148
Multiplying a sum by a number
Textbook: Part 4, lesson 138, pp. 48–49
GoalMultiply a sum by a number: multiply each addend and add the results.
New words
sum · yig‘indiaddend · qo‘shiluvchibracket · qavsdistribution (sharing out) · taqsimot
Explanation
To multiply a sum by a number, we can multiply each addend by that number and add the results: (20 + 40) × 10 = 20 × 10 + 40 × 10 = 200 + 400 = 600. Both ways give 600. In a picture: two rectangles 4 cm by 3 cm and 4 cm by 5 cm have area 4 × 3 + 4 × 5 = 4 × (3 + 5) = 32 cm².
Worked examples
(3 + 5) × 6 = 3 × 6 + 5 × 6 = 18 + 30 = 48.
5 × (8 + 3) = 5 × 8 + 5 × 3 = 40 + 15 = 55.
Class activity
“Two gardens”: one garden has 20 plants and another has 10, each plant gives 5 kg. Children calculate two ways: (20 + 10) × 5 and 20 × 5 + 10 × 5 – and see that the results match.
Practice
1
(2 + 9) × 4 = ?
44
2
(3 + 8) × 6 = ?
66
3
(20 + 30) × 5 = ?
250
4
5 × (8 + 3) = ?
55
5
One watermelon weighs about 5 kg. The first crate has 20 and the second has 10. What is the total mass in kilograms?
150