Expert Answers
rogal eNotes educator| Certified Educator

A fraction is made up of two parts, the numerator and the denominator. The numerator is the upper number of the fraction, while the denominator is its lower part. For example, in `\frac{2}{5}`

` `  2 is the numerator, while 5 is the denominator. ` `

In order to divide two fractions, we change the division sign into a multiplication sign. We then multiply the first fraction by the reciprocal of the second fraction.

In order to find the reciprocal of the second fraction, we turn it upside down. In other words, its numerator now becomes the denominator, and its denominator becomes the numerator. 

Here is an example:

Evaluate  `\frac{2}{7} \div \frac{5}{42}`

This becomes  `\frac{2}{7} \times \frac{42}{5}`

This gives us `\frac{12}{5}`

This can be written as `2 \frac{2}{5}`

In order to divide more than two fractions, we work from left to right and start with the first two fractions. We then follow the same steps as above.

Here is an example:

Evaluate `\frac{2}{15} \div \frac{3}{5} \div \frac{2}{3}`

Working from left to right, this becomes `\frac{2}{15} \times \frac{5}{3} \times \frac{3}{2}`

When simplified, this gives us `\frac{1}{3}` ` `

 

rmiller25 eNotes educator| Certified Educator

You divide fractions by inverting the divisor and multiplying. Take, for example, 3/8 divided by 1/4. Invert the divisor, 1/4, to make it 4/1, then multiply it times 3/8. Remember that to multiply fractions you multiply the two numerators times each other and the two denominators times each other. In this example, the two numerators are 3 and 4, and the two denominators are 1 and 8. The product of the numerators is 12, which we put over the product of the denominators, 8, giving us 12/8. Because the numerator is larger in this case (it won't always be), we generally want to change it to a mixed number. Do this by dividing 12 by 8 and writing the remainder over 8, giving 1 4/8. Reduce 4/8 to get 1 1/2.

If you start with a mixed number, you will need to change it into an improper fraction before inverting and multiplying.

dodsonangelyn | Student

There are two numbers in every fraction: the number on top is called the numerator and the number on the bottom is called the denominator. The reciprocal is found simply by reversing those two numbers.

The first step when dividing fractions is to change the division sign into a multiplication sign. Next, find the reciprocal of the second fraction simply by reversing the numerator and the denominator. Then, multiply the first fraction by the reciprocal of the second fraction. It is always best to finish a problem with fractions by reducing to the simplest form.

Here is an example: `1/4 divide 1/2` ` `

Step one: change to multiplication `1/4 times 1/2` ` `

Step two: find reciprocal of second fraction `1/4 times 2/1` ` `

Step three: multiply the numerators and the denominators `1/4 times 2/1 = 2/4`

Step four: reduce `2/4 = 1/2`

The final answer is 1/2!

baker214 | Student

Division is an operation that at its core evaluates how many groups of one number (the divisor) are in another number (the dividend).

If you think back to third grade when you first start exploring division in school typically, you may have started with a problem such as 6 divided by 2. Now, you may already know that the answer is 3, however do you remember why?

The answer is 2 because there are 2 groups of 3 in 6.

Now, let's relate this understanding to a basic fraction problem, `2 -:(1)/(4)` ``

This problem is really making us think about how many groups of one fourth there are in two wholes. Now, if we think about groups of one fourth we know that four fourths make up one whole... which leads to our understanding that eight fourths make up two wholes. Therefore if I looked at two wholes and counted the number of groups containing one fourth within those two wholes, it would be 8 groups. So, our answer is 8.

Now, reasoning through a problem like this can get very complicated when you have a higher end problem, such as `(3)/(5) -:(1)/(4)`

This is where a quick strategy called "Keep Change Flip" comes into play. Now, the mathematical way of saying this is multiply by the reciprocal, but sometimes the fancy word reciprocal can really confuse students who are just learning the division of fractions. Let's solve the problem shown above using the "Keep Change Flip Strategy." When I rewrite the problem using this strategy I keep the first fraction the same, change the division sign to a multiplication sign, and then flip the second fraction.

