% %ȉ̕RgƂ̂łC_ł͂܂ł܂B
% ̃^Cg
[Title]
105_CCZx
% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
% tHg̑傫B1`10C܂TeX̃R}hw肷B
% ftHǵC5i\normalsizej
% 1\tinyC 2\scriptsizeC3\footnotesizeC4\smallC 5\normalsize
% 6\hugeC7\hugeC     8\hugeC       9\hugeC 10\Huge
[FontSize]
5

% vAuɒǉpbP[Wt@Cw肷B
[usepackage]
\usepackage{color,amssymb}

% ꂼ̖𓚂$\displaystyle $tꍇ́C@ON ܂1
% ꂼ̖𓚂$\displaystyle $tȂꍇ́COFF܂0
% up̕ҏWv|u[U[ݒv̉ɂݒ
% @@@@@@@@@@@@@@@@@ꍇɎw肵ĂB
% LqȂ΁Cup̕ҏWv|u[U[ݒv
% @@@@@@@@@@@@@@@@@@@ɂݒ肪D悳܂B
[displaystyle]
OFF


% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
̊{
ԋʂƔʂ킹140܂B
ԋʂ̌͔ʂ̌$2.5${łBʂ̌͉łB

process
$140\times\displaystyle\frac{2}{7}=40$

40

݂Ђ낳Ƃ̔N߂킹77˂łB܂C
̔N߂́C݂Ђ낳̔N߂6{łB݂Ђ낳̔N߂͉˂łB

process
$140\times \displaystyle\frac{2}{7}=11$

11

{$70{\rm cm}$܂B̃{̂悤ɕƂCB͉̒cmɂȂ܂B\\
${\rm A:B}=4:1$

process
$70\times \displaystyle\frac{1}{5}=14$

14cm

{$70{\rm cm}$܂B̃{̂悤ɕƂCB͉̒cmɂȂ܂B\\
${\rm A:B}=1.8:1$

process
$70\times \displaystyle\frac{1}{2.8}=25$

25cm

$\displaystyle\frac{1}{5}:\displaystyle\frac{3}{6}$Ɠ́C\textcircled{\small 1}$\sim$\textcircled{\small 4}̂̂ǂłB
ꂼ̔̒l狁߂ȂB\\
\textcircled{\small 1}\,$10:28$~~~
\textcircled{\small 2}\,$1.8:3.3$~~~
\textcircled{\small 3}\,$12:32$~~~
\textcircled{\small 4}\,$\displaystyle\frac{1}{3}:\displaystyle\frac{15}{18}$

process
$\displaystyle\frac{1}{5}:\displaystyle\frac{3}{6}=2:5$\\
\textcircled{\small 4}\,$\displaystyle\frac{1}{3}:\displaystyle\frac{15}{18}=6:15=2:5$

\textcircled{\small 4}

$16:22$Ɠ́C\textcircled{\small 1}$\sim$\textcircled{\small 4}̂̂ǂłB
ꂼ̔̒l狁߂ȂB\\
\textcircled{\small 1}\,$1:1.3$~~~
\textcircled{\small 2}\,$\displaystyle\frac{1}{3}:\displaystyle\frac{3}{6}$~~~
\textcircled{\small 3}\,$1.5:1.8$~~~
\textcircled{\small 4}\,$56:77$

process
$\displaystyle\frac{22}{16}= \displaystyle\frac{11}{8}$

\textcircled{\small 4}

$5:3$Ɠ́C\textcircled{\small 1}$\sim$\textcircled{\small 4}̂̂ǂłB
ꂼ̔̒l狁߂ȂB\\
\textcircled{\small 1}\,$16:14$~~~
\textcircled{\small 2}\,$0.15:0.09$~~~
\textcircled{\small 3}\,$\displaystyle\frac{4}{6}:\displaystyle\frac{12}{18}$~~~
\textcircled{\small 4}\,$0.25:0.18$

process
\textcircled{\small 2}\,$0.15:0.09=15:9=5:3$

\textcircled{\small 2}

$10:12$Ɠ́C\textcircled{\small 1}$\sim$\textcircled{\small 4}̂̂ǂłB
ꂼ̔̒l狁߂ȂB\\
\textcircled{\small 1}\,$7:8.2$~~~
\textcircled{\small 2}\,$\displaystyle\frac{3}{15} : \displaystyle\frac{4}{15}$~~~
\textcircled{\small 3}\,$0.25:0.3$~~~
\textcircled{\small 4}\,$46:48$

process
$\displaystyle\frac{12}{10}=1.2$łB\textcircled{\small 3}$30\div 25=1.2$

\textcircled{\small 3}

$x$ɂĂ͂܂鐔߂ȂB\\
$5:3=100:x$

60

$x$ɂĂ͂܂鐔߂ȂB\\
$1.6:2=x:5$

process
$x=5\times \displaystyle\frac{1.6}{2}=5\times 0.8=4$

4

$x$ɂĂ͂܂鐔߂ȂB\\
$24:x=4:6$

36

$x$ɂĂ͂܂鐔߂ȂB\\
$x:7=\displaystyle\frac{15}{20}:\displaystyle\frac{1}{4}$

process
$x:7=3:1$

21

̂ڂ`ƃ\[_$2:9$̊ōāC\[_܂B
̂ڂ`$36{\rm mL}$ɂƂC\[_͉${\rm mL}$΂悢łB

process
$36\times\displaystyle\frac{9}{2}=162$mL

162mL

ႪƋ̔䂪$7:2$ɂȂ悤ɂāC}bV|eg܂B
120ggƂCႪ͉gKvłB

420g

$x$߂ȂB\\
$x:8.4=15:6$

process
$\displaystyle \frac{x}{8.4}=\displaystyle \frac{15}{6}$\\
$x=8.4 \times \displaystyle \frac{5}{2}=4.2 \times 5=21$

