Add and Subtract Fractions
Lessons in this chapter
About Add and Subtract Fractions
Fractions and their Addition and Subtraction tackles the case 4th grade avoided: adding fractions whose denominators do not match.
Estimate Sums and Difference of Fractions comes first on purpose. Rounding each fraction to 0, a half or 1 gives a rough answer, so a child adding two thirds and three quarters expects something near one and a half, and an answer of five sevenths is visibly wrong.
Add Fractions with Unlike Denominators is the core method. The pieces have to be the same size before they can be counted together, so both fractions are rewritten with a common denominator, usually the least common multiple from 4th grade's factors chapter.
Subtract Fractions with Unlike Denominators follows the same route, with the extra complication of borrowing from a whole number when the first fraction is smaller than the second. Converting one whole into the right number of parts is the step that needs practice.
Five sevenths is exactly the answer a child gets by adding the tops and the bottoms, which is why the estimation lesson earns its place at the front of the chapter.
All three lessons open as a 5th grade math worksheet in the page. Estimate Sums and Difference of Fractions, Add Fractions with Unlike Denominators and Subtract Fractions with Unlike Denominators each set their own math problems, scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Estimate Sums and Difference of Fractions comes first on purpose, because rounding each fraction to 0, a half or 1 catches the classic error before it is made. Add Fractions with Unlike Denominators is the core method, where both fractions are rewritten with a common denominator so the pieces are the same size, and Subtract Fractions with Unlike Denominators follows the same route with the extra step of borrowing from a whole number. The chapter sits in the Common Core domain Number and Operations with Fractions (5.NF).
Because you can only count pieces that are the same size. Thirds and quarters are different sizes, so both have to be rewritten as twelfths before they can be combined.
Use the least common multiple of the two denominators. For thirds and quarters that is 12, so both are rewritten as twelfths.
Because it catches the classic error. Adding tops and bottoms turns two thirds plus three quarters into five sevenths, and an estimate of about one and a half shows instantly that it is wrong.
Borrow from the whole number by converting one whole into the same kind of parts. In 3 and one fifth minus 2 and three fifths, one whole becomes five fifths, giving six fifths to subtract from.
Adding the denominators as well as the numerators. The denominator names the size of the pieces, so it does not get added.