17
The distributive law of multiplication and its uses
Textbook, pp. 68–72
GoalUse the distributive law of multiplication with fractions and mixed numbers.
New words
distributive law · taqsimot qonunicommon factor · umumiy ko‘paytuvchitaking out of brackets · qavsdan chiqarishconvenient calculation · qulay hisoblash
Explanation
The distributive law says (a + b) · c = a · c + b · c. We can also read it backwards: a · c + b · c = (a + b) · c, taking the common factor out of brackets. When multiplying a mixed number by a natural number, it is handy to multiply the whole and the fractional parts separately: 3 1/2 · 4 = 3 · 4 + 1/2 · 4 = 12 + 2 = 14. The law also works with subtraction: 99 · 37 = (100 − 1) · 37 = 3,700 − 37. It makes calculations easier.
Worked examples
4 2/3 · 6 = 4 · 6 + 2/3 · 6 = 24 + 4 = 28.
3/8 · 11 + 3/8 · 5 = 3/8 · (11 + 5) = 3/8 · 16 = 6.
Class activity
“Brackets game”: cards show examples such as 5/7 · 3 + 5/7 · 4. Pupils take out the common factor and find the answer quickly. A pupil who can explain the method gets an extra point.
Practice
1
Compute 3 1/2 · 4 with the distributive law.
14
2
Compute 5/7 · 3 + 5/7 · 4 conveniently.
5
3
Compute 99 · 37 as (100 − 1) · 37.
3663
4
Why does 6 1/4 · 8 = 6 · 8 + 1/4 · 8?
Because 6 1/4 = 6 + 1/4, and the distributive law multiplies each addend: 48 + 2 = 50.