The application of the laws of operation Operation

The application of the laws of operation

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

Fill in the blanks by using the laws of operation, then explain which law you used. ① 13400÷ 25÷ 4=13400÷（ × 25 ）4 Property of division ② 125× 8= 8× 125 Commutative law of multiplication ③ （4+40）× 25= 4 × 25 + 40 × 25 Distributive law of multiplication

Make tens I say “ 1” You say “ 9”

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

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 ＝ 25×（4× 7） ＝（ 25× 4 ） × 7 ＝ 100× 7 ＝ 700 If you split the number well, the calculation is simple. 25× 28 ＝ 25×（20＋8） ＝ 25× 20＋25× 8 ＝ 500＋200 ＝ 700

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

Example 2: What’s the sum of 101 99 s? Step 1：Write the number sentence Step 2: Discuss with your deskmate which number you want to split Step 3: Have a try by yourself. 101× 99 ＝（100＋1）× 99 ＝ 100× 99＋1× 99 ＝ 9900 ＋ 99 ＝ 9999 101× 99 ＝ 101×（100－1） ＝ 101× 100 － 101× 1 ＝ 10100 － 101 ＝ 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.

1. According to the requirements, split the number reasonably: ⑴ 23× 99 (100－1) ⑶ 201× 63 (200 + 1) ⑵ 44× 25 (11× 4) (40＋4) ⑷ 888× 125 (111× 8) (800＋80＋8)

2. Don’t calculate, just write the key steps. ① 17× 17＋83× 17 ＝(17＋83) × 17 ② 53× 99＋53 ＝ 53× 99＋53× 1 ＝ 53×(99＋1) ③ 39× 39＋39× 62－39 ＝ 39× 39＋39× 62－39× 1 ＝ 39×(39＋62－1)

3. Choose the correct answer. ① （125＋9）× 8 ＋ （B） ② 125 × × 9 × 8 （A） commutative law of multiplication distributive law of multiplication A: ＝ 125× 8× 9 ＝ 1000× 9 ＝ 9000 B: ＝ 125× 8＋9× 8 ＝ 1000＋72 ＝ 1072

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

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

Thank you!