Subtracting Fractions With Common Denominators
Subtracting fractions with common denominators is a Grade 6 math skill in Saxon Math, Course 1 that establishes the foundational rule: when fractions share the same denominator, subtract the numerators and keep the denominator unchanged. For example, 7/9 − 3/9 = (7−3)/9 = 4/9. Students also apply this to mixed numbers when the fraction parts have the same denominator. The result must always be simplified to lowest terms. If the first numerator is smaller than the second in a mixed number subtraction, borrowing (regrouping) from the whole number part is required—a key skill for more complex fraction subtraction.
Key Concepts
Property When subtracting fractions that have the same denominator, we subtract the numerators. The denominator does not change. This rule can be written as $ \frac{a}{c} \frac{b}{c} = \frac{a b}{c} $.
Examples $ \frac{5}{8} \frac{2}{8} = \frac{3}{8} $ $ \frac{7}{8} \frac{2}{8} = \frac{5}{8} $ $ \frac{3}{4} \frac{2}{4} = \frac{1}{4} $.
Explanation Picture a chocolate bar with 8 squares. If you start with 7 squares and eat 2, you're left with 5. You only subtracted the number of squares you had (the numerators), not the total number of squares the bar was broken into (the denominator). So, keep the bottom number the same and just subtract the top numbers!
Common Questions
How do you subtract fractions with the same denominator?
Subtract the numerators and keep the denominator the same. For 8/11 − 3/11: subtract numerators (8 − 3 = 5) and keep the denominator 11, giving 5/11.
Do you ever change the denominator when subtracting fractions with common denominators?
Never. The denominator represents the size of each part and stays the same. Only the numerators change.
What should you do after subtracting fractions?
Check if the result can be simplified. Find the GCF of the numerator and denominator and divide both. For example, 6/8 simplifies to 3/4 by dividing by 2.
What is borrowing in fraction subtraction?
When subtracting mixed numbers and the first fraction is smaller than the second (like 3 1/5 − 1 4/5), borrow 1 from the whole number, converting it to 5/5, then add it to the fraction: 3 1/5 becomes 2 6/5.
Why is having a common denominator necessary for fraction subtraction?
To subtract, the parts must be the same size. Fractions with different denominators represent different-sized pieces and cannot be directly subtracted, just as you cannot subtract inches from centimeters without converting.