The Great Fraction Subtraction
Subtracting fractions with unlike denominators requires three steps—Shape, Operate, Simplify. In Grade 6 Saxon Math Course 1 (Chapter 6: Geometry and Number Operations), students first find the LCD (Shape), rename both fractions with that denominator, then subtract the second numerator from the first while keeping the denominator (Operate), and finally reduce the result to lowest terms (Simplify). For 5/6 - 1/4: LCD = 12; rename as 10/12 - 3/12 = 7/12. Students also handle subtraction requiring renaming when the first numerator is smaller than the second after reaching a common denominator.
Key Concepts
Property To subtract fractions, first give the fractions a common denominator (Shape). Next, subtract the second numerator from the first while keeping the denominator the same (Operate). Lastly, reduce the resulting fraction to its simplest form if you can (Simplify).
Examples $\frac{5}{6} \frac{1}{2} \rightarrow \text{Shape: } \frac{5}{6} \frac{3}{6} \rightarrow \text{Operate: } \frac{2}{6} \rightarrow \text{Simplify: } \frac{1}{3}$.
$\frac{7}{10} \frac{1}{2} \rightarrow \text{Shape: } \frac{7}{10} \frac{5}{10} \rightarrow \text{Operate: } \frac{2}{10} \rightarrow \text{Simplify: } \frac{1}{5}$.
Common Questions
What are the three steps for subtracting fractions with unlike denominators?
Shape: find the LCD and rename both fractions. Operate: subtract the numerators, keep the denominator. Simplify: reduce the result to lowest terms.
Subtract 5/6 minus 1/4.
LCD = 12. Rename: 10/12 - 3/12 = 7/12. Already in lowest terms.
Subtract 3/4 minus 2/3.
LCD = 12. Rename: 9/12 - 8/12 = 1/12.
Do you subtract the denominators when subtracting fractions?
No. Only the numerators are subtracted. The denominator stays the same once a common denominator has been found.
What happens if after renaming the first numerator is smaller than the second?
You need to regroup (borrow 1 from the whole number if it is a mixed number, converting it to an equivalent improper portion) before subtracting.