# Tricks for Solving Multiplication and Division.

Learn the tricks to solve multiplication and division problems using powerful calculation skills. If both the top digits of a dividend and divisor are the same, and the first two digits of the dividend are not enough, then the first digit of the quotient will be 8 or 9. Compare 574 and 522, and see why the first digit of quotient is 9.

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## About Tricks for Solving Multiplication and Division.

PowerPoint presentation about 'Tricks for Solving Multiplication and Division.'. This presentation describes the topic on Learn the tricks to solve multiplication and division problems using powerful calculation skills. If both the top digits of a dividend and divisor are the same, and the first two digits of the dividend are not enough, then the first digit of the quotient will be 8 or 9. Compare 574 and 522, and see why the first digit of quotient is 9.. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

2. MULTIPLICATION MULTIPLICATION DIVISION DIVISION power power

3. If the top digits of dividend and the divisor is the same , in addition the first two digits of the dividend is not enough. At this time, the first digit of quotient was 8 or 9. EX.5742÷58=99 ， 4176÷48=87 57<58 58*9=522 58*8=464 574compare against The first digit of quotient is 9

4. When the first two digits of the number of interim dividend consisting of less than the divisor and the first three digits of the number of provisional composition of the divisor and greater than or equal to 10 times of the divisor,the quotient can be a digit of "9." Generally, if the dividend is m, the divisor is n, only when 9n ≤ m <10n, n divide m is 9. This is the gist of the method. EX. 4508÷49=92 ， 6480÷72=90

5. When the divisor is 11, 12 ............ 18 and 19, and in addition to the first two digit of the dividend is not enough to be divided by dividor, you can use method to know the first digit of the quotient according to the difference between the divisor and the first two digit of the dividend. The difference the first digit of the quotient 1 、 2 9 3 、 4 8 5 、 6 7 7 、 8 6 9 5 EX. 1476÷18=82 （ the difference between 18 and 14 is 4 ， so the first digit of the quotient is 8 ）； 1278÷17=75 （ the difference between 17 and 12 is 5 ， the first digit of the quotient is 7 ）。

6. 23×27= ？ 2 × （ 2+1 ） =6 3 × 7=21 Result:621 Explanation: When a ＋ b ＝ 10 ， （ A×10 ＋ a ）（ A×10 ＋ b ） = A×A×100+A× （ a+b ） ×10+ab =A×(A ＋１ )×100 ＋ ab

7. 18×98=? 17=1 × 9+8 64=8 × 8 Result:1764 Explanation: When A+B=10 （ A × 10+a ）（ B × 10+a ） = （ AB+a ） × 100+a^2

8. 32 × 28=? 3 is the bigger one of the tens digits. 8=3 × 3-1. 2 is the bigger units digit of the two number. 96=100-2 × 2. Result:896 Explanation: （ A × 10+a ） × [(A-1) × 10 ＋ (10-a)] =(A^2-1) × 100+(100-a^2)

9. 66×37=? 24=6 × (3+1) 42=6 × 7 Result:2442 Explanation: when a+b=10 （ A × 10 ＋ A ）（ a × 10 ＋ b ） =A(a ＋ 1) × 100 ＋ Ab

10. learn from a 2 =(a+b)(a-b)+b 2 EX 15 2 =(15+5)x(15-5)+5 2 5 3 2 =(53+3)x(53-3)+3 2 EXPAND 863 2 =900x?+37 2 B ecause the difference between 9 00 and 863 is the same as t hat between 900 and ?, so 9 00+? m ust be twice a s much as 863. ? -800=63x2-100=26 8 63 2 =900x826+37 2 3 7 2 =40x34+3^ 2

11. How about cube? we know that a 3 =aa 2 = a(a 2 -b 2 )+ab 2 =a(a+b)(a-b)+ab 2 E ither a+b or a-b is time s as much as 10, it w ould be the best if they both are. E X 13 3 =10x13x16+13x3 2 way easier?

14. Xu ZeYu 13122674 Zhu WeiTao 13122041 Hu Chao 13121197