[Title]
101A_̌vZilZj

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\usepackage{color}


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[Problem]
̎̌vZB




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5





[Level1]
ZCZ
$(-5)+(-8)$

$-13$

$(-3)-(+6)=$

$-9$

$(+8)-(-7)$

$15$

$346+187$

$533$

$1279-496$

$783$

$28-39+58$

$47$

$(-7)+(-2)$

$-9$

$(-6)+(+3)$

$-3$

$(+4)+(-9)$

$-5$

$(+5)-(+8)$

$-3$

$(+9)-(-3)$

$12$

$(-1)-(+10)$

$-11$

$(+3.6)+(-2.7)$

$0.9$

$(-2.7)-(+7.1)$

$-9.8$

$(-9)+(-4.5)$

$-13.5$

$+4+2-4$

$2$

$-2+3-4$

$-3$

$+10-2+3$

$11$

$-5-(+2)$

$-7$

$-3-(+4)$

$-7$

$-9-(-12)-18$

$-15$

$7-(-3)$

10

$-17-(-33)$

16




[Level2]
GȑZCZ
$+4-2+5-6$

$1$

$-7+4-11+5$

$-9$

$-8+5-13+2$

$-14$

$(-4)+(+3)-(-5)+(-2)$

$2$

$7+(-26)-(-39)-15$

$5$

$14-(2+7)-3$

$2$

$(+7)-(+4)+(-1)$

$2$

$(-4)+(-7)-(+2)$

$-13$

$(+2)-(-5)+(-3)$

$4$

$(-6)-(-3)+(-5)$

$-8$

$5.3+(-3.6)-(-10.5)$

$12.2$

$(-6)+(+3)+(-5)$

$-8$

$(+0.7)-(-1.4)$

$2.1$

$934-350-134$

$450$

$458-140+642$

$960$

$(+8)-(+9)+(+2)$

$1$

$(+5)+(-7)-(-6)$

$4$

$(-7)-(-5)-(-3)$

$1$

$8+(-5)-(-9)$

$12$

$(-4)+5+(-8)-2$

$-9$

$357+17999+1$

process
$357+(17999+1)=18357$

$18357$

$357+17999$

process
$(356+1)+17999=356+(1+17999)=18356$

$18356$

$899+1343+101$

process
$(899+101)+1343=1000+1343$

$2343$

$(+7)-4-(-10)$

13

$-8-3+7+(-4)$

$-8$

$(+4)-(+7)+(-2)$

$-5$

$(-14)-(-12)+(-3)-(-5)$

process
$-14+12-3+5$

0

$(-1)-(-2)+(-3)-(+4)-(-5)$

process
$-1+2-3-4+5=1-3+1=2-3$

$-1$






[Level3]
ZCZ
$(-2) \times 3 \times(-3)$

$18$

$45\div 5\div 3$

$3$

$(-3) \times(-5) \times 4$

$60$

$21 \times 9\div 7$

$27$

$16\div(-2) \times 7$

$-56$

$8.1\div 4.05$

$2$

$3.8 \times 2.1$

$7.98$

$273 \times 68$

$18564$

$18\div 24 \times 4\div 3$

$1$

$(+6)\div(-21) \times(-28)$

$8$

$48\div(-6) \times 2$

$-16$

$-54 \div (-9) \times 2$

$12$

$-0.2 \times (-15)$

$3$

$(-32)\div(-8) \div 2$ 

$2$

$(-2)^4$

$16$

$(-3)^2 \times (-4)$

$-36$

$-48 \div (-2)^2$

$-12$

$(-9) \div 6 \times(-2^2)$

$6$

$(-3) \times 5 \times 0$

$0$

$4^3$

$64$

$(-2)^5$

$-32$

$1001\times 715$

$715715$

$101010101\times 57$

$5757575757$

$11111\times 1111$

$12344321$

$123123123\div 123$

$1001001$

$37\times 25 \times 4$

process
$37 \times (25\times 4)=37 \times 100=3700$

$3700$

$125\times 37 \times 8$

process
$37 \times (125 \times 8)=37 \times 1000=37000$

$37000$

$1001 \times 20$

process
$(1000+1) \times 20=1000\times 20+1\times 20=20000+20=20020$

$20020$

$1001 \times 102$

process
$1001\times (100+2)=1001 \times 100+1001 \times 2\\
=(1000+1)\times 100+(1000+1)\times 2\\
=100000+100+2000+2=102102$