`(3)/(5) xx(4)/(1)`

Once you have your problem rewritten using the strategy you can use your multiplication skills to finish out the problem. Multiply the numerators, multiply the denominators, and then simplify your product if necessary.

An important note to make is that if your problem includes a mixed number, you do need to change that to a fraction greater than one before you can use the Keep Change Flip strategy.

danielchurch | Student

The simplest way to divide fractions is to multiply by the reciprocal of the divisor. The reciprocal is the inverse of a number, so to find the reciprocal simply flip the fraction upside down. For example to solve 1/2 divided by 3/4, we would instead solve 1/2 times 4/3. 1 x 4 is 4 and 2 x 3 is 6, so we get 4/6 which simplifies to 2/3. ` `

To understand why we multiply instead of dividing, we can use algebra. A fraction is actually a division problem, so 3/4 is 3 divided by 4. To solve this same problem 1/2 divided by 3/4 we could first multiply both 1/2 and 3/4 by 4. Because we make the same change to both fractions, the value of the expression does not change. 1/2 times 4 is 2 and 3/4 times 4 is 3. Now we have 2 divided by 3, which we can write as a fraction 2/3.

Important to remember:

  • Always keep the first fraction the same (the dividend)
  • Always flip the second fraction
  • Multiply the numerators and multiply the denominators
  • Simplify your answers

kmcgre4 | Student

When dividing two fractions we teach students to use the saying KCF which stands for KEEP, CHANGE, FLIP.

You must

- KEEP the first fraction the same (aka write it down the exact same way)

- CHANGE the division sign to a multiplication sign

- FLIP the second fraction. In other words we are using the reciprocal of the second fraction. You do this by switching the current numerator (top number) and the current denominator (bottom number) ex. if the second fraction reads `2/3` you would write it as `3/2` .``

Here is an example of dividing fractions using KCF

`3/4-:5/8`

You Would

- K (KEEP) the first fraction exactly the same `3/4`

- C (CHANGE) the division sign to a multiplication sign

- F (FLIP) the second fraction : `8/5`

Now we have `3/4 X 8/5`

To finish the problem we are going to multiply straight across. This means multiply both numerators (top numbers) and put that answer in the new numerator (top number).

3 X 8 = 24

Then multiply both denominators (bottom numbers) and put that answer as the new denominator (bottom number).

4 X 5 = 20

we are left with our answer of `24/20`

nchristensen145 | Student

When dividing fractions we have to be careful and know all parts of the fraction. With a whole numbers in division, we can solve by not only dividing, but multiply the first number by the reciprocal of the second number.

For example

564 `-:` 4 = 141

We would also do `564 xx 1/4 = 141`

As you see, you produce the same answer. This is the same for dividing fractions. When we divide fractions, we are actually multiplying the first fraction by the seconds reciprocal. A reciprocal is when the numerator and the denominator change places (flip).

The easiest way to remember how to divide fractions is three simple words:

KEEP. CHANGE. FLIP.

You keep the first fraction the same. Change division to multiplication. Flip the second fraction.

5/6 ÷ 2/3

Keep the 5/6 Change ÷ to X Flip 2/3 to 3/2

Your new equation

5/6 X 3/2

Now we just multiply the numerators: 5 X 3 = 15

Multiply the denominators: 6 X 2= 12

Your answer is now 15/12, but you must always simplify. You will now divide 12 into 15 to get your answer as a mixed number

15/12 = 1 3/12 which can be simplified to your final answer 1 1/4

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cupidjomo | Student

Dividing fractions is more of multiplying than dividing.

A fraction, which is made up of two parts, can be divided by another fraction or a whole number. There are two parts in a fraction, the numerator, which is the upper part and a demoninator which is the lower part of a fraction. For example, `2/3`

The 2 here is the numerator and 3 is the denominator.

When dividing fractions, for instance, `3/4 -: 1/4`

You multiply the first fraction by the reciprocal of the second fraction. ( A reciprocal is just the inverse of a fraction, you just turn it upside down and you get a reciprocal. 1/4 becomes 4/1.)

