They play the video, pause it, and copy the strategies until they feel comfortable and confident.  Doing the problems as a “Work with Me” challenge is like having a personal tutor.

How to Divide Fractions
Online Tutoring in Math: Challenge 2
Work With Me
Singing Camels

Kami & Connie Camel love to sing. They walk around their paddock and sing to all the on lookers.  Kami & Connie’s paddock is 8/9 miles long.

If Kami& Connie break the paddock into portions that are 3/4 miles, how many portions will our “Singing Camels” walk and sing?

Hint: How many 3/4’s are in 8/9?

Watch this Free Tutoring for Math Video!

Gather your materials and press PLAY.  We’ll solve this problem together, while you watch the math tutorial video below.
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I have scaffold the problems in each lesson. 

The first problem in this article is a “Watch Me” problem.  The second is a “Work with Me” problem.  All the rest are “On Your Own” problems. 

*If your child needs a bit more support, they should complete the “On Your Own” problems as a “Work with Me” problem.  I have a number of students with gaps in their learning and others with a variety of  learning disabilities.  I have had incredible success, by having those students complete 5 to 7 problems within each lesson as a “Work with Me” problem.  They play a bit of the video, then pause it  and copy, then watch a bit more, pause it and copy.  My students Play – Pause – and Copy until the entire problem is solved.  This is like having a personal tutor working through each and every problem with your child.  Every one of my students who has used this strategy has passed the Common Core Proficiency Exam.

How to Divide Fractions
Online Tutoring in Math: Challenge 3
On Your Own
Honovi the Honey Loving Grizzly Bear

Honovi is always on the lookout for bees. She follows them back to the hive and collects as much honey as possible. Yesterday, Hovoni found a hive. While the bees crawled under her fur and stung again and again, Honovi stole 4/5 pounds of honey. If Hovoni divides the honey into portions that are each 1/8 pound, how many portions can she make?

Hint: How many 1/8’s are in 4/5?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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Do your children get frustrated when they make a mistake?

We all make mistakes.  As a matter of fact, making mistakes is an essential part of the learning process.  This is why at the end of each of the following “On Your Own” challenges I encourage children to fix their mistakes.  Finding and fixing your own mistake is the fastest way to learn.

 

How to Divide Fractions
Online Tutoring in Math: Challenge 4
On Your Own
Shelby & Sherman Seahorse

Shelby & Sherwood are a couple of hungry seahorses.  They love nothing more than a big old mouthful of plankton.  The marine biologist that feeds them has a 2/5 bucket of plankton.

A serving of the plankton is 3/8 of the bucket.

How many servings are in the bucket?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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How to Divide Fractions
Online Tutoring in Math: Challenge 5
On Your Own
Elyssa the Thirsty Elephant

Elyssa Elephant is thirsty.  There is very little water on the African Plains at this time of the year.  Luckily for Elyssa and her herd, a local farmer gives a bucket of cool water to each elephant in Elyssa’s family.  Each bucket holds 5/6 gallons of water.

If Elyssa’s trunk holds 2/7 of a gallon, how many trunkfuls of water will Elyssa get to drink?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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How to Divide Fractions
Online Tutoring in Math: Challenge 6
On Your Own
Daisy the Ditzy Giraffe

Daisy is a bit scatterbrained.  She forgets everything.  Just last night, her mother asked her to gather four piles of grass, leaves, and twigs for her family to eat. Daisy got distracted and only made one pile for all her family to share.  The pile is 5/7 of a square yard.  Each giraffe eats 2/5 of a square yard.

Does Daisy the Ditzy Giraffe have enough for all four members of her family? 

How many servings does Daisy have?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!

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How to Divide Fractions
Online Tutoring in Math: Challenge 7
On Your Own
Hide and Go Seek Zeek

Hide and Go Seek Zeek does not like leaving his perfect hiding spot.  He refuses to come out once he is hidden.  Today, we find Zeek hiding in a hollow stump.  However, he is hungry, so his mother must bring him his food.  Zeek eats 3/8 pound of bamboo leaves at each meal.  However, he will only take bites that are 3/9 of a pound, while he is hiding.