$102102$

$101^2$

process
$(100+1)^2=100^2+2 \times 100 \times 1+1^2=10000+200+1=10201$

$10201$

$1002^2$

process
$(1000+2)^2=1000^2+2\times 1000\times 2+2^2\\
=1000000+4000+4=1004004$

$1004004$

$99^2$

process
$(100-1)^2=100^2-2\times 100 \times 1+1^2=10000-200+1=9801$

$9801$

$998^2$

process
$(1000-2)^2=1000^2-2\times 1000\times 2+2^2\\
=1000000-4000+4=996004$

$996004$

$101\times 99$

process
$(100+1)\times (100-1)=100^2-1^2=10000-1=9999$

$9999$

$(-2)^2\times (-3)$

$-12$

$7-(-6)\times(-5)$

$-23$

$2\times(-3^2)+(-4)\times(-3)^2$

$-54$

$(-3)^3\div(-3)^2\times (-2)$

process
$-\displaystyle\frac{3^3}{3^2}\times (-2)=-3 \times (-2)$

$6$

$(-3)^2\times (-1)^3\div (-3^2)$

process
$9\times \displaystyle\frac{-1}{9}=9\times \displaystyle\frac{1}{9}$

1


[Level4]
WJ̌p̌vZ
$49^{2}$

process
$(50-1)^2=50^2-2\times 50 +1=2500-100+1$

$2401$

$502 \times 498$

process
$(500+2)(500-2)=500^2-2^2=250000-4$

$249996$

$503 \times 497$

process
$(500+3)(500-3)=500^2-3^2=250000-9$

$249991$

$102 \times 98$

process
$(100+2)(100-2)=100^2-2^2=10000-4$

$9996$

$103 \times 97$

process
$(100+3)(100-3)=100^2-3^2=10000-9$

$9991$

$202 \times 198$

process
$(200+2)(200-2)=200^2-2^2=40000-4$

$39996$

$203 \times 197$

process
$(200+3)(200-3)=200^2-3^2=40000-9$

$39991$

$302 \times 298$

process
$(300+2)(300-2)=300^2-2^2=90000-4$

$89996$

$303 \times 297$

process
$(300+3)(300-3)=300^2-3^2=90000-9$

$89991$

$402 \times 398$

process
$(400+2)(400-2)=400^2-2^2=160000-4$

$159996$

$403 \times 397$

process
$(400+3)(400-3)=400^2-3^2=160000-9$

$159991$

$9.8^2-0.2^2$

process
$(9.8-0.2)(9.8+0.2)=9.6 \times 10=96$

96

$9.7^2-0.3^2$

process
$(9.7-0.3)(9.7+0.3)=9.4 \times 10=94$

94

$9.6^2-0.4^2$

process
$(9.6-0.4)(9.6+0.4)=9.2 \times 10=92$

92

$10.2^2-0.2^2$

process
$(10.2-0.2)(10.2+0.2)=10 \times 10.4=104$

104

$10.3^2-0.3^2$

process
$(10.3-0.3)(10.3+0.3)=10 \times 10.6=106$

106

$10.4^2-0.4^2$

process
$(10.4-0.4)(10.4+0.4)=10 \times 10.8=108$

108

$10.2^2-0.2^2$

process
$(10.2-0.2)(10.2+0.2)=10 \times 10.4=104$

104

$5.2^2-4.8^2$

process
$(5.2-4.8)(5.2+4.8)=0.4 \times 10=4$

4

$5.3^2-4.7^2$

process
$(5.3-4.7)(5.3+4.7)=0.6 \times 10=6$

6

$5.4^2-4.6^2$

process
$(5.4-4.6)(5.4+4.6)=0.8 \times 10=8$

8

$5.5^2-4.5^2$

process
$(5.5-4.5)(5.5+4.5)=1 \times 10=10$

10

$5.6^2-4.4^2$

process
$(5.6-4.4)(5.6+4.4)=1.2 \times 10=12$

12

$5.7^2-4.3^2$

process
$(5.7-4.3)(5.7+4.3)=1.4 \times 10=14$

14

$5.8^2-4.2^2$

process
$(5.8-4.2)(5.8+4.2)=1.6 \times 10=16$

16

$5.9^2-4.1^2$

process
$(5.9-4.1)(5.9+4.1)=1.8 \times 10=18$

18

$2005 \times 1995$

process
$(2000+5)(2000-5)=2000^2-5^2\\
=4000000-25$

$3999975$

$(10^2+1)(10-1)(10+1)$

process
$(10^2+1)(10^2-1)=( 100^2-1 )=10000-1$

$9999$

$17.75^2-12.25^2$

process
$(17.75-12.25)(17.75+12.25)\\
=5.50\times 30=165$

$165$

\hspace{8pt} }͑傫Ȑ`CȐ`؂̂łB
ΐ̖ʐς߂B\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/101_̌vZ/fig7301.tex}
\end{center}

process
${\rm 45^2-15^2=\left( 45-15 \right)\left( 45+15 \right)=30 \times 60=1800\,cm^2}$

${\rm 1800\,cm^2}$

\hspace{8pt} }͑傫Ȑ`CȐ`؂̂łB
ΐ̖ʐς߂B\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/101_̌vZ/fig7302.tex}
\end{center}

process
${\rm 55^2-15^2=\left( 55-15 \right)\left( 55+15 \right)=40 \times 70=2800\,cm^2}$

${\rm 2800\,cm^2}$

\hspace{8pt} }͑傫Ȑ`CȐ`؂̂łB
ΐ̖ʐς߂B\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/101_̌vZ/fig7303.tex}
\end{center}

process
${\rm 65^2-25^2=\left( 65-25 \right)\left( 65+25 \right)=40 \times 90=3600\,cm^2}$

