Multiplying and dividing by parts
Multiply and divide two-digit numbers by one-digit numbers by splitting the number into easy parts, and check with the inverse operation.
- Russia: grade 3
Guide
To multiply 23 · 4, split 23 into tens and ones, multiply each part and add: 23 · 4 = (20 + 3) · 4 = 20 · 4 + 3 · 4 = 80 + 12 = 92. This method is taught in Grade 3 in Russian schools.
To divide, split the dividend so that both parts divide exactly by the divisor: 48 : 3 = (30 + 18) : 3 = 30 : 3 + 18 : 3 = 10 + 6 = 16. Not every split works: 40 + 8 is a poor choice because neither part divides exactly by 3.
Check the result with the inverse operation: division by multiplication (16 · 3 = 48). The child analyses the problem, writes an expression with brackets, picks a convenient split and checks the answer.