問題
次の式を計算しなさい。
- (1) \(\dfrac{1}{4}(x-3y)-\dfrac{1}{6}(2x-3y)\)
\(\\\) - (2) \(4x-y-6(\dfrac{x}{2}+\dfrac{2}{3}y)\)
\(\\\) - (3) \(2(\dfrac{5}{2}x-3y)-\dfrac{1}{3}(6x-21y)\)
\(\\\) - (4) \(12(\dfrac{2a-b}{4}-\dfrac{a-2b}{3})\)
\(\\\) - (5) \(x-\dfrac{1}{3}y-\dfrac{x-3y}{4}\)
\(\\\) - (6) \(x-\dfrac{3x-4y}{5}-\dfrac{x-2y}{3}\)
\(\\\) - (7) \(\dfrac{5x-2y}{3}-\dfrac{2x-3y}{2}-\dfrac{3x+2y}{5}\)
\(\\\) - (8) \(\dfrac{a+b}{4}-(\dfrac{3}{2}a-\dfrac{4a-2b}{3})\)
\(\\\) - (9) \(\dfrac{x+y}{2}-\dfrac{3x-y}{6}+x-2y\)
\(\\\) - (10) \(5x-\dfrac{1}{2} \lbrace-3x+4y-3(x+2y)\rbrace\)
\(\\\) - (11)
\(\dfrac{13x-7y+2}{6}-(\dfrac{7x-5y}{8}-\dfrac{8x-6y}{9})\times12-x-3\)
\(\\\)
解説
マイナスと分数の係数に注意して計算すると、
- (1) \(\dfrac{1}{4}(x-3y)-\dfrac{1}{6}(2x-3y)\)
\(\\\)
\(=(\dfrac{1}{4}x-\dfrac{1}{3}x)+(\dfrac{1}{2}y-\dfrac{3}{4}y)\)
\(\\\)
\(=-\dfrac{1}{12}x-\dfrac{1}{4}y\)
\(\\\) - (2) \(4x-y-6(\dfrac{x}{2}+\dfrac{2}{3}y)\)
\(\\\)
\(=(4x-3x)-(y\)\(+\)\(4y)\)
\(\\\)
\(=x-5y\)
\(\\\) - (3) \(2(\dfrac{5}{2}x-3y)-\dfrac{1}{3}(6x-21y)\)
\(\\\)
\(=(5x-2x)+(7y-6y)\)
\(\\\)
\(=3x+y\)
\(\\\) - (4) \(12(\dfrac{2a-b}{4}-\dfrac{a-2b}{3})\)
\(\\\)
\(=3{2a-b}-4(a-2b)\)
\(\\\)
\(=(6a-4a)+(8b-3b)\)
\(\\\)
\(=2a+5b\)
\(\\\) - (5) \(x-\dfrac{1}{3}y-\dfrac{x-3y}{4}\)
\(\\\)
\(=(x-\dfrac{1}{4}x)+(\dfrac{3}{4}y-\dfrac{1}{3}y)\)
\(\\\)
\(=\dfrac{3}{4}x+\dfrac{5}{12}y\)
\(\\\) - (6) \(x-\dfrac{3x-4y}{5}-\dfrac{x-2y}{3}\)
\(\\\)
\(=\dfrac{15x-3(3x-4y)-5(x-2y)}{15}\)
\(\\\)
\(=\dfrac{(15x-9x-5x)+(12y+10y)}{15}\)
\(\\\)
\(=\dfrac{x+22y}{15}\)
\(\\\) - (7) \(\dfrac{5x-2y}{3}-\dfrac{2x-3y}{2}-\dfrac{3x+2y}{5}\)
\(\\\)
\(=\dfrac{10(5x-2y)-15(2x-3y)-6(3x+2y)}{30}\)
\(\\\)
\(=\dfrac{(50x-30x-18x)+(45y-20y-12y)}{30}\)
\(\\\)
\(=\dfrac{2x+13y}{30}\)
\(\\\) - (8) \(\dfrac{a+b}{4}-(\dfrac{3}{2}a-\dfrac{4a-2b}{3})\)
\(\\\)
\(=\dfrac{a+b}{4}-\dfrac{9a-2(4a-2b)}{6}\)
\(\\\)
\(=\dfrac{a+b}{4}-\dfrac{a+4b}{6}\)
\(\\\)
\(=\dfrac{3(a+b)-2(a+4b)}{12}\)
\(\\\)
\(=\dfrac{a-5b}{12}\)
\(\\\) - (9) \(\dfrac{x+y}{2}-\dfrac{3x-y}{6}+x-2y\)
\(\\\)
\(=\dfrac{3(x+y)-(3x-y)+6x-12y}{6}\)
\(\\\)
\(=\dfrac{6x-8y}{6}\)
\(\\\)
\(=\dfrac{3x-4y}{3}\)
\(\\\) - (10) \(5x-\dfrac{1}{2} \lbrace-3x+4y-3(x+2y)\rbrace\)
\(\\\)
\(=5x-\dfrac{1}{2}(-6x-2y)\)
\(\\\)
\(=5x+3x+y\)
\(\\\)
\(=8x+y\)
\(\\\) - (11)
\(\dfrac{13x-7y+2}{6}-(\dfrac{7x-5y}{8}-\dfrac{8x-6y}{9})\times12-x-3\)
\(\\\)
\(=\dfrac{13x-7y+2}{6}-\dfrac{-x+3y}{72}\times12-x-3\)
\(\\\)
\(=\dfrac{13x-7y+2}{6}-\dfrac{3y-x}{6}-x-3\)
\(\\\)
\(=\dfrac{13x-7y+2-(3y-x)}{6}-x-3\)
\(\\\)
\(=\dfrac{14x-10y+2}{6}-x-3\)
\(\\\)
\(=\dfrac{7x-5y+1}{3}-x-3\)
\(\\\)
\(=\dfrac{7x-5y+1-3(x+3)}{3}\)
\(\\\)
\(=\dfrac{4x-5y-8}{3}\)
となります。
