Laws of operations and convenient calculation
Use the commutative, associative and distributive laws to calculate conveniently, and simplify expressions with rational numbers.
- Germany: grade 5
- Ukraine: grade 5
Guide
This follows the Ukrainian books: Year 5 item 7 "Properties of addition" and item 17 "Associative and distributive properties of multiplication"; Year 6 part 2 items 33, 36 and 37 (the same laws for rational numbers, the coefficient). The child picks a convenient order or types the answer on the keypad under the exercise.
Commutative law of addition: a + b = b + a. Associative: (a + b) + c = a + (b + c). For multiplication likewise: (ab)c = a(bc). Distributive law: a(b + c) = ab + ac. It also holds for subtraction and for all rational numbers.
These laws are for calculating conveniently: 64 + 23 + 77 = 64 + (23 + 77) = 64 + 100, and 25 · 867 · 4 = 867 · (25 · 4) = 867 · 100.