The application of the laws of operation

Operation Properties a+b=b+a a×b=b×a (a+b)+c=a+(b+c) (a×b)×c=a×(b×c) Commutative law of addition a+b=b+a Commutative law of multiplication a×b=b×a Associative law of addition (a+b)+c=a+(b+c) Associative law of multiplication (a×b)×c=a×(b×c) Property of division a÷b÷c=a÷ (b×c) (b.c 0) Distributive law of multiplication (a+b)×c=a×c+b×c

Fill in the blanks by using the laws of operation, then explain which law you used. 13400÷25÷4=13400÷（ × ） 125×8= × （4+40）×25= ×25 + ×25 25 4 Property of division 8 125 Commutative law of multiplication 4 40 Distributive law of multiplication

Make tens I say “1” You say “9”

Make hundreds/thousands 25×4= 25 100 100÷4= 100÷25= 50×2= 100 4 1000÷8= 125 125×8= 1000 1000÷125= 8

Sally and Danny moved home to live in the same neighbourhood Sally and Danny moved home to live in the same neighbourhood. This area had a total of 25 buildings, each building has 28 families. How many families are in this neighborhood in total? 25×28 ＝ 500＋200 ＝ 700　　 25×28 25×28 ＝ 25×（20＋8） ＝ 25×（4×7） ＝ 25×4 ×7 ＝ 25×20＋25×8 （ ） ＝ 100×7 ＝ 700 If you split the number well, the calculation is simple.

Use different methods to do this simple calculation. Have a try : Use different methods to do this simple calculation. 125×88 ＝125×（ ＋ ） ＝ ＝ ＝ 125×88 ＝125×（ × ） ＝ ＝ ＝ 8 11 80 8 (125×8)×11 125×80＋125×8 1000×11 10000＋1000 11000 11000　

Example 2: What’s the sum of 101 99s? Step1：Write the number sentence Step2: Discuss with your deskmate which number you want to split Step3: Have a try by yourself. 101×99 ＝101×（100－1） ＝101×100 － 101×1 ＝10100 － 101 ＝9999　 101×99 ＝（100＋1）×99 ＝100×99＋1×99 ＝9900 ＋ 99 ＝9999　 If the two factors are both close to hundreds, you split only one of the factors, then do a simple calculation using distributive law of multiplication.

⑴23×99 ⑵44×25 ⑶201×63 ⑷888×125 (100－1) (11×4) (40＋4) (111×8) (200 + 1) 1. According to the requirements, split the number reasonably: ⑴23×99 ⑵44×25 ⑶201×63 ⑷888×125 (100－1) (11×4) (40＋4) (111×8) (200 + 1) (800＋80＋8)

①17×17＋83×17 ＝(17＋83) ×17 ＝53×99＋53×1 ＝53×(99＋1) ＝39×39＋39×62－39×1 2. Don’t calculate, just write the key steps. ①17×17＋83×17 ②53×99＋53 ③39×39＋39×62－39 ＝(17＋83) ×17 ＝53×99＋53×1 ＝53×(99＋1) ＝39×39＋39×62－39×1 ＝39×(39＋62－1)

（ ） A （ ） B ＋ × （125＋9）×8 125 ×9 ×8 3. Choose the correct answer. （ ） A （ ） B commutative law of multiplication distributive law of multiplication B: ＝ 125×8＋9×8 ＝ 1000＋72 ＝ 1072 A: ＝ 125×8×9 ＝ 1000×9 ＝ 9000

35×13 ＋38×13＋87×73 35×13 ＋38×13＋87×73 4. Expand exercises ＝ (35＋38) × 13＋87×73 ＝ 73×13 ＋87×73 ＝ (13＋87) ×73 ＝100× 73 ＝ 7300

Use the laws of operation correctly Conclusion According to the number characteristics You can make a simpler calculation. Split the number reasonably Use the laws of operation correctly

Challenge 39×170＋610×17 39×170＋610×17 39×170＋610×17 ＝ 390×17＋610×17 ＝ 39×170＋61×170 ＝ (390＋610) ×17 ＝(39＋61) ×170 ＝ 1000×17 ＝100 × 170 ＝ 17000 ＝ 17000

Thank you!