Why divide fractions

Can that help us compute fraction division? For each division problem, rewrite it as a missing factor multiplication question. Then find the quotient using what you know about multiplying fractions. Skip to content Fractions. We conclude But how much more? Can we figure it out exactly? We conclude:. Common denominator method If two fractions have the same denominator, then when you divide them, you can just divide the numerators.

Is the method useless, or can you find a way to make it work? Since they will be entering an advanced program in science and math, those are the areas we're concentrating on.

In a review of fractions, I stumbled when I could not come up with a practical explanation of how division of fractions works.

Other than stating the rule about inverting the second fraction and multiplying to get the correct answer, I could not give a concrete example to help them understand the concept.

However, I was unable to explain why division using whole numbers results in a smaller amount, but dividing by fractions produces an answer greater than what you started with. I hope I am clear. The kids left a few moments ago and my brain still feels like mush.

Doctor Twe took it on, starting with an abstract view: You're right, dividing fractions is confusing and seems counterintuitive. The logic, of course, is that division is the inverse function of multiplication. But that is distinctly unsatisfying. The "real world" doesn't provide much help, either. There simply aren't many examples in the real world of dividing by a fraction. When we visualize division, we picture splitting something into more than one part - not less than one part.

The first one is nice because it correlates directly with what we do with integers. Here they are: Integer example: I went to a dairy farm and bought a gallon canister of milk. The canister won't fit in my refrigerator, so I want to pour it into several 2-gallon jugs. How many jugs do I need?

How many containers do I need? This shows that dividing a fraction by a smaller fraction produces a value larger than one you need more than one of the smaller containers. Then, as I did in one answer above, he observed that this example motivates a different method of division: This also demonstrates an alternative way to solve dividing fractions.

The "real world" problem can be solved using integers by converting the quantities to pints. The equivalent mathematical operation is called "eliminating the fraction," and is accomplished by multiplying both the dividend and divisor by a number that will eliminate the denominators.

The most efficient value to use is the Least Common Multiple LCM of the denominators of the two fractions - in this example 8.

Eliminating the fraction can be accomplished by multiplying both the dividend and divisor by A final thought: We eliminate the fraction in the "real world" situations by converting to a smaller unit pints instead of gallons, or minutes instead of hours. Take a look at the example below:. Imagine the example equation as a cake. You can solve most division problems by following these three steps:.

A reciprocal is what you multiply a number by to get the value of one. If you want to change two into one through multiplication you need to multiply it by 0.

In fraction form this looks like:. To find the reciprocal of a fraction you simply flip the numbers. The denominator becomes the numerator and vice versa. Dividing and multiplying are opposites of each other.

In a division problem, when you turn the divisor into a reciprocal, you also need to change the equation from division to multiplication.

Fractions symbolize a part of a whole. This means many fractions represent the same value, so why not make the fraction as simple as possible? To get a fraction down to its simplest form, you divide the numerator and denominator by their greatest common factor.

Creating a reciprocal and multiplying an equation rather than dividing lets you skip several steps in an equation. The three-step strategy is great for basic fraction problems, but what happens when you run into whole numbers, mixed fractions, improper fractions, and word-based problems? The process remains the same for the most part, but depending on the type of problem, there could be a couple more steps. An improper fraction is when you have a numerator with a value that is greater than the denominator.

Seeing these fractions can cause confusion, but the order of operations does not change. No matter where the improper fraction is placed, you still flip the divisor into a reciprocal and then multiply the two fractions. A mixed fraction is when you have a whole number along with a fraction. How do you divide a mixed fraction? Change your mixed fraction into an improper fraction and then proceed with the three-step strategy. Using this pattern, we determine that dividing the 20 screwdrivers by a number less than 1 would get us a larger answer than if we divided the 20 by 10, 5, or 2.

This does not mean that we end up with 40 screwdrivers, though. What it means is that we end up with 40 parts of screwdrivers. You have to imagine that each of the screwdrivers were split into 2.

Twenty screwdrivers split in half would give us 40 pieces in the end. The question now becomes, how do we do this mathematically? The answer lies in using what is known as a reciprocal.

Here is the definition. Reciprocal : A number that has a relationship with another number such that their product is 1. This means that, when you take a number such as 5 and then multiply it by its reciprocal, you will end up with an answer of 1.

We could also write the number 5 as a fraction.