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The distributive property
Textbook: Part 4, lesson 139, pp. 50–51
GoalUse the distributive property both ways: multiplying a sum and taking out a common factor.
New words
distributive property · taqsimot xossasicommon factor · umumiy ko‘paytuvchiexpression · ifodaeasy calculation · qulay hisoblash
Explanation
(a + b) × c = a × c + b × c. It is useful to read this equality backwards too: 3 × 5 + 7 × 5 = (3 + 7) × 5 = 10 × 5 = 50 – we took the common factor 5 out of the brackets. Yard area: width 2 m, length 2 m + 5 m gives (2 + 5) × 2 = 14 m² or 2 × 2 + 5 × 2 = 4 + 10 = 14 m².
Worked examples
4 × 4 + 5 × 4 = (4 + 5) × 4 = 9 × 4 = 36.
2 × 7 + 3 × 7 = (2 + 3) × 7 = 5 × 7 = 35.
Class activity
“Yard area”: girls split the yard into two parts (2 m × 2 m and 2 m × 5 m). Children draw two rectangles in their notebooks, calculate the area both ways and compare.
Practice
1
3 × 5 + 7 × 5 = ?
50
2
4 × 4 + 5 × 4 = ?
36
3
2 × 7 + 3 × 7 = ?
35
4
(5 + 2) × 5 = ?
35
5
One crate holds 5 kg of cucumbers and 4 kg of tomatoes. How many kilograms of vegetables are in 6 such crates?
54