*Contributor: Katie Schnabel. Lesson ID: 14173*

Who knew having a pizza party could turn into a fraction extravaganza? Discover how adding three fractions with different denominators may make your stomach growl.

categories

subject

Math

learning style

Auditory, Kinesthetic, Visual

personality style

Lion, Golden Retriever

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Picture this: a hot, cheesy pizza arrives at your table, and the smell of melted cheese and spicy pepperoni fills the air.

Your stomach rumbles—you and your two friends can’t wait to dig in!

- But wait, how will you divide the pizza so everyone gets their fair share?

As you each take a slice, you'll need to figure out how much of the pizza everyone has eaten.

- Ready to see how pizza can help you add three fractions?

Dive in

**It's Time for the Pizza Party Challenge!**

You and your two friends ordered three pizzas to share, but there's a twist! Each pizza was cut into a different number of pieces.

The cheese pizza was cut into 6 pieces.

The pepperoni pizza was cut into 4 pieces.

The veggie pizza was cut into 3 pieces.

The three of you dig in! You ate until you were full and couldn't stand to eat one more bite.

- But now, the big question: How much pizza did you all eat together?

You ate 2 slices of the cheese pizza or ^{2}/_{6} of the whole pizza.

Jamie ate 1 slice of the pepperoni pizza or ^{1}/_{4} of the whole pizza.

Lars ate 1 slice of the veggie pizza or ^{1}/_{3} of the whole pizza.

Now, it’s time to add up the pizza you all ate. Break it down.

**Step 1: Write the problem.**

You ate ^{2}/_{6}, Jamie ate ^{1}/_{4}, and Lars ate ^{1}/_{3}.

So this is the math problem.

2 | + | 1 | + | 1 | = | |

6 | 4 | 3 |

**Step 2: Can you add these fractions as they are?**

Nope! The bottom numbers, or *denominators*, are different.

You need to find a common denominator before adding them.

**Step 3: Find the least common multiple (LCM).**

The LCM is the smallest number all the denominators can divide into evenly. List out the multiples for each denominator.

For 6: 6, 12, 18, 24...

For 4: 4, 8, 12, 16...

For 3: 3, 6, 9, 12...

It looks like 12 is the first number they all have in common! So, the LCM is 12.

**Step 4: Convert the fractions.**

Now that you know the common denominator is 12, change each fraction so it has the same denominator.

For ^{2}/_{6}: Multiply both the top and bottom by 2. You get ^{4}/_{12}.

For ^{1}/_{4}: Multiply both the top and bottom by 3. You get ^{3}/_{12}.

For ^{1}/_{3}: Multiply both the top and bottom by 4. You get ^{4}/_{12}.

**Step 5: Add them up!**

Now that the fractions have the same denominator, you can add the top numbers, or numerators, together.

4 | + | 3 | + | 4 | = | 11 | |

12 | 12 | 12 | 12 |

So, together, you and your friends ate ^{11}/_{12} of a whole pizza!

**Try Another Example**

2 | + | 1 | + | 1 | = | ||

6 | 5 | 3 |

First, find the LCM for the denominators 6, 5, and 3.

For 6: 6, 12, 18, 24, 30…

For 5: 5, 10, 15, 20, 25, 30…

For 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

The LCM is 30!

Now, convert the fractions so they all have a denominator of 30:

Multiply ^{2}/_{6} by ^{5}/_{5} to get ^{10}/_{30}.

Multiply ^{1}/_{5} by ^{6}/_{6} to get ^{6}/_{30}.

Multiply ^{1}/_{3} by ^{10}/_{10} to get ^{10}/_{30}.

Now, add the fractions together.

10 | + | 6 | + | 10 | = | 26 | |

30 | 30 | 30 | 30 |

Yes! ^{26}/_{30}.

- Can this be simplified?

Yes! Divide both the top and bottom by 2, and you get ^{13}/_{15}.

26 | ÷ | 2 | = | 13 | |

30 | 15 |

Well done!

You’ve now mastered how to add fractions with unlike denominators.

- Ready to test your skills?

Head to the *Got It?* section to try some practice problems!