Adding Fractions

I had a question about adding fractions and I wanted to explain the way I teach it.

Numerator- the number on top that tells me how many parts I have

Denominator- the number on the bottom that tells me how many parts make one whole

When you add fractions you ONLY add the numerators, because the amount that it takes to make one whole would still be the same.

For example... If I had two pies that were cut into six slices each, and I had four of those slices.. the fraction is 4/6. The the next week I have 3 slices, the fraction sentence would be 4/6 + 3/6 = 7/6
7/6 is an improper fraction because the numerator is greater than the denominator.
If I wanted to change it into a mixed number, I would have to write how many WHOLES I have, as well as the fractional part.
6/6 is one whole, so in 7/6 I have one whole and 1/6 left over.

Drawing pictures is so helpful for these concepts. I am constantly drawing circles and cutting them  up.

Fractions can also be parts of a group.
For example. I have a class of 17 students. 8 of those students are boys. The fraction of boys in my classroom is 8/17. If I add the fraction of boys 8/17 plus the fraction for girls 9/17, I get one whole class!

If I have 17 kids make up one class, but then I have three more students who aren't in my class show up... My fraction is 17/17 plus 3/17 = 20/17 because now I have more kids than make up one class.

I hope this helps!