2 ways to divide a whole number by a fraction

Just when you thought you had division down, the teacher asks you to divide a whole number by a fraction!

"WHAT?! Is that even possible?", you might think.

Take a deep breath and let me show you a couple of ways you can make that happen!

Images created by Wendy F. McMillian

Before you start dividing fractions, you need to understand how division works. Division splits things into equal parts or groups, and is the result of "fair sharing".

Take the example above. The problem is asking how many 2s are in 6. The answer is three.

You could also say that you're taking 6 items and splitting them into equal parts of 2, with 3 items in each group.

Think of it like this: I have 6 cookies that I want to divide between 2 friends. How many cookies will each friend get? The answer is 3.

Dividing Fractions

This same concept applies to dividing whole numbers by fractions, only now you're being asked how many fractional parts are in a whole part.

Take a pizza, for example.

You have one whole pizza, but you want to divide it among your 8 friends. How many slices (or fractional parts) of the pizza will each person get?

The answer depends on how you slice the pizza! 🍕

If you made 4 diagonal cuts (as shown in the picture), you would have exactly 8 pieces. Each person would get 1/8 of the pizza.

Remember!

A fraction tells you:

• How many parts (numerator)

• The whole (denominator)

If you have 8 slices (whole/denominator) and give each person 1 slice (part/numerator), each person has 1/8 of a whole pizza.

One way to divide a whole number by a fraction is by using a visual model. Visual models help you see how a whole can be divided.

Fraction bars, for example, allow you to see how a whole can be broken into parts (fractions). They provide a visual way to see fractions.

You can easily see how a whole can be 2 halves, or 10/10ths.

You can also see how many 1/8ths are in a whole: 8!

What happens when you have more than one whole to divide?

Like this problem:

Let's draw it out. Take a look at this picture of two wholes:

Now, divide each whole into four sections. Like this:

So, how many of the four sections do we have? 8

Think of it like this: you have two whole pizzas and want to divide them into 4 slices each. How many slices would you have? You'd have 8.

You can easily divide a fraction by multiplying a whole number by the reciprocal of the fraction. You can use "KEEP, CHANGE, FLIP" to remember it.

Let’s look at the previous example again:

Remember that division and multiplication are inverse operations. This means you can undo division with multiplication or vice versa.

Reversing the division problem, we can say, "What number, when multiplied by 1/4, will give me 2?" The only answer that will work is 8.

If you...

• keep 2

• change the division to multiplication,

• flip 1/4 to 4/1

...you'll get the same answer!

Photo by Thought Catalog on Unsplash

Now it's time to practice dividing a whole number by a fraction! If you need some additional help, check out these resources: