How Do You Divide 2 Fractions

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This article is written by David Jia. David Jia is an academic tutor and founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grade levels in a variety of subjects, as well as advising on college admissions and exam preparation for the SAT, ACT, ISEE, and more. After scoring a perfect 800 in math and a 690 in English on the SAT, David received a Dickinson Scholarship from the University of Miami, where he graduated with a bachelor’s degree in business administration. In addition, David has worked as an online video instructor for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

How Do You Divide 2 Fractions

How Do You Divide 2 Fractions

Dividing fractions by a whole number is not as difficult as it may seem. To divide a fraction by a whole number, all you need to do is convert the whole number into a fraction, find the reciprocal of that fraction, and multiply the result by the first fraction. To learn how to do this, follow these steps:

Dividing Mixed Number By Fractions Worksheets

This article is written by David Jia. David Jia is an academic tutor and founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grade levels in a variety of subjects, as well as advising on college admissions and exam preparation for the SAT, ACT, ISEE, and more. After scoring a perfect 800 in math and a 690 in English on the SAT, David received a Dickinson Scholarship from the University of Miami, where he graduated with a bachelor’s degree in business administration. In addition, David has worked as an online video instructor for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 826,472 times.

How Do You Divide 2 Fractions

To divide a fraction by a whole number, first write the whole number down to 1 to make it look like a fraction. Then, by changing the numerator and denominator, find the reciprocal of the whole number. Your reciprocity must be equal to 1 in the whole number. When you “divide” fractions by whole numbers, you are actually multiplying the fraction by the reciprocal of the whole number. To do this, multiply the numerator and denominator of the two fractions. Finally, simplify the result as much as possible. If you want to learn more, like how to simplify a subtraction after you’re done, read on! Welcome to this free step-by-step guide to fraction division. This guide will teach you how to use a simple three-step method called Keep-Change-Flip to easily divide fractions by fractions (as well as fractions by whole numbers).

Below are several examples of dividing fractions using the Keep-Change-Flip method, along with an explanation of why this method works for any math problem involving division of fractions. Plus, this free guide includes an animated video lesson and a free practice sheet with answers!

How Do You Divide 2 Fractions

Dividing Fractions: 3/5 ÷ 1/2 (video)

Before you learn how to divide fractions using the Keep-Change-Flip method, you need to know how to multiply fractions (which is even easier than division!).

Because fraction multiplication is usually taught before fraction division, you may already know how to multiply two fractions together. If so, you can move on to the next section.

How Do You Divide 2 Fractions

Rule for multiplying fractions: Whenever you multiply fractions together, multiply the numerators and then multiply the denominators as follows.

Using Subtraction To Divide Fractions

Now that you know how to multiply fractions, you’re ready to learn how to divide fractions using the simple 3-step Keep-Change-Flip method.

How Do You Divide 2 Fractions

To solve this example (and any problem where you need to divide fractions, we’ll use the Keep-Change-Flip method)

If we think of 1/2 ÷ 1/4 in the form of a question, how many 1/4 are there in 1/2?

How Do You Divide 2 Fractions

Unit 3 Fractions Preview

And then if we visualize 1/4 and 1/2, we clearly see that there’s 2 1/4 in 1/2, and therefore the final answer is 2.

As in example 01, you can solve this problem with the keep change flip method as follows:

How Do You Divide 2 Fractions

What if you want to divide a fraction by a whole number? The process appears to be exactly the same as the previous examples!

Ex 2.7, 5

Note that in this example you are dividing a fraction by a whole number. But actually converting a whole number to a fraction is very simple. All you need to do is rewrite the number as a fraction, where the numerator and denominator are 1.

How Do You Divide 2 Fractions

Now that you’ve rewritten the whole number as a fraction, you can use the Keep-Change-Flip method to solve the problem.

Watch the video lesson below to learn how to divide fractions by fractions and fractions by whole numbers:

How Do You Divide 2 Fractions

Dividing Fractions Maze 1

Looking for extra fraction division practice? Click on the links below to download free worksheets and answer keys: This just means that we will flip the fraction so that the numerator is converted to the denominator and the denominator is converted to the numerator.

We care because it helps us create a sense of identity. In other words, when a number is multiplied by its reciprocal, it always equals one!

How Do You Divide 2 Fractions

Throughout this lesson we will learn that the reciprocal of a whole number is always a unit fraction. The multiplicative inverse of a complex number will always be a true fraction.

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The converse is key to fraction division because the only operations we are allowed to do on fractions are:

How Do You Divide 2 Fractions

So we need to have a way to convert division into a reverse multiplication operation, and the way we do that is reverse our subtraction!

Before we get into the steps, let’s see a visual representation of how diving fractions work by looking at an area model.

How Do You Divide 2 Fractions

Fractions Multiply And Divide, Free Pdf Download

And as we saw with multiplication, although an area model represents the process of division, its use is not always practical.

Now we evaluate our numerical expression by multiplying the first fraction by three-fifths by the reciprocal of the second fraction.

How Do You Divide 2 Fractions

We’ll also see that our rules will be useful for multiplying fractions too, because after converting our division problems as mentioned on the prodigy blog, we want to reduce our fractions before multiplying. The math you did in grade school sounds scary. for adults because there are many special rules and words. And dividing fractions is no different: you need to flip fractions and know words like divisor and divisor and reciprocal. It may seem difficult to remember, but with a little practice you won’t succeed.

Multiplying And Dividing Fractions Exercise

Because math is all about remembering rules and terms, and if you can do that, dividing fractions is pretty easy. Division is the inverse of multiplication, so one thing to remember when dividing fractions is that the answer is always greater than any part of the problem. You are actually trying to figure out how many divisors (the second number in the problem) can be found in the dividend (the first number).

How Do You Divide 2 Fractions

The first step in dividing fractions is to look at both fractions, take a deep breath, and tell yourself that if a sixth grader can do it, you can probably do it too.

The first step is that simple. Suppose you are trying to find the answer 2/3 ÷ 1/6. Do nothing! Keep these numbers as they are.

How Do You Divide 2 Fractions

How To Visualise Dividing With Fractions

The second step is to multiply two fractions. So you just need to change the ÷ sign to the x sign: 2/3 ÷ 1/6 becomes 2/3 x 1/6.

The third step is to do the reciprocal of the divisor – but don’t be afraid! It just means you’re returning the numerator (top number) and denominator (bottom number) of the fraction to the right of the division sign, called the divisor.

How Do You Divide 2 Fractions

For example, if you divide 2/3 by 1/6, you start working on the problem by flipping the divisor: 2/3 x 6/1 = 12/3.

How To Divide Fractions In 3 Easy Steps With Examples, Worksheets & More

The fraction may no longer be a true fraction, in which case it will be less than the denominator. This is an improper fraction, meaning that the number represented by the fraction is greater than 1.

How Do You Divide 2 Fractions

No, it’s close, but not quite your definitive answer. All you have to do is simplify the fraction 12/3. You do this by finding the largest number that is divisible by the numerator and denominator, which in this case is 3, meaning the fraction simplifies to 1/4, or just 4.

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How Do You Divide 2 Fractions

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