21

$x$߂ȂB\\
$\displaystyle \frac{3}{2}:x=6:1$

process
$x \div \displaystyle \frac{3}{2}=\displaystyle \frac{1}{6}$\\
$x = \displaystyle \frac{3}{2} \times \displaystyle \frac{1}{6}$

$\displaystyle \frac{1}{4}$

$x$߂ȂB\\
$x:5=1.2:\displaystyle \frac{2}{3}$

process
$x:5=1.2:\displaystyle \frac{2}{3}
=\displaystyle \frac{12}{10}:\displaystyle \frac{2}{3}=\displaystyle \frac{6}{5}:\displaystyle \frac{2}{3}
=\displaystyle \frac{18}{15}:\displaystyle \frac{10}{15}\\
=18:10=9:5$

$x=9$

$x$߂ȂB\\
$\displaystyle \frac{3}{4}:\displaystyle \frac{2}{5}=x:4$

process
$\displaystyle \frac{3}{4}:\displaystyle \frac{2}{5}
=\displaystyle \frac{15}{20}:\displaystyle \frac{8}{20}
=15:8=\displaystyle \frac{15}{2}:4$

$x=\displaystyle \frac{15}{2}$

400cm̐j܂ȂāCĂƉ̒̔䂪$3:5$̒`ƁC͉̒cmɂȂ܂B

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   & 悱 & +悱 \\
 \hline
 3 & 5 & 8 \\
 \hline
  & $x$ & 200\\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{200}=\displaystyle \frac{5}{8}$B$x=200 \times \displaystyle \frac{5}{8}
=25 \times 5=125$

$125cm$

AB̊C$A:B$̌`ŕ\ȂB\\
A2{B$\displaystyle \frac{1}{3}$ɓƂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 1 &  & 2 \\
 \hline
  & 3 & 1 \\
 \hline
 1 & 6 & 2\\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B=1:6$

AB̊C$A:B$̌`ŕ\ȂB\\
A$\displaystyle \frac{4}{5}$B$\displaystyle \frac{3}{4}$ƂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 5 &  & 4 \\
 \hline
  & 4 & 3 \\
 \hline
 15 & 16 & 12\\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B=15:16$

ACBCC\,3l̏̔$1:2:3$łBCD̏̔$6:5$łB
BD̏̔߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & D\\
 \hline
 1 & 2 & 3 & \\
 \hline
   &   & 6 & 5 \\
 \hline
  2 & 4 & 6 & 5\\
 \hline
\end{tabular}
\end{center}
\end{table}

$B:D=4:5$

24΂̎o18΂̒̔NCłȒPȐ̔ŕ\ƁC$[A]:[C]$łB

process
$24:18=3 \times 8:3 \times 6=8:6=2 \times 4: 2 \times 3 =4:3$

$4:3$

ACB2lC6~̎v$2:3$̔ɕzĎ󂯎B
A󂯎z[A][C]~łB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A+B & A & B \\
 \hline
 5 & 2 & 3 \\
 \hline
 6~ & $x$ & \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{6}=\displaystyle \frac{2}{5}$B
$x=6 \times \displaystyle \frac{2}{5}=\displaystyle \frac{12}{5}=\displaystyle \frac{24}{10}=2.4~$B

$24~$

ACB2lC6~̎v$2:3$̔ɕzĎ󂯎B
B󂯎z[A][C]~łB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A+B & A & B \\
 \hline
 5 & 2 & 3 \\
 \hline
 6~ & & $x$\\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{6}=\displaystyle \frac{3}{5}$B
$x=6 \times \displaystyle \frac{3}{5}=\displaystyle \frac{18}{5}=\displaystyle \frac{36}{10}=3.6~$B

$36~$

ACBCC3loĎƂn߂BAC̏oz̊$3:2$ŁC
BC̊$5:3$łBA450~oƂƁCB͂oƂɂȂ邩H

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 3 &    & 2 \\
 \hline
  &  5  & 3 \\
 \hline
 9 & 10 & 6 \\
 \hline
 450~ & $b$ & \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{b~}{450~}=\displaystyle \frac{10}{9}$\\
$b~=450 \times \displaystyle \frac{10}{9}=500~$\\

500~

A$\displaystyle \frac{2}{3}${B$\displaystyle \frac{3}{4}${ƂC
$A:B$̔߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 3 &  & 2 \\
 \hline
  & 4 & 3 \\
 \hline
 9 & 8 & 6 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B=9:8$

ACBCC̗e킪C̒ɂꂼꓯʂ̐ꂽƂC
Aɂ͂$\displaystyle \frac{1}{3}$CBɂ͂$\displaystyle \frac{2}{5}$CCɂ͂0.75܂B
3̗e̗eς̔Ƃ񂽂Ȑ̔ŕ\ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & D\\
 \hline
 3 &  &  & 1 \\
 \hline
  & 5 & & 2 \\
 \hline
  &  & 4 & 3 \\
 \hline
 18 & 15 & 8 & 6 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B:C=18:15:8$

zACBCC3lŕ̂ɁC$A:B=2:1$C$A:C=3:2$ŕƁC
C1200~ɂȂ܂BB͉~łH

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 2 & 1 &  \\
 \hline
 3 &  & 2 \\
 \hline
 6 & 3 & 4 \\
 \hline
  & $x$ & 1200~ \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{1200}=\displaystyle \frac{3}{4}$B
$x=1200 \times \displaystyle \frac{3}{4}=900~$

900~

zACBCC3lŕ̂ɁC$A:B=2:1$C$A:C=3:2$ŕƁC
C1200~ɂȂ܂BA͉~łH

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 2 & 1 &  \\
 \hline
 3 &  & 2 \\
 \hline
 6 & 3 & 4 \\
 \hline
 $x$ &  & 1200~ \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{1200}=\displaystyle \frac{6}{4}$B
$x=1200 \times \displaystyle \frac{6}{4}=1800~$