${\rm 3600\,cm^2}$








[Level5]
lvZibj
$7-(-3) \times 2$

$13$

$-3^2+6 \div 3$

$-7$

$3 \times(-2)-24 \div(-2)$

$6$

$(-4)^2-(2-8) \div 3$

$18$

$8-5 \times 2$

$-2$

$8-(-6+2) \times 2$

$16$

$6-5 \times 3$

$-9$

$-2-(-3-2) \times 3$

$13$

$2.8-0.23-(-0.125)$

$2.695$

$162.8-(12.8+7.3 \times 2.8)$

$129.56$

$3 \times(9-4)\div 5 \times 4$

$12$

$356-\{96-(76-55)\div 3\}$

$267$

$12345 \times 9+6$

$111111$

$1234 \times 9+5$

$11111$

$45-(-9) \times(-12)\div(-4)$

$72$

$48-24\div 6$

$44$

$-3-2 \times(-7)$

$11$

$5-3 \times 6$

$-13$

$5+3 \times 6$

$23$

$8+3 \times 6$

$26$

$7+4 \times(-5)$

$-13$

$3 \times 9-12$

$15$

$(-2)\times 5+11$

$1$

$6 +16 \div 2$

$14$

$12 +21 \div(-7)$

$9$

$9-36 \div 6$

$3$

$(-25) \div(-5)+3$

$8$

$5 \times (-3)+6$

$-9$

$7 +4 \times (-8)$

$-25$

$8 +25 \div(-5)$

$3$

$-12 \times (-3)+(-8) \div(-4)$

$38$

$3 \times (-2)+(-3)^2$

process
$-6+9=3$

$3$

$3-(-4) \div 2$

process
$3-(-2)=3+2=5$

$5$

$(-3^2)+(-3)^2 \times 3$

process
$-9+9 \times 3=-9+27=18$

$18$

$17+(-3) \times 8$

$-7$

$5 \times (-2)-6$

$-16$

$24-(-12) \div (-2)$

$18$

$(-5+3) \times (-4)$

$8$

$(-7) \times (-3-4)$

$49$

$(-9+3) \div (-2)$

$3$

$(-6 \div 3) + (-2)^2$

$2$

$(-7)^2 - 3^2$

$40$

$(-5)^2 +6 \times (-4)$

$1$

$3^2 + (-3^2) + (-3)^2$

$9$

$(-2)^2 \times 5 + 2 \times (-3)$

$14$

$(-4)^2 + 9 \div (-3^2)$

$15$

$16 \div (5+3)$

$2$

$5 + 2 \times (-7)$

$-9$

$5 - 8 \div (-2)$

$9$

$3 - 7 \times (6-7)$

$10$

$7 - 5 \times 3 -8 \div(-4)$

$-6$

$6-2 \times (-3)^2$

$-12$

$4+(-3)\times(-2)$

10

$-2^2+(-3)+(-6)^2$

29

$-12-(-2)\times 5$

$-2$

$(-3)^2-6^2\times (-2)$

81