How many 3/9 bites must Hide and Go Seek Zeek take in order to complete his meal?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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How to Divide Fractions
Online Tutoring in Math: Challenge 8
On Your Own
Stealthy Sea Otters

Simon, Stanley, and Otto are Stealthy Sea Otters.  They hang out on the dock and wait for unsuspecting fisherman to return with their haul.  Then they sneak in and steal a bucket of fish.  Today they are laughing at a fisherman they just stole from.  They took a bucket that was 2/3 full of fish.  Simon, Stanley, and Otto each hope to eat 4/7 of a full bucket.

Do the Stealthy Sea Otters have enough?

How many servings do they have?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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How to Divide Fractions
Online Tutoring in Math: Challenge 9
On Your Own
Madeline Marmot

Madeline Marmot is all about appearance.  She has company coming over for dinner, so she has decided to make new place mats for her dinning room table.  There will be a total of four marmots coming to tonight’s meal.  Madeline has 5/6 yards of grass.  Each place mat uses 2/7 yards.

Does she have enough grass?

Exactly how many place mats can she make?

complete her race?Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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How to Divide Fractions
Online Tutoring in Math: Challenge 10
On Your Own
Randy & Candy

Randy & Candy love frolicking in the pasture. They kick, buck, prance, and dance as they run round and round.  When Montana Mike walks to the barn with a bucket of food, both horses race for their stalls.

Montana Mike’s buck is 3/4 full of oats.  Each horse’s serving is 2/6 of a bucket.

Does Montana Mike have enough oats?

How many servings does Montana Mike have in all?

Watch this Free Tutoring for Math Video!

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
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Drill & Kill

Here is where we Drill until we Kill all our mistakes!

  1. The following problems can all be solved with the same strategies we used to solve the first ten problems.
  2. Solve all four problems on each page.
  3. Watch the video & correct your work.
  4. Review your work with your teacher.
  5. If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book within this series.

Good Luck!

Drill & Kill Any Mistakes
Challenge
11

Problem 1

2/3 ÷ 5/8?

 

Problem 2

3/4 ÷ 2/7?

 

Problem 3

4/5 ÷ 3/6?

 

Problem 4

5/6 ÷ 4/9?

 

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!

Drill & Kill Any Mistakes
Challenge
12

Problem 1

5/8 ÷ 1/3?

 

Problem 2

5/7 ÷ 2/4?

 

Problem 3

5/6 ÷ 2/5?

 

Problem 4

7/9 ÷ 4/6?

 

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!

Drill & Kill Any Mistakes
Challenge
13

Problem 1

3/5 ÷ 1/2?

 

Problem 2

3/4 ÷ 5/6?

 

Problem 3

5/6 ÷ 5/6?

 

Problem 4

1/3 ÷ 2/3?

 

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!

Drill & Kill Any Mistakes
Challenge
14

Problem 1

3/8 ÷ 1/4?

 

Problem 2

5/9 ÷ 1/2?

 

Problem 3

3/7 ÷ 5/6?

 

Problem 4

5/6 ÷ 1/4?

 

Once you complete the problem – Hit PLAY on the math tutorial video below.  Good Luck!
Need Help with Multiplication?

I have a series on Multiplication that is specifically designed for children who do not have all of their multiplication facts memorized.   The series is designed in a similar manner to this series on division, where each and every problem is linked to a video tutorial.  Here is a link to my series on Multiplication.

Need Help with Division?

I have a series on division that is specifically designed for children who do not have all of their multiplication facts memorized.   The series is designed in a similar manner to this series on multiplication, where each and every problem is linked to a video tutorial.  Here is a link to my series on Division.

Thank you for reading this article!

Want More Tutorials?

TeachersDungeon is an Educational Fantasy Game.  It is 100% FREE!  The game is set to the Common Core Educational Standards, and is web-based, so it can be played on any device.  Many of the questions are accompanied by tutorials like the ones you saw here.

One Last Thing

If you like this post and found it helpful, please leave a brief comment.   As a teacher, perhaps the greatest reward I receive is from parents, children, and fellow teachers who use my strategies of education and succeed.

My mission in life and as an educator is to make people feel empowered, self-assured, and happy about who they are in this world!  We all have gifts to bestow upon our world.  Go forth and do so, and know that you are awesome!

Have a fantastic day – Brian McCoy

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