1800~

$A:B =4:3$C$B:C =5:3$C$A:D =2:3$̂ƂC$C:D$߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & D\\
 \hline
 4 & 3 & & \\
 \hline
  & 5 & 3 &  \\
 \hline
  2 &  &  & 3 \\
 \hline
  20 & 15 & 9 & 30 \\
 \hline
\end{tabular}
\end{center}
\end{table}
\C$C:D=9:30=3:10$

$C:D=3:10$

݂60܂BAqBq$3:[A]$̔ŕƁCAq36ɂȂ܂B

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cc}
  A & B \\
 \hline
 3 & $x$ \\
 \hline
 36 & 24 \\
 \hline
\end{tabular}
\end{center}
\end{table}
\C$A:B=36:24=3:2$

2

$4m$̂ЂZ$\displaystyle \frac{2}{3}$ɂȂ悤2ɐ؂܂B
̂Ђ̒߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   & Z & S \\
 \hline
 3 & 2 & 5 \\
 \hline
 $x$ & & 4 \\
 \hline
\end{tabular}
\end{center}
\end{table}
\C$\displaystyle \frac{x}{4}= \displaystyle \frac{3}{5}$B
$ x=4 \times \displaystyle \frac{3}{5}=4 \times \displaystyle \frac{6}{10}=\displaystyle \frac{24}{10}=2.4 $

$2.4m$

$6m$̂ЂZ$\displaystyle \frac{2}{3}$ɂȂ悤2ɐ؂܂B
̂Ђ̒߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   & Z & S \\
 \hline
 3 & 2 & 5 \\
 \hline
 $x$ & & 6 \\
 \hline
\end{tabular}
\end{center}
\end{table}
\C$\displaystyle \frac{x}{6}= \displaystyle \frac{3}{5}$B
$ x=6 \times \displaystyle \frac{3}{5}=6 \times \displaystyle \frac{6}{10}=\displaystyle \frac{36}{10}=3.6 $

$3.6m$

$8m$̂ЂZ$\displaystyle \frac{2}{3}$ɂȂ悤2ɐ؂܂B
̂Ђ̒߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   & Z & S \\
 \hline
 3 & 2 & 5 \\
 \hline
 $x$ & & 8 \\
 \hline
\end{tabular}
\end{center}
\end{table}
\C$\displaystyle \frac{x}{8}= \displaystyle \frac{3}{5}$B
$ x=8 \times \displaystyle \frac{3}{5}=8 \times \displaystyle \frac{6}{10}=\displaystyle \frac{48}{10}=4.8 $

$4.8m$

ĂƉ̒̔䂪$5:7$̒`̌`܂B
̌̎̒$192m$̂ƂC͉̒$m$łH

process
$+悱=192 \div 2=96$B
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   & 悱 & S \\
 \hline
 5 & 7 & 12 \\
 \hline
  & $x$ & 96 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{96}=\displaystyle \frac{7}{12}$B\\
$x=96 \times \displaystyle \frac{7}{12}=56$

$悱=56m$

3̐ACBCCɂāCAB$\displaystyle \frac{1}{3}$C
BC$\displaystyle \frac{2}{3}$łƂC$A:B:C$Ȃׂ񂽂Ȕŕ\ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 1 & 3 &  \\
 \hline
  & 2 & 3 \\
 \hline
 2 & 6 & 9 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B:C=2:6:9$

NX̒jqƏq̐l̔$9:7$ŁCl̍4lłB
̂ƂCq͉l܂H

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  jq & q &  \\
 \hline
 9 & 7 & 2  \\
 \hline
 18 & 14 & 4 \\
 \hline
\end{tabular}
\end{center}
\end{table}

14l

Nʂ1~CACBCČZ3lŕB
$A:B:C=4:3:1$̔ŕƂCB͂炦܂B

process
$A:B:C:S=4:3:1:8$C\\
$10000 \times \displaystyle \frac{3}{8}=1250 \times 3=3750$

$3750~$

36{̂҂ABN$5:iAj$ɂȂ悤ɕƂC
A20{ɂȂ܂BiAjɓ鐔𓚂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & A+B \\
 \hline
 20 & 16 & 36 \\
 \hline
 5 & 4 &  \\
 \hline
\end{tabular}
\end{center}
\end{table}

4

45{̂҂ABN$4:iAj$ɂȂ悤ɕƂC
A20{ɂȂ܂BiAjɓ鐔𓚂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & A+B \\
 \hline
 20 & 25 & 45 \\
 \hline
 4 & 5 &  \\
 \hline
\end{tabular}
\end{center}
\end{table}

5

Op`̓p̔䂪$1:2:3$ɂȂĂ܂Bԑ傫p͉xłB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & A+B+C \\
 \hline
 1 & 2 & 3 & 6 \\
 \hline
  & & $x$ & 180 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{180}=\displaystyle \frac{3}{6}$\\
$x=180 \times \displaystyle \frac{3}{6}=90$

90

lp`̓p̔䂪$1:2:3:4$ɂȂĂ܂Bԑ傫p͉xłB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccccc}
  A & B & C & D & A+B+C+D \\
 \hline
 1 & 2 & 3 & 4 & 10 \\
 \hline
   & & & $x$ & 360 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{360}=\displaystyle \frac{4}{10}$\\
$x=360 \times \displaystyle \frac{4}{10}=144$

144

18m̃e[v2ɐ؂CZ$\displaystyle \frac{4}{5}$ɂȂ܂B
̃e[v͉mcmłB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  Z &  & S \\
 \hline
 4 & 5 & 9 \\
 \hline
 8 & 10 & 18 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$10m0cm$

32m̃e[v2ɐ؂CZ$\displaystyle \frac{3}{5}$ɂȂ܂B
̃e[v͉mcmłB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  Z &  & S \\
 \hline
 3 & 5 & 8 \\
 \hline
 12 & 20 & 32 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$20m0cm$

