Subtraction of Mixed Numbers
Welcome to our lesson on subtracting mixed numbers! This is an important skill that builds on what you already know about fractions and will help you solve many real-world problems.
What is Subtracting Mixed Numbers?
Subtracting mixed numbers means finding the difference between two mixed numbers.
Remember: A mixed number has two parts:
Whole Part + Fractional Part
For example: 3¾ − 1½ means finding what remains after taking away 1½ from 3¾.
Important: Unlike addition, order matters in subtraction! Always subtract the smaller number from the larger one to get a positive result.
Visual Understanding
Visual representation: 3¾ − 1½ = 2¼
METHOD 1: Subtracting Parts Separately
Same Denominators (No Borrowing)
Steps:
- Check that the first fraction ≥ second fraction
- Subtract the whole numbers
- Subtract the numerators
- Keep the denominator the same
- Simplify if needed
Example: 5⁴⁄₇ − 2²⁄₇
= (5 − 2) + (⁴⁄₇ − ²⁄₇)
= 3 + ²⁄₇
= 3²⁄₇
When Borrowing is Needed
When? When the fraction being subtracted is LARGER than the first fraction.
Example: In 5²⁄₅ − 2⁴⁄₅, we can't do ²⁄₅ − ⁴⁄₅ directly!
How Borrowing Works:
- Borrow 1 from the whole part
- Convert 1 to a fraction: 1 = n⁄n
- Add to the existing fraction
- Now subtract normally