Deepen your understanding of rational numbers — their properties, and how to add and subtract them with confidence.
Rational numbers follow the commutative property (order doesn't matter for addition/multiplication), the associative property (grouping doesn't matter), and the distributive property (a × (b + c) = a×b + a×c).
Verify the commutative property for addition: 2/3 + 1/4 and 1/4 + 2/3.
2/3 + 1/4 = 8/12 + 3/12 = 11/12; 1/4 + 2/3 = 3/12 + 8/12 = 11/12 — both equal
Use the distributive property to find: 3/4 × (2/5 + 1/5)
3/4 × 3/5 = 9/20
To add or subtract rational numbers, first convert them to a common denominator, then combine the numerators while keeping the denominator the same.
Find: 2/5 + (−3/10)
4/10 + (−3/10) = 1/10
Find: (−5/6) − (−1/3)
(−5/6) − (−2/6) = (−5/6) + 2/6 = −3/6 = −1/2
1. Verify the commutative property for addition: −1/3 + 2/5 and 2/5 + (−1/3).
2. Find: 3/7 + (−2/7)
3. Find: (−4/9) − (−2/3)
4. Use the distributive property to find: 2/3 × (1/2 + 1/4)
5. Find: 5/8 + (−3/4)