̒190m̒`̓ynCĂƉ̔䂪$9:10$ɂȂĂ܂B
͉̒młB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   &  & + \\
 \hline
 9 & 10 & 19 \\
 \hline
  & $x$ & 95 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{95}=\displaystyle \frac{10}{19}$B
$x=95 \times \displaystyle \frac{10}{19}=50$

$50m$

̒260m̒`̓ynCĂƉ̔䂪$5:8$ɂȂĂ܂B
͉̒młB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
   &  & + \\
 \hline
 5 & 8 & 13 \\
 \hline
  & 80 & 130 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$80m$

$A:B=3:4$C$B:C=10:9$C$A:D=1:2$̂ƂC$C:D$߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & D \\
 \hline
 3 & 4 &  &  \\
 \hline
  & 10 & 9 &  \\
 \hline
 1 &  &  & 2 \\
 \hline
 15 & 20 & 18 & 30 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$C:D=18:30=3:5$

$C:D=3:5$

$A:B=4:5$C$B:C=6:7$C$A:D=3:4$̂ƂC$C:D$߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  A & B & C & D \\
 \hline
 4 & 5 &  &  \\
 \hline
  & 6 & 7 &  \\
 \hline
 3 &  &  & 4 \\
 \hline
 24 & 30 & 35 & 32 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$C:D=35:32$

$C:D=35:32$

A$\displaystyle \frac{4}{5}$B$\displaystyle \frac{5}{6}$ƂC$A:B$߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 5 &  & 4 \\
 \hline
  & 6 & 5 \\
 \hline
 25 & 24 & 20 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B=25:24$

ACBCC3̐܂BAB$\displaystyle \frac{3}{4}$CBC$\displaystyle \frac{2}{5}$łB
$A:B:C$߂ȂB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 3 & 4 &  \\
 \hline
  & 2 & 5 \\
 \hline
 3 & 4 & 10 \\
 \hline
\end{tabular}
\end{center}
\end{table}

$A:B:C=3:4:10$

݂ACBCC3lŕ܂B̔$A:B=3:4$C$A:C=1:2$C36łB
B͉łB

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
 3 & 4 &  \\
 \hline
 1 &  & 2 \\
 \hline
 3 & 4 & 6 \\
 \hline
  & 24 & 36 \\
 \hline
\end{tabular}
\end{center}
\end{table}

24

496y[W̖{1ɑŜ$\displaystyle \frac{1}{4}$ǂ݁C
2ڂɎc$\displaystyle \frac{3}{4}$ǂ݂܂BǂłȂy[W͂Ɖy[WłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic107.tex}
\end{center}
1ڂ$496 \times \displaystyle \frac{1}{4}=124$y[Wǂ񂾂ƂɂȂ̂ŁC
c$496-124=372$y[WB\\
2ڂ$372 \times \displaystyle \frac{3}{4}=279$
y[Wǂ񂾂ƂɂȂ̂ŁCc$372-279=93$y[WB

93y[W

420y[W̖{1ɑŜ$\displaystyle \frac{2}{7}$ǂ݁C
2ڂɎc$\displaystyle \frac{3}{5}$ǂ݂܂BǂłȂy[W͂Ɖy[WłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic111.tex}
\end{center}
1ڂ$420 \times \displaystyle \frac{2}{7}=120$y[Wǂ񂾂ƂɂȂ̂ŁC
c$420-120=300$y[WB\\
2ڂ$300 \times \displaystyle \frac{3}{5}=180$
y[Wǂ񂾂ƂɂȂ̂ŁCc$300-180=120$y[WB

120y[W

1200~̏i8\% ̏łƂɂȂ邩B

process
$1200\times 1.08=1296~$

1296~

200y[W̖{1ԂɑŜ40\% ǂ݁C2ڂɎc60\% ǂ񂾁B
܂ǂłȂy[W͉y[W邩߂ȂB

process
1ځF\\
$200\times \displaystyle\frac{40}{100}=80$y[WCc$200-80=$120y[W\\
2ځF\\
$120\times \displaystyle\frac{60}{100}=72$y[WCc$120-72=$48y[W

48y[W

wZ̍N̓w҂345lŁCN15\%܂B
N̓w҂͉lłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic110.tex}
\end{center}
N̓w҂1Ƃ΁CN1.15B
N̓w҂$345\div 1.15=300l$

300l

90500̉{łH

process
$90 \div 500=0.18$

0.18{

240~600~̉\%łH

process
$240 \div 600 \times 100=40\%$

$40\%$

AN̎Z̃eXg1ڂ80_C2ڂ64_łB
2ڂ̃eXg1ڂ̃eXgɑ΂ĉ\%܂B

process
$80-64=16$B$16 \div 80=0.2$

20\%

v싅ÍC܂ł̑ŐȐ900ɑ΂āCŐ288{łB
̑Ïł̊iŗjŋ߂B

process
$\displaystyle \frac{288}{900} =\displaystyle \frac{96}{300}=0.32$

0.32

ACBCC3lĂ邨ׂƂC
AB3\,:\,2CAC2\,:\,3B
B1600~ĂB
C͂玝Ă܂H

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  A & B & C \\
 \hline
  3 & 2 &  \\
 \hline
  2 &  & 3 \\
 \hline
  6 & 4 & 9\\
 \hline
    & 1600 & ? \\
\end{tabular}
\end{center}
\end{table}
$1600 \div 4=400$C$9 \times 400=3600~$

3600~

AN600~Ă܂B
̂C150~ł𔃂܂B͂͂߂̂̉\%łB

process
$\displaystyle\frac{150}{600}\times 100=25\%$

25\%

AN50AĂ܂B
̂C20FBɂ܂B
cĂÁC͂߂̉\%łB

process
cĂA$50-20=30$B\\
$\displaystyle\frac{30}{50}\times 100=60\%$

60\%

1640̉\%łB

process
$\displaystyle\frac{16}{40}\times 100=40\%$

40\%

\fbox{@@}25\%8łB

process
$x \times 0.25=8$C$x=\displaystyle\frac{8}{0.25}=32$

32

wZ̐ḱCj킹560lłB
̂Cq̐k͒jq̐k$\displaystyle\frac{3}{5}$łB
̊wZ̏q̐k߂ȂB

process
iqjFijqj$=3:5$ł邩C\\
iqjFiSkj$=3:8$B\\
$560\times \displaystyle\frac{3}{8}=210$l

