Dan bought cupcakes for the birthday party. 5/12 of the cupcakes were blueberry, 1/3 of the cupcakes were chocolate chip, and there were 9 plain cupcakes. How many cupcakes did Dan buy for the birthday part in total

To find the total number of cupcakes Dan bought for the birthday party, we need to sum up the fractions of cupcakes for each flavor and the plain cupcakes.

Given:

- 5/12 of the cupcakes were blueberry,

- 1/3 of the cupcakes were chocolate chip, and

- There were 9 plain cupcakes.

First, let's find the total fraction of cupcakes for each flavor:

Blueberry cupcakes: 5/12

Chocolate chip cupcakes: 1/3

Now, let's find a common denominator to add these fractions:

The least common multiple (LCM) of 12 and 3 is 12.

So, to make the denominators the same, we can rewrite the fractions with a denominator of 12:

Blueberry cupcakes: (5/12) * (12/12) = 5/12

Chocolate chip cupcakes: (1/3) * (4/4) = 4/12

Now, let's add these fractions together:

Total cupcakes for blueberry and chocolate chip flavors: 5/12 + 4/12 = 9/12

Now, let's add the plain cupcakes:

Total cupcakes = Total cupcakes for blueberry and chocolate chip flavors + Plain cupcakes

Total cupcakes = 9/12 + 9 (since there were 9 plain cupcakes)

To add the fractions and the whole number, we need to express 9 as a fraction with a denominator of 12:

9 = (9 * 12) / 12 = 108/12

Now, let's add:

Total cupcakes = 9/12 + 108/12 = (9 + 108) / 12 = 117/12

Now, let's simplify the fraction:

117/12 = 9 9/12

So, Dan bought a total of 9 9/12 cupcakes for the birthday party.

9 9/12 cupcakes can be simplified to 10 cupcakes and 1/2 cupcake, but it's uncommon to have a fraction of a cupcake, so we typically consider it as 10 cupcakes.

Therefore, Dan bought a total of 10 cupcakes for the birthday party.