Therefore, the math will be `3/4 xx4/1`

In multiplying fractions, you first multiply the numerators and then the denominators. In this example you will have 3 x 4 and 4 x 1, which will give you 12 and 4 respectively.

Thus: `3/4 xx 4/1 = 12/4`

From the answer above, you can simplify by dividing the numerator and the denominator by 4 to get 3/1, which can simply be put down as 3. You get 3.

The same process is repeated when you divide a fraction by a whole number or vice versa. You make a reciprocal of the whole number by simply making the whole number a denominator with 1 as the numerator above it.

` `

eobrien70 | Student

To divide fractions, we use the idea of inverse operations. Multiplication and division are inverse operations; what we can multiply, we can also divide. For example, 5 x 3 = 15, so `15-:3 = 5.`

When we use inverse operations with fractions, we can change a division problem into a multiplication problem. We change the divisor (the number we're dividing by) to its reciprocal, which allows us to multiply to find the answer. You can prove that this works by using a simple example:

` `

`1-:2=1/2`

`1*1/2 = 1/2`

Once you've changed the division problem into a multiplication problem by using the reciprocal of the divisor, you follow the procedure for multiplying fractions: multiply numerators, multiply denominators. Here's another example:

`3/4-:2/5`

Use the reciprocal of the divisor in order to change the operation to multiplication:

`3/4*5/2=15/8`

You can leave your answer as an improper fraction, or use division to convert it to a mixed number:

`15-:8=1 7/8`

` `

jlrusse5 | Student

Steps to dividing fractions:

1. Write your problem out.

Example: `4/6-: 1/2 =`

2. Flip your second fraction (reciprocal fraction) and change the division sign into a multiplication sign.

Example: `4/6 x 2/1 =`

3. Solve the problem.

`4/6 x 2/1 = 8/6`

4. Simplify your answer and/or change your answer into a mixed number.

Example: `8/6 = 1 2/6 = 1 1/3`

` `

` `

cheyenneb-95 | Student

I use a simple three step process for when divide fractions.

Step one: Turn the second fraction the one that you want to divide by upside down this is now reciprocal. (Reciprocal means: a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.)

Step two: Multiply the first fraction by that reciprocal.

Step three: Simplify the fraction if it is needed.

Example: 1/2 divided by 1/6

Step 1: 1/6 - 6/1

Step 2: 1/2*6/1= 1*6/2*1=6/2

Step 3: 6/2=3

siddhar-8 | Student

A fraction contains two parts, a numerator (upper one) and a denominator (lower one). In smaller classes we had studied that if the one fraction is divided by the other fraction, we need to evaluate that by using reciprocal method. Its the easiest and convenient wy to solve a fraction.

e.g.:-(2/7)÷(4/21).

Now the sign of division ➗ changes to tge sign of multiplication ✖ and (4/21) becomes (21/4).

i.e., (2/7)×(21/4)

Now,2 divides the 4 by 2 and 7 divides 21 by 3 and you wil got, (3/2) as an answer.

There are few solved questions in given image, you can take help from there and keep practising.

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s2001-sidd | Student

A fraction consist of two parts. 1st one is numerator which is upper value and second one is denominator which is lower value. U just have to do that see that ques. Quietly and then.. Follow below steps.

e.g.:- anwer is in image with ques..

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apawola | Student

In order to divide fractions, use the strategy "Keep, Change, Flip". Using this strategy, you "keep" the first fraction the same, "change" the division sign to a multiplication sign, and "flip" the second fraction, so that the numerator (top number) becomes the denominator (bottom number), and vice versa. You then multiply straight across. Multiply the two numerators by each other and then multiply the two denominators by each other.

For example:

2/3 `-:` 4/5

This problem would become 2/3 x 5/4 = 10/12

You can then simplify the answer by dividing the numerator and denominator by the Greatest Common Factor, of GCF. 10 and 12 are both divisible by 2, so dividing both 10 and 12 by the GCF would simplify the fraction to 5/6. Thus, the answer is 5/6.

There will be some problems that will end with an improper fraction as the answer. In those instances, you would need to change the improper fraction to a mixed number by dividing the numerator by the denominator. Use long division, and write your remainder as a fraction.