210l

XɂȂƁC̐ς͖1.1{ɂȂ܂B
ł́CXɂȂƑ̐ς͉\%܂B
ľܓŏ1ʂ܂ŋ߂ȂB

process
iXjFij$=1.1:1$ł邩C\\
i̐ρjFi͂߂̕X̑̐ρj$=1.1-1.0:1.1=0.1:1.1$\\
$\displaystyle\frac{0.1}{1.1}\times 100=9.09\cdots\%$

9.1\%

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
\hspace{8pt} AƔBɓĂ݂̌̔$3:2$ŁC
BƔCɓĂ݂̌̔$4:5$łB
3̔ACBCCɓĂ݂̌̍v120̂ƂC
BɓĂ݂̌߂ȂB\\
\textcircled{\small 1}\,$32$~~~
\textcircled{\small 2}\,$34$~~~
\textcircled{\small 3}\,$36$~~~
\textcircled{\small 4}\,$38$~~~
\textcircled{\small 5}\,$40$

process
$A:B:C=6:4:5$ł邩C\\
߂́C
$120\times \displaystyle\frac{4}{15}=32$

\textcircled{\small 1}

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
40b
70ł@B
̈@ŁC1ԂɈł閇߂ȂB\\
\textcircled{\small 1}\,$4200$~~~
\textcircled{\small 2}\,$4800$~~~
\textcircled{\small 3}\,$5600$\\
\textcircled{\small 4}\,$6300$~~~
\textcircled{\small 5}\,$8400$

process
$60 \times 60 \times \displaystyle\frac{70}{40}=6300$

\textcircled{\small 4}

ԂЂƐЂ̒̔䂪$5:3$C
ЂƔЂ̒̔䂪$4:7$̂ƂC
ԂЂƔЂ̒̔߂ȂB\\
\textcircled{\small 1}\,$5:7$~~~
\textcircled{\small 2}\,$12:35$~~~
\textcircled{\small 3}\,$15:28$\\
\textcircled{\small 4}\,$20:21$~~~
\textcircled{\small 5}\,̑

\textcircled{\small 4}

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
$\displaystyle\frac{5}{14}: \displaystyle\frac{10}{21}$
łȒPȐ̔ŕ\ȂB\\
\textcircled{\small 1}\,$1:2$~~~
\textcircled{\small 2}\,$2:3$~~~
\textcircled{\small 3}\,$3:4$~~~
\textcircled{\small 4}\,$4:5$~~~
\textcircled{\small 5}\,$5:6$

process
$\displaystyle\frac{5}{7 \times 2}:\displaystyle\frac{5\times 2}{7 \times 3}=\displaystyle\frac{1}{2}:\displaystyle\frac{2}{3}=3:4$

\textcircled{\small 3}

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
ʐ$0.3{km}^2$̖q750̋B
1̖ʐς߂ȂB\\
\textcircled{\small 1}\,$40{\rm m^2}$~~~
\textcircled{\small 2}\,$225{\rm m^2}$~~~
\textcircled{\small 3}\,$400{\rm m^2}$~~~
\textcircled{\small 4}\,$2250{\rm m^2}$~~~
\textcircled{\small 5}\,$4000{\rm m^2}$

process
$\displaystyle\frac{0.3 \times 1000 \times 1000}{750}=\displaystyle\frac{0.3 \times 1000 \times 1000}{3\times 250}\\
=0.1 \times 4000=400 m^2/$

\textcircled{\small 3}

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
鐅cł́C$10a$iA[j$600kg$̕ĂnłB
̐c$20ha$i$=20\times 100 a$j͉$t$̕Ănłƍl邩B\\
iӁj$1t=1000kg$łB\\
\textcircled{\small 1}\,$30t$~~~
\textcircled{\small 2}\,$300t$~~~
\textcircled{\small 3}\,$12t$~~~
\textcircled{\small 4}\,$120t$~~~
\textcircled{\small 5}\,$1200t$

process
$600kg \times \displaystyle\frac{20 \times 100}{10}=600 \times 200\\
=120,000kg=120t$

\textcircled{\small 4}








[Level2]
̉p
ANɍsCŏɏ2gCɎc3gƂCc840~ƂȂB
͂߂̏͂łB

process
͂߂̏$x$ƂƁC$x \times 0.8 \times 0.3=840$

$840~$

ACBCC3lĂ鉔M̖{̔$5:3:2$ŁC
AB5{CC2{ƂCAB̉M̖{ɂȂB
̂ƂC͂߂CĂM̖{͉{H

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
        & A & B & C \\
 \hline
 ͂ & $5a$ & $3a$ & $2a$ \\
 \hline
 Bɂ & &  5炤  & \\
 \hline
 Cɂ & &    & 2炤\\
 \hline
  & $5a-7$ & $3a+5$ & $2a+2$ \\
 \hline
\end{tabular}
\end{center}
\end{table}
$5a-7=3a+5$ $a=6$B\\
͂߂C̖{$2a=2 \times 6=12{$

12{

j킹39l̃NX܂B
̃NX̒jq$\displaystyle \frac{2}{7}$Əq$\displaystyle \frac{1}{3}$
̐l͓Ȃ܂B̃NX̒jq͉lłH

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{cccc}
  鐔 & jq & q & S \\
 \hline
 2 & 7 & &  \\
 \hline
 1 &  & 3 &  \\
 \hline
 2 & 7 & 6 & 13 \\
 \hline
  & $x$ &  & 39 \\
 \hline
\end{tabular}
\end{center}
\end{table}
$\displaystyle \frac{x}{39}=\displaystyle \frac{7}{13}$B$x=39 \times \displaystyle \frac{7}{13}=21$

