# Fractions

Everyone likes pizza, so let’s pretend we’ve ordered a large pizza from our favorite Italian restaurant. The restaurant cuts one large pizza into 8 slices. As soon as the pizza arrives, you grab two piping hot slices and, as the cheese is sliding off the slice, stuff them into your mouth. You have just eaten a fraction of the pizza – 1/4 to be exact.

Simply put, a fraction is one part of a whole. You have less than one whole thing, but more than zero of that same thing. You only have one part of it.

A fraction just tells you how much of that part you have. It’s simply a number between two whole numbers. Not quite one whole number, but not quite another. Just somewhere in the middle.

In this case, you ate a part of the pizza, so therefore you ate only a fraction of it. Now you see that learning fractions for dummies isn’t so hard when you use food references, right?

Now, fractions have two numbers – a top number and a bottom number.

The bottom number is called the denominator. It tells us how many parts the whole has been divided into. In our pizza example from above, the denominator is eight because the whole pizza was divided into eight slices.

The top number in a fraction is called the numerator. It tells you how many of the parts you have. In our pizza example from above, the numerator is two because you ate two slices.

If the pizza had four slices and you ate three, what fraction (part) would you have eaten? Four is the number of parts (slices) the whole pizza has been divided into. Therefore, four is our denominator.

You ate three slices, so the numerator (the number of parts you have) is three. Your fraction in the new example is 3/4.

**Fraction Number Lines**

Remember that when we’re talking about fractions, we’re talking about equal parts of a whole.

This means that when we put fractions on a number line, those fractions are always going to show up between two whole numbers on the line.

You can think of it like a ruler. On a ruler, there are large whole numbers between 1 and 12 marked to denote each increasing inch (1, 2, 3, and so on). Between those whole numbers are smaller tick marks that represent the measurements in between those whole numbers. They represent fractions of an inch – not quite an entire inch.

When putting fractions on a number line, it’s helpful to start with two whole numbers at each end of the line, depending on what the fraction is. For instance, if the fraction is 1/3, it is between whole numbers 0 and 1. If the fraction is 1 1/3 (one whole and 1/3 of a whole), it would be placed between whole numbers 1 and 2 because it is more than 1 but not quite 2. If the fraction is 2 1/3 (2 wholes and 1/3 of a whole), it would be placed between whole numbers 2 and 3 because it is more than 2 but not quite 3.

For our first example, let’s stick with 1/3. In order to place 1/3 on a number line, it is helpful to place 0 and 1 as the whole numbers at each end of the line since 1/3 is between 0 and 1. Then, since fractions represent equal parts of a whole, go ahead and divide the number line into equal parts. Each time, the denominator will tell us how many parts in which to divide the line. In this case, it is three.

**0 ——————– ——————– ——————– 1**

The first section of the line would be 1/3, the first two sections 2/3, and all three sections 3/3 (or one whole).

To properly place more than one fraction on a number line, it is important to first understand how to compare and order fractions. This is easiest if the fractions have the same denominator. If this is the case, simply order the fractions from least to greatest based on their numerators and place them on the number line as you have learned above.

**Remember: the smaller the denominator, the bigger the fraction! This is the opposite of what most people have learned when it comes to numbers, but it is essential knowledge for placing fractions on a number line.**

If each number does not have the same denominator, we much first find the least common denominator. This is the smallest number that can function as the same denominator for all of our fractions so that we can compare and order them. There are a few ways to do this:

- Multiply all denominators together.
- List the multiples of all denominators and find the smallest number that each has in common.

For example, if we want to compare 1/3 and 1/6, we would simply list the multiples for each denominator:

Multiples of 3: 3,6,9,12,15,18,21,24…

Multiples of 6: 6,12,18,24,30, 36…

The smallest number that each has in common is 6. This is the least common denominator. Now, we’ll have to turn 1/3 into an equivalent fraction by ensuring that it has a denominator of 6. To do this, we’ll simply multiply the numerator by the same number we multiplied the denominator by. Since we multiplied 3 x 2 to get a denominator of 6, we’ll have to multiply 1 x 2 to get a numerator of 2.

Now, try placing 1/6 and 2/6 on a number line.

0 ————————————————————————————- 1

**How To Do Fractions Step By Step**

Next, we’ll show you four ways to do fractions using the basic mathematical functions of addition, subtraction, multiplication, and division.

**Adding & Subtracting Fractions:**

In order to add fractions, you’ll first want to make sure they both have a common denominator. Use the method from the previous section to find the LCD / equivalent fraction for 1/3 + 1/6.

Once you have two fractions with the same denominator (in this case the LCD is 6), then simply add the two numerators together to get one fraction:

2/6 + 1/6 = 3/6

In this case, the fraction needs to be simplified, which simply means reduced to its lowest form. To accomplish this, we will divide the numerator and denominator by the same number, which is 3.

Once we do that, our final answer will be 1/2.

The process is the exact same for subtracting fractions. Just replace the addition sign with a subtraction one!

**Multiplying Fractions:**

The good news is that multiplying fractions is just as simple as adding them.

First, you’ll simplify the fractions as much as you possibly can. Then, you’ll multiply the numerators. Then, multiply the denominators. You will use those numbers to form your new fraction.

Here’s an example:

1/5 x 2/3 = 1×2/5×3 = 2/15

**Dividing Fractions:
**

Dividing fractions is a little more complicated, but not terribly so. We’ll start the process with: 2/3 ¸ 1/4.

First, we’ll have some fun by turning our second fraction upside down. This is called making a reciprocal fraction. Now 1/4 will become 4/1.

Then, we’ll multiply the fractions just like we did in the last example. 2 x 4 / 3 x 1 = 8 / 3.

We could leave the answer as an improper fraction (one where the numerator is larger than the denominator), but it’s probably best to simplify it and make it a mixed number (a combination of a whole number and fraction).

In this case, our final answer is 2 2/3 (2 wholes and 2/3 of a whole).

**Fraction Calculator**

Using a fraction calculator is difficult because most traditional calculators don’t allow for entering fractions in their numerator/denominator form. For those who want to work with fractions using a standard calculator, it is best to turn those fractions into decimals. Luckily, this is very easy to do by pushing just a few buttons.

In order to turn a fraction into a decimal using a calculator, we simply need to treat the fraction like a division problem, dividing the top number by the bottom number. For example, if we want to turn 1/6 into a decimal, we simply type in: 1 (division sign or slash, depending on your computer) 6. That will give us the number 0.166666666…. which is the decimal equivalent of 1/6.

When it comes to working with a mix fraction calculator, the same principal applies. The only change is that the whole number in the mixed fraction will go in front of the decimal. Sticking with our earlier example, 1 1/6 would be 1.166666666…

**Practice Fractions For Adults**

While there are many fractions worksheets with answer key to be found online, here are just a few problems to get you started with testing your knowledge of what you have just learned:

- Sam has one medium pizza cut into six slices. Sam and a friend each eat one slice of the pizza. How much of the pizza did they eat? Express your answer in fraction form.

- Identical twins Mary and Missy had two cakes at their birthday party. Mary’s friends ate 2/3 of her cake, while Missy’s friends ate 1/6 of her cake. How much cake was left for the twins to take home at the end of their party. Hint: add the two values together to get your answer.

- Place the fraction 5/6 on a number line.