1. Law of Multiplication(3) Shanghai Luwan No.2 Primary School
Murphey Chen
陈默华

2. addition and multiplication !
We have a law between
addition and multiplication !

3. Review: 3 sixs add 4 sixs is 7 sixs, 7 sixs is 42！
3× ×6 =( )×6 =( ) 7 42

4. Review: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋48×11
23×25＋17×25
=20×9=180
（25+75）×8=
=100×8=800
（64+36）×13=
=100×13=1300
（52+48）×11=
=100×11=1100
（23+17）×25=
=40×25=1000
The sum of 2 numbers multiplied by another number.
We can multiply the 2 addends by the number respectively and then
add the 2 products. The result remains the same.
This is called the distributive law of multiplication.

5. Say: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋11×48 23×25＋17×25
（25+75）×8=
（64+36）×13=
（52+48）×11=
（23+17）×25=
The sum of ( )and( ) multiplied by ( ). We can multiply ( )and ( ) by ( ) respectively and then add the 2 products. The result remains the same. 13 7 9 13 7 9

6. Say: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋11×48 23×25＋17×25
（25+75）×8=
（64+36）×13=
（52+48）×11=
（23+17）×25=
The sum of ( )and( ) multiplied by ( ). We can multiply ( )and ( ) by ( ) respectively and then add the 2 products. The result remains the same. 25 75 8 25 75 8

7. Say: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋11×48 23×25＋17×25
（25+75）×8=
（64+36）×13=
（52+48）×11=
（23+17）×25=
The sum of ( )and( ) multiplied by ( ). We can multiply ( )and ( ) by ( ) respectively and then add the 2 products. The result remains the same. 64 36 13 64 36 13

8. Say: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋11×48 23×25＋17×25
（25+75）×8=
（64+36）×13=
（52+48）×11=
（23+17）×25=
The sum of ( )and( ) multiplied by ( ). We can multiply ( )and ( ) by ( ) respectively and then add the 2 products. The result remains the same. 52 48 11 52 48 11

9. Say: （13+7）×9= 13×9＋7×9 8×25＋8×75 64×13＋36×13 52×11＋11×48 23×25＋17×25
（25+75）×8=
（64+36）×13=
（52+48）×11=
（23+17）×25=
The sum of ( )and( ) multiplied by ( ). We can multiply ( )and ( ) by ( ) respectively and then add the 2 products. The result remains the same. 23 17 25 23 17 25

10. The distributive law of multiplication
(a+b)×c
=a×c+b×c
The sum of 2 numbers multiplied by another number.
We can multiply the 2 addends by the number respectively
and then add the 2 products.
The result remains the same.

11. Use 2 ways to calculate
The playground is a rectangle, the original 65 meters long, 32 meters wide.
After the expansion, long unchanged,15 meters wide increase. What is the area of the expanded playground?
65 meters
As 1 rectangle: （ ＋ ）× = 32 15 65
3055 m2
32 meters
original area 32 65 15 65
3055 m2
As 2 rectangles: × ＋ × =
15 meters
increased area
Different ways, but the answer is ( ).
same
（ ＋ ）× = × ＋ × 32 15 65 32 65 15 65

12. Use 2 ways to calculate
1 circle means 1 student.How many students are there on the playground altogether?
As 1 group: （ ＋ ）× = 6 4 7 70
As 2 groups: × ＋ × = 6 7 4 7 70
7 rows
Different ways, but the answer is ( ).
same 6 4 7 6 7 4 7
（ ＋ ）× = × ＋ ×
6 students
4 students

13. The sum of 2 numbers multiplied by another number
The sum of 2 numbers multiplied by another number. We can multiply the 2 addends by the number respectively and then add the 2 products. The result remains the same.
The sum of 2 numbers
another number
respectively
65×（32＋15）=65× ×15 65
32＋15 65 65
（6+4）×7=6×7＋4×7
6+4 7 7 7
（a + b）×c = a × c + b × c
a + b c c c

14. Calculate in easier ways:
（1） 75×91+25×91 （2） 136×15－36×15
=(75+25)×91
=100×91
=9100
=(136－36)×15
=100×15
=1500

15. Solve Problem : Shirt: ₤32/per Trouser: ₤45/per Jacket: ₤65/per
(1) I want to buy 5 jackets and 5 trousers.
How much money should I pay altogether?

16. 65×5
＋45×5
=325＋225
=550
Total price
(65+45) ×5
=110×5
=550
Total price

17. Solve Problem : T-shirt: ₤32/per Trouser: ₤45/per Jacket: ₤65/per
(1) I want to buy 5 jackets and 5 trousers.
How much money should I pay altogether?
(2) How much more do you have to pay for 5 jackets than 5 T-shirts?