21l

bC2l1̎̔$4:5$C
xo̔$3:4$łCc͂Ƃ3~łB
̂ƂC̎͂炩H

process
\begin{table}[!h]
\begin{center}
\begin{tabular}{ccc}
  & b &  \\
 \hline
  & $4a$ & $5a$ \\
 \hline
 xo & $3b$ & $4b$ \\
 \hline
 c & $4a-3b$ & $5a-4b$ \\
 \hline
\end{tabular}
\end{center}
\end{table}
$4a-3b=3$c\textcircled{\small 1}\\
$5a-4b=3$c\textcircled{\small 2}\\
\textcircled{\small 1}\textcircled{\small 2}C$a=3$C$b=3$B̎$=5a=5 \times 3=15$~

15~

rɁĈ72 cm2{̖_ACB܂ɗĂƂCA͂$\displaystyle \frac{3}{4}$C
B͂$\displaystyle \frac{3}{5}$ʂ̏ɏo܂Br̐[͉cmłH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic101.tex}
\end{center}
}C$2 \times 24=48cm$

48cm

ACB2{̂ڂ܂BRbvɐāC2{̖_𐂒ɗĂƂ
A͂$\displaystyle \frac{2}{5}$CB͂$\displaystyle \frac{5}{8}$ʂo܂B
2{̖_̘̒a26 cm̂ƂC̐[߂ȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic102.tex}
\end{center}
}C$3 \times 2=6 cm$

6 cm

}$\triangle$ABCɂDC̒߂ȂB\\
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic103.tex}
\end{center}

process
$肽l=킩Ăl \times \displaystyle \frac{肽}{킩Ă}$\\
$肽l=3 \times \displaystyle \frac{3}{5}=3 \times \displaystyle \frac{6}{10}
=\displaystyle \frac{18}{10}=1.8$

1.8

ɐC̍$24cm$̖_ACBꂽƂCA$\displaystyle \frac{2}{3}$C
B$\displaystyle \frac{4}{5}$ʂo܂B̐̐[͉cmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic104.tex}
\end{center}

$12cm$

ɐC̍$15cm$̖_ACBꂽƂCA$\displaystyle \frac{3}{5}$C
B$\displaystyle \frac{3}{7}$ʂo܂B̐̐[͉cmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic105.tex}
\end{center}
}C$4 \times 5=20cm$

$20cm$

ɐC̍$24cm$̖_ACBꂽƂCA$\displaystyle \frac{2}{3}$C
B$\displaystyle \frac{4}{5}$ʂo܂B̐̐[͉cmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic104.tex}
\end{center}

$12cm$

ɐC̍$15cm$̖_ACBꂽƂCA$\displaystyle \frac{3}{5}$C
B$\displaystyle \frac{3}{7}$ʂo܂B̐̐[͉cmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic105.tex}
\end{center}
}C$4 \times 5=20cm$

$20cm$

ɐC̘a$78cm$̖_ACBꂽƂCA$\displaystyle \frac{5}{7}$C
B$\displaystyle \frac{2}{3}$ʂo܂B̐̐[͉cmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic106.tex}
\end{center}
}̔𑫂ƁC$2+5+2+4=13$B$78 \div 13=6$C[$2 \times 6=12$

$12cm$

^ォ痎ƂƁC80\%̍ɂ͂˂{[܂B
2ڂ̍$240cm$łB
̃{[ŏɗƂƂ͉̍$m$$cm$łB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic107.tex}
\end{center}
}C1ڂ̍$240 \times \displaystyle \frac{10}{8}=300cm$B\\
ŏ̍$300 \times \displaystyle \frac{10}{8}=375cm$B

$3m75cm$

鐁ty̏q̐l͑Ŝ40\%łB
̂$\displaystyle \frac{1}{3}$8lt[g𐁂Ă܂B
̐ty̒jq͉l܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic109.tex}
\end{center}
q̐l$8 \div \displaystyle \frac{1}{3}=24$lB\\
Ŝ̐l$24 \div 0.4=60l$B\\
jq$60-24=36$lB

$36l$

Zƒ̒z̔$5:3$łB
Ƃ낪CZ͂7,500~gC1,000~̂ŁCZƒ̒z̔$3:4$ɂȂB
Z̏߂̒z͂炩B

process
߂̌Z̒z$5x$C̒z$3x$ƂƁC
Ƃ̌Z̒z$5x-7500$C̒z$3x1000$ƂȂ邩CӂC\\
$\displaystyle \frac{5x-7500}{3x+1000}=\displaystyle \frac{3}{4}$\\
$4\left(5x-7500\right)=3\left(3x+1000\right)$C$x=3000$

$15,000$~

Y񂪐V̂y[W𒲂ׂCŜ$\displaystyle\frac{4}{7}$͋LŁC
c͑SLłB
܂CL$\displaystyle\frac{1}{3}$͎ʂ̏㔼ɂ܂B
ʂ̉ɂL͑Ŝ̉̂łB

process
Ŝ1ƂƁC\\
iLj$=\displaystyle\frac{4}{7}$CiLj$=\displaystyle\frac{3}{7}$\\
i̍Lj$=\displaystyle\frac{3}{7}\times\displaystyle\frac{2}{3}=\displaystyle\frac{2}{7}$\\
i̋Lj$=$ij$-$i̍Lj\\
$=\displaystyle\frac{1}{2}-\displaystyle\frac{2}{7}
=\displaystyle\frac{3}{14}$

$\displaystyle\frac{3}{14}$







[Level3]
Zx̊{
3\%̐H200gɉg̐2\%̐HɂȂ܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic01.tex}
\end{center}

100g

5\%̐H600g400g̐ƁC\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic02.tex}
\end{center}

3\%

H30gg̐ɗnƁC20\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic03.tex}
\end{center}

