Smart ways to multiply and divide
Multiply and divide by 5, 25, 50, 11, 101, 9 and 99 in handy ways, as the book does.
- Germany: grade 5
- Ukraine: grade 3
- Russia: grade 3
Guide
A studio for Ukrainian grade 3 (НУШ textbooks, part 2, «rational ways of calculating»). The book shows that multiplying by 25 can go through 100: a · 25 = a · 100 : 4. And dividing by 25: a : 25 = a · 4 : 100.
Multiplying by 5 and 50 goes through 10 and 100 and halving: a · 5 = a · 10 : 2, a · 50 = a · 100 : 2. Multiplying by 11 and 101 uses addition: a · 11 = a · 10 + a, a · 101 = a · 100 + a. Multiplying by 9 and 99 uses subtraction: a · 9 = a · 10 − a, a · 99 = a · 100 − a.
In each task build such a line from the cards and find the result. Multiplying by 25 is handier with numbers divisible by 4, and by 5 with even numbers.
The «why?» question asks why the method works.