dividing fractions problem solving

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Unit 2: Lesson 5

Dividing fractions word problems

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Dividing Fractions Word Problems Worksheets

Toss off solutions to our pdf worksheets on dividing fractions word problems to foster a sense of excellence in identifying the dividend and the divisor and solving word problems on fraction division. Equipped with answer key, our worksheets get children in grade 5, grade 6, and grade 7 rattling their way through the division of fractions and mixed numbers in regular and themed problems. A flurry of everyday scenarios, our free worksheet for dividing fractions word problems is worth a shot!

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Dividing Fractions and Whole Numbers Word Problems

Prepare the child through and through so they divide fractions and whole numbers with word problems. Let them take the reciprocal of the divisor and multiply it with the dividend, and they’re good to go!

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Dividing Fractions by Cross Cancelling Word Problems

Exceed every learning expectation with our dividing fractions word problems worksheets! Apply cross cancellation after inverting the divisor, find products of what's left, and do write the correct units.

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Dividing Mixed Numbers Word Problems

Give 5th grade and 6th grade students a good round of practice to hone their skills in fraction division. Convert mixed numbers into improper fractions, and proceed to divide them as usual.

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Dividing Mixed Numbers and Fractions Word Problems

The road to mastery in word problems on dividing mixed numbers and fractions is made smooth with our printable worksheets. Read the problems, identify the dividends and divisors, and find the answers.

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Themed Fraction Division Word Problems

If grade 6 and grade 7 learners are bent on proving they're real gifted at tackling fraction division, nothing can stop them! With our themed word problems pdfs, problem-solving is at its most exciting.

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» Adding Fractions Word Problems

» Subtracting Fractions Word Problems

» Multiplying Fractions Word Problems

» Fraction Word Problems

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Dividing fractions word problems

Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.

Dividing fractions word problems: a few examples

3 friends share 4/5 of a pizza. what fraction of pizza does each person get?

The amount to share is 4/5

Since the amount will be shared between 3 friends, the amount must be divided between 3 people.

So each person must get 4/5 divided by 3

(4 / 5) / 3 = (4 / 5) / (3 / 1) = 4 / 5 × 1 / 3 = (4 × 1) / (5 × 3)= 4 / 15

Each person will eat 4/15.

Indeed, 4 / 15 + 4 / 15 + 4 / 15 = 12 / 15 = 4/5 (divide 12 and 15 by 3 to get 4 / 5)

On June 21st, there were 9/10 of a billion stars visible to the naked eye.

On December 21st, there were 4/5 of a billion stars out visible to the naked eye.

How many times more stars were there visible on June 21st than December 21st?

9/10 divided by 4/5 = ?

Find the reciprocal of the divisor.

9/10 × 5/4 = ?

9/10 × 5/4 = 9/2 × 1/4

Solve 9/2 × 1/4 = 9/8

Simplify again

Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !

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Multiplying fractions word problems

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Word Problems with Division of Fractions

Today we are going to look at problems involving the division of fractions.

Are you ready to begin? Well, the first thing that we must remember is that in a problem with fractions we should follow all the necessary steps to solve any problem , only we have to add a step for the simplification of the result:

Now that we have already recalled what is fundamental for solving a problem with fractions, we can move on to review word problems with division of fractions . We will look at a problem where it is necessary to divide fractions to solve.

Let’s look at an example:

Priscilla bought cheese that weighs ¾ pounds. If she divides it into portions that are each 1/8 pound, how many portions can she make?

The first thing we should do are steps 1, 2, and 3: read carefully, understand the question, and think about the relevant details.

Priscilla bought cheese that weighs ¾ of a pound. If she divides it into portions that are each 1/8 of a pound, how many portions can she make?

That is to say…

If she divided ¾ of a pound into equal portions of 1/8 of a pound, how many portions did she make?

We already know that the operation is division. We are going to move on to steps 4 and 5 (solve and simplify).

We divide by taking the reciprocal of the second fraction and multiplying:

$division of fractions$

Then we simplify:

$division of fractions$

She made 6 portions.

Now, all we have left is to check that the solution makes sense, and we have solved the problem!

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Division with unit fractions

Unit fractions word problems.

Unit fractions are fractions with 1 as the numerator. Below are word problems involving the division of whole numbers by unit fractions, or vice versa.

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Dividing Fractions: Problems

We’ve spent the last couple of chapters talking about dividing fractions: how to make sense of the operation, how to picture what’s going on, and how to do the computations. But all of this kind of begs the question: When would you ever want to divide fractions, anyway? How does that even come up?

It’s important that teachers are able to come up with situations and problems that model particular operations, which means you have to really understand what the operations mean and when they are used.

Think / Pair / Share

$1\frac 3 4 \div \frac 1 2$

When to Multiply, When to Divide?

A common answer to

Come up with a situation where you would want to compute .

Is something like this:

My recipe calls for cups of flour, but I only want to make half a recipe. How much flour should I use?

$\frac 1 2$

Why is it so hard to come up with division problems that use fractions? Maybe it’s because fractions are already the answer to a division problem, so you’re dividing and then dividing some more. Maybe it’s because they just make it look so complicated. In any case, it’s worth spending some time thinking about division problems that involve fractions and how to recognize and solve them.

One handy trick: Write a problem that involves division of whole numbers, and then see if you can change the numbers to fractions in a sensible way.

Here are some division problems involving whole numbers:

Here are some very similar problems, rewritten to use fractions instead:

$1 \frac 3 4$

For each one of the fraction division questions, we can understand why it’s a division problem:

$20 \div 4$

You try it.

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Dividing fractions.

Division indicates how many times one quantity is contained in another quantity. For example, in the illustration below, you can see that the whole number 2 contains 6 thirds.

Since 2 contains 6 one-thirds, we can say that 2 divided by one-third is 6.

As you can see, dividing a first fraction by a second, nonzero fraction is the same as multiplying the first fraction by the reciprocal of the second fraction. This leads us to the following procedure.

Procedure: To divide a first fraction by a second, nonzero fraction, multiply the first traction by the reciprocal of the second fraction.

This method of dividing fractions is also referred to as invert and multiply since we are inverting the divisor and then multiplying. Basically, we are changing the division problem to a multiplication problem after inverting the divisor. This allows us to multiply the first fraction by the reciprocal of the second fraction.

Example 1: Divide.

Example 2: Divide.

In example 2, it was necessary to divide out common factors.

Example 3: Divide.

In example 3, it was necessary to simplify the result.

Example 4: Divide

Example 5: A candy bar is 3/4 of an inch long. If it is divided into pieces that are 1/8 of an inch long, then how many pieces is that?

Analysis: To solve this problem, we will divide 3/4 by 1/8.

Answer: There will be 6 pieces of candy.

Summary: To divide a first fraction by a second, nonzero fraction, multiply the first fraction by the reciprocal of the second fraction. Simplify the result, if necessary.

Directions: Divide the fractions in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

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VIDEO

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