120g

240g̐ɉg̐HnƁC20\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic04.tex}
\end{center}

60g

20g̐HƐ180gƉ\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic05.tex}
\end{center}

10\%

4\%̐H300g9\%̐H200gƉ\%̐HɂȂ܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic06.tex}
\end{center}

6\%

15 \%̐H200gɐ100gƁC\%̐HɂȂ܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic07.tex}
\end{center}

10\%

6\%̐H200gɐ5\%̐Hɂɂ͉g̐΂悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic08.tex}
\end{center}

40g

6\%̐H400g15\%̐HƂC9\%̐Hł܂B15\%̐Hg܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic09.tex}
\end{center}

200g

5\%̐H600gB10\%̐H400gčB
̂ƂCH̔Zx͉\%ɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic10.tex}
\end{center}

7\%

8\%̐H240gB20\%̐HgāC12\%̐H낤ƎvBg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic11.tex}
\end{center}

120g

4\%̐H100gBɁC10\%̐H20gčB̂ƂCH̔Zx͉\%ɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic12.tex}
\end{center}

5\%

6\%̐H200gBɁC12\%̐HgčāC8\%̐HB
̂ƂC12\%̐HgƂɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic13.tex}
\end{center}

100g

12\%̐H300gB̐HɐāC10\%̐H邽߂ɂ́Cg΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic14.tex}
\end{center}

60g

6\%̐H180gBɐH10\%̐H肽BHgꂽ悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic15.tex}
\end{center}

8g

12\%̐H200gɐ6\%ɂBg΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic16.tex}
\end{center}

200g

9\%̐H200gɉg̐6\%̐H肽B鐅͉gH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic17.tex}
\end{center}

100g

3\%̐H80gB8\%̐HāC7\%̐H肽B
8\%̐Hg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic18.tex}
\end{center}

320g

H120g360g̐ɗnƁC\%̐Hł邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic19.tex}
\end{center}

25\%

300g̐ɍāC20\%̍ɂ́Cgꂽ悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic21.tex}
\end{center}
$ 300 \times \displaystyle \frac{1}{4}=75 $

75g

8\%̐H100g3\%̐H5\%̐H肽B3\%̐H͉g΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic26.tex}
\end{center}
$ 100 \times \displaystyle \frac{3}{2}=150 $ g

150g

6\%̐H100g16\%̐H12\%̐H肽B16\%̐H͉g΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic27.tex}
\end{center}
$ 100 \times \displaystyle \frac{3}{2}=150 $ g

150g

15\%̐H200gɐH20\%̐H肽BHg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic28.tex}
\end{center}
$ 200 \times \displaystyle \frac{5}{80}=12.5 $ g

12.5g

3 \% ̐H200g8\%̐H6\%̐H肽B
8\%̐Hg΂悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic44.tex}
\end{center}

300g

4\%̐H200g10\%̐H100gƁC\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic45.tex}
\end{center}

6\%

2\%̐H100g5\%̐H200gƉ\%̐Hł܂H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic46.tex}
\end{center}

4\%

Zx9\%̐H200gɐāCZx5\%̐Hɂɂ́CgƂ悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic47.tex}
\end{center}

160g

2\%̐H100g10\%̐H8\%̐HɂB
10\%̐Hgꂽ悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic48.tex}
\end{center}

300g

12\%̐H400gɐ10\%̐HɂB
gꂽ悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic49.tex}
\end{center}

80g

8\%̐H200gƁCāC2\%̐H肽B
g΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic32.tex}
\end{center}

600g

5\%̐H8\%̐H100gC6\%̐HłB
͂߂ɁC5\%̐H͉gĂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic55.tex}
\end{center}

200g

\fbox{@@}\% ̐H300gɐ100g9\% ̐HɂȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/figp1402.tex}
\end{center}

12

8\% ̐H100g2\% ̐H\fbox{@@}g4\% ̐HɂȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/figp1403.tex}
\end{center}

200g

3\% 15\% ̐H8\% ̐H900g肽B
3\% ̐H͉g΂悢B

process
$900\times \displaystyle\frac{7}{12}=300\times \displaystyle\frac{7}{4}=525$
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/figp1401.tex}
\end{center}

525g

8\% ̐H
300gɐ$x$g5\% ̐HƂC$x$̒l߂ȂB\\
\textcircled{\small 1}\,$140$~~~
\textcircled{\small 2}\,$150$~~~
\textcircled{\small 3}\,$160$~~~
\textcircled{\small 4}\,$170$~~~
\textcircled{\small 5}\,$180$

\textcircled{\small 5}

14\% ̐H210g7\% ̐H$x$g10\% ̐HƂC
$x$̒l߂ȂB\\
\textcircled{\small 1}\,$210$~~~
\textcircled{\small 2}\,$240$~~~
\textcircled{\small 3}\,$280$~~~
\textcircled{\small 4}\,$320$~~~
\textcircled{\small 5}\,$350$

\textcircled{\small 3}

5\% ̐H
280g$x\% $̐H120g8\% ̐HƂC$x$̒l߂ȂB\\
\textcircled{\small 1}\,$14$~~~
\textcircled{\small 2}\,$15$~~~
\textcircled{\small 3}\,$16$~~~
\textcircled{\small 4}\,$17$~~~
\textcircled{\small 5}\,$18$

\textcircled{\small 5}

10\% ̐H360g15\% ̐H$x$g12\% ̐HƂC
$x$̒l߂ȂB\\
\textcircled{\small 1}\,$240$~~~
\textcircled{\small 2}\,$260$~~~
\textcircled{\small 3}\,$280$~~~
\textcircled{\small 4}\,$300$~~~
\textcircled{\small 5}\,$320$

\textcircled{\small 1}

15\% ̐H200g
ɐ8\% ̐Hɂ́C
g΂悢łB\\
\textcircled{\small 1}\,$160$~~~
\textcircled{\small 2}\,$165$~~~
\textcircled{\small 3}\,$170$~~~
\textcircled{\small 4}\,$175$~~~
\textcircled{\small 5}\,$180$