$30 \div\{ (-7)+(-3) \}$

$-3$

$7-(-2)\times 8$

23

$5+(-3)\times 2$

$-1$

$(-4)^2\div (-2^2)$

$-4$

$(-4)^2-3^2$

process
$16-9=7$

$7$

$(-3)^2+24\div (-2^2)$

process
$9-\displaystyle\frac{24}{4}=9-6=3$

$3$

$(-3)\times 8-(-3)\times 5$

process
$-24+15$

$-9$

$12\div(-4)-(-5)\times 2$

process
$-3+10$

$7$

$(-2)\times (-5)+(-18)\div 3$

process
$10-6$

$4$

$-2^2\times 5+(-3)^2$

process
$-4\times 5+9=-20+9=-11$

$-11$

$-12-(3-8)\times 4$

process
$-12-(-20)=-12+20$

8

$\{ (-1)^2-(-3)^2 \}\div (-4)+2$

process
$(1-9)\div (-4)+2=(-8)\div (-4)+2=2+2$

4

$5-4\times (1-3)$

process
$5-4\times (-2)=5+8=13$

13

$4-\{ 3-(-2) \}$

process
$4-(3+2)=4-5$

$-1$

$(-6)-2\times (-7)$

process
$-6+14$

8

$10 \div(-8)\times 4+12$

$7$

$9+8\times (-2)\div 4$

$5$

$2\times (-3)^2-5 \times 2$

$8$



[Level6]
lvZi3悠j
$(-2)^3+14 \div(-7)$

$-10$

$(-3)^3-(-2^2)-3^2$

$-32$

$(-21) \times(-6^{2})\div(-3)^{3}$

$-28$

$(-4)\div(-2)^{2}-(-3)^{3} \times(-5)$

$-136$

$2^{3}-3(1-2^{2})^{2}$

$-19$

$16 \div (-2)^3-(-27)\div(-3^2)$

$-5$

$15 \times(-1)^3-6^2 \div(-9)$

$-11$

$(-2)^3-3 \times(-5)$

process
$-8-(-15)=-8+15=7$

$7$

$-2^3+(-3)^2$

process
$-8+9=1$

$1$

$(-0.1)^3 \times 10^4+(-10)^2 \times 0.5$

process
^$=-\left( \displaystyle \frac{1}{10} \right)^3 \times 10^3 \times 10+100 \times \displaystyle \frac{5}{10}\\
=-10+50=40$

$40$

$-4^2-(-4)^3\times \left( \displaystyle\frac{1}{2} \right)^2$

process
$-16+\displaystyle\frac{4^3}{4}=-16+16=0$

$0$

$\{ -9^2-7\times(-2)^3 \}\div (-5)$

process
$(-81+56)\div (-5)=(-25)\div (-5)$

5

$3^3-(-2^2)\times (-2)^3$

process
$27-(-4)\times (-8)=27-32=-5$

$-5$





[Level7]



[Level8]


[EOF]