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.

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.

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