\textcircled{\small 4}

12\% ̐H150g8\% ̐H350gĂłH̔Zx߂ȂB\\
\textcircled{\small 1}\,$9.2\% $~~~
\textcircled{\small 2}\,$9.4\% $~~~
\textcircled{\small 3}\,$9.6\% $~~~
\textcircled{\small 4}\,$9.8\% $~~~
\textcircled{\small 5}\,$10\% $

process
$8+4 \times \displaystyle\frac{3}{10}=8+1.2=9.2\%$

\textcircled{\small 1}

10\% ̐H300g6\% ̐HĔZx9\% ɂB
6\% ̐Hg΂悢B

100g

15\% ̐H200g6\% ̐H10\% ̐HƂC
6\% ̐H͉g΂悢B

250g





[Level4]
Zx̉p
4\%̐H9\%̐H킹āC7\%̐H400g肽B
4\%̐Hg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic20.tex}
\end{center}
$ 400 \times \displaystyle \frac{2}{5}=160$

160g

2\%̐H200g5\%̐H300gƉ\%̐Hł邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic22.tex}
\end{center}
$ 3 \times \displaystyle \frac{3}{5}=3 \times \displaystyle \frac{6}{10}=1.8 \% B2+1.8=3.8$

3.8\%

5\%̐H400g9\%̐H600gƉ\%̐Hł邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic23.tex}
\end{center}
$ 4 \times \displaystyle \frac{3}{5}=4 \times \displaystyle \frac{6}{10}=2.4 \%B5+2.4=7.4 $

7.4\%

4\%̐H200g6\%̐H300gƉ\%̐Hł邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic24.tex}
\end{center}
$ 2 \times \displaystyle \frac{3}{5}=2 \times \displaystyle \frac{6}{10}=1.2 \%B4+1.2=5.2 $

5.2\%

4\%̐H10\%̐HƂC6\%̐H600gł܂B4\%̐H͉głH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic25.tex}
\end{center}
$ 600 \times \displaystyle \frac{2}{3}=400 $ g

400g

4\%̐H300g2\%̐H100gƁC\%ɂȂ邩B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic29.tex}
\end{center}
$ 2 \times \displaystyle \frac{3}{4}=1.5 $

3.5\%

6\%̐H12\%̐H10\%̐H600g肽B
6\%̐Hg΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic30.tex}
\end{center}

200g

5\%̐H8\%̐H6\%̐H300g肽B
5\%̐Hg΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic31.tex}
\end{center}

200g

6\%12\%̐HāC8\%̐H180g肽B
6\%̐Hg΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic33.tex}
\end{center}

120g

7\%̐H13\%̐H킹āC9\%̐H450g肽B
7\%̐Hg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic56.tex}
\end{center}
$ 450 \times \displaystyle \frac{2}{3}=300$

300g

4\% ̐H120gɁC9\% ̐HĔZx7\% ɂB
9\% ̐H͉g΂悢߂ȂH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic112.tex}
\end{center}

180g

12\% ̐H7\% ̐H10\% ̐H600gƂC
12\% ̐H͉g΂悢B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic57.tex}
\end{center}

360g







[Level5]

8\%̐H400gBꂩ牽g̐10\%̐HɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic41.tex}
\end{center}
10\%̐Hɐ$x$g8\%̐H400gɂȂB
$ 400 \times \displaystyle \frac{1}{5}=80 $

80g

7\%̐H200gBꂩ牽g̐10\%̐HɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic54.tex}
\end{center}
10\%̐Hɐ$x$g7\%̐H200gɂȂB
$ 200 \times \displaystyle \frac{3}{10}=60 $

60g

3\%̐H600g100g̐ƁC\%̐HɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic42.tex}
\end{center}
$x$ \%̐Hɐ$100$g3\%̐H600gɂȂB
$ 3 \times \displaystyle \frac{1}{5}=0.6 $B$3+0.6=3.6\%$

3.6\%

4\%̐H140g60g̐ƁC\%̐HɂȂ邩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic51.tex}
\end{center}
$x$ \%̐Hɐ$60$g4\%̐H140gɂȂB

7\%

8\%̐H150gBMĐ10\%̐H肽B
g悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic50.tex}
\end{center}
10\%̐Hɐ$x$gƁC8\%̐H150gɂȂB
}C$2 \times 15=30$g

30g

10\%̐H240gBMĐ12\%̐H肽B
g悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic53.tex}
\end{center}
12\%̐Hɐ$x$gƁC10\%̐H240gɂȂB
}C$2 \times 20=40$g

40g

5\%̐H200g琅āC8\%̐HƂ邽߂ɂ́Cg΂悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic43.tex}
\end{center}
8\%̐Hɐ$x$g5\%̐H200gɂȂB
$200 \times \displaystyle \frac{3}{8}=75$

75g

8\%̐H200g琅āC10\%̐HƂ邽߂ɂ́Cg΂悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic52.tex}
\end{center}
10\%̐Hɐ$x$g8\%̐H200gɂȂB
$200 \times \displaystyle \frac{2}{10}=40$

40g

8\%̐H200g琅āC10\%̐HƂ邽߂ɂ́Cg΂悢łH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic52.tex}
\end{center}
10\%̐Hɐ$x$g8\%̐H200gɂȂB
$200 \times \displaystyle \frac{2}{10}=40$

40g

8\% ̐H100g琅āC10\% ̐Hɂ邽߂ɂ́Cg΂悢H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/105_CCZx/pic113.tex}
\end{center}
10\% ̐Hɐ$x$g8\% ̐H100gɂȂB
$ 200 \times \displaystyle \frac{2}{10}=20 $

20g





[Level6]


[Level7]


[EOF]
% t@C̍Ōɂ
