Adding Fractions Adventure
Adding fractions follows a three-step method: Shape (find the common denominator), Operate (add the numerators keeping the denominator), Simplify (reduce the result to lowest terms). In Grade 6 Saxon Math Course 1 (Chapter 6: Geometry and Number Operations), students find the LCD of the two denominators, rename each fraction as an equivalent one with that LCD, then add. For 1/4 + 2/3: LCD = 12; rename as 3/12 + 8/12 = 11/12. If the sum is improper, convert to a mixed number. The Shape-Operate-Simplify framework applies to both two-fraction and multi-fraction addition.
Key Concepts
Property To add fractions, you must first reshape them to have a common denominator. Once they are in the correct shape, operate by adding the numerators together while keeping the denominator the same. Lastly, simplify the resulting fraction or mixed number if possible.
Examples $\frac{1}{2} + \frac{1}{6} \rightarrow \text{Shape: } \frac{3}{6} + \frac{1}{6} \rightarrow \text{Operate: } \frac{4}{6} \rightarrow \text{Simplify: } \frac{2}{3}$.
$\frac{2}{3} + \frac{1}{4} \rightarrow \text{Shape: } \frac{8}{12} + \frac{3}{12} \rightarrow \text{Operate: } \frac{11}{12} \rightarrow \text{Simplify: Stays } \frac{11}{12}$.
Common Questions
What are the three steps for adding fractions?
Shape: find the LCD and rename fractions. Operate: add the numerators, keep the denominator. Simplify: reduce to lowest terms or convert an improper fraction to a mixed number.
Add 1/4 and 2/3.
LCD = 12. Rename: 3/12 + 8/12 = 11/12.
Add 5/6 and 3/4.
LCD = 12. Rename: 10/12 + 9/12 = 19/12 = 1 and 7/12.
Do you add the denominators when adding fractions?
No. Only the numerators are added after both fractions have been renamed with a common denominator.
Add 2/5 + 1/2.
LCD = 10. Rename: 4/10 + 5/10 = 9/10.