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数学演習 中学校1年生/文字の式/解答
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数学演習 中学校1年生
|
文字の式
目次
1
文字式の表し方
2
代入と式の値
3
1次式の加減
4
1次式と数の乗除
文字式の表し方
編集
2
a
{\displaystyle 2a}
5
a
x
{\displaystyle 5ax}
−
x
+
y
{\displaystyle -x+y}
a
3
b
2
{\displaystyle a^{3}b^{2}}
a
7
{\displaystyle {\frac {a}{7}}}
または
1
7
a
{\displaystyle {\frac {1}{7}}a}
x
+
y
5
{\displaystyle {\frac {x+y}{5}}}
x
+
y
5
{\displaystyle x+{\frac {y}{5}}}
代入と式の値
編集
5
x
+
7
=
5
×
(
−
3
)
+
7
=
−
15
+
7
=
−
8
{\displaystyle 5x+7=5\times (-3)+7=-15+7=-8}
4
−
2
x
=
4
−
2
×
(
−
3
)
=
4
−
(
−
6
)
=
10
{\displaystyle 4-2x=4-2\times (-3)=4-(-6)=10}
−
12
x
=
−
12
−
3
=
−
(
−
4
)
=
4
{\displaystyle -{\frac {12}{x}}=-{\frac {12}{-3}}=-(-4)=4}
x
2
=
(
−
3
)
2
=
9
{\displaystyle x^{2}=(-3)^{2}=9}
−
x
2
=
−
(
−
3
)
2
=
−
9
{\displaystyle -x^{2}=-(-3)^{2}=-9}
1次式の加減
編集
5
x
+
3
x
=
(
5
+
3
)
x
=
8
x
{\displaystyle 5x+3x=(5+3)x=8x}
5
a
−
4
a
=
(
5
−
4
)
a
=
a
{\displaystyle 5a-4a=(5-4)a=a}
7
a
+
3
−
5
a
−
6
=
7
a
−
5
a
+
3
−
6
=
(
7
−
5
)
a
+
(
3
−
6
)
=
2
a
−
3
{\displaystyle 7a+3-5a-6=7a-5a+3-6=(7-5)a+(3-6)=2a-3}
3
x
−
2
−
x
+
9
=
3
x
+
x
−
2
+
9
=
(
3
−
1
)
x
+
(
−
2
+
9
)
=
2
x
+
7
{\displaystyle 3x-2-x+9=3x+x-2+9=(3-1)x+(-2+9)=2x+7}
(
3
a
+
2
)
+
(
6
a
−
5
)
=
3
a
+
2
+
6
a
−
5
=
9
a
−
3
{\displaystyle (3a+2)+(6a-5)=3a+2+6a-5=9a-3}
(
5
x
−
9
)
+
(
−
3
x
+
9
)
=
5
x
−
9
−
3
x
+
9
=
2
x
{\displaystyle (5x-9)+(-3x+9)=5x-9-3x+9=2x}
(
5
a
−
3
)
−
(
3
a
+
2
)
=
(
5
a
−
3
)
+
(
−
3
a
−
2
)
=
5
a
−
3
−
3
a
−
2
=
2
a
−
5
{\displaystyle {\begin{matrix}(5a-3)-(3a+2)&=&(5a-3)+(-3a-2)\\\ &=&5a-3-3a-2&=&2a-5\end{matrix}}}
(
a
−
7
)
−
(
2
a
+
7
)
=
(
a
−
7
)
+
(
−
2
a
−
7
)
=
a
−
7
−
2
a
−
7
=
−
a
−
14
{\displaystyle {\begin{matrix}(a-7)-(2a+7)&=&(a-7)+(-2a-7)\\\ &=&a-7-2a-7&=&-a-14\end{matrix}}}
1次式と数の乗除
編集
3
x
×
4
=
3
×
x
×
4
=
3
×
4
×
x
=
12
x
{\displaystyle 3x\times 4=3\times x\times 4=3\times 4\times x=12x}
2
5
a
×
(
−
10
)
=
2
5
×
a
×
(
−
10
)
=
2
5
×
(
−
10
)
×
a
=
−
4
a
{\displaystyle {\frac {2}{5}}a\times (-10)={\frac {2}{5}}\times a\times (-10)={\frac {2}{5}}\times (-10)\times a=-4a}
3
(
x
+
6
)
=
3
×
x
+
3
×
6
=
3
x
+
18
{\displaystyle 3(x+6)=3\times x+3\times 6=3x+18}
−
4
(
2
x
−
5
)
=
(
−
4
)
×
2
x
+
(
−
4
)
×
(
−
5
)
=
−
8
x
+
20
{\displaystyle -4(2x-5)=(-4)\times 2x+(-4)\times (-5)=-8x+20}
5
a
−
3
7
×
14
=
(
5
a
−
3
)
×
14
7
=
2
(
5
a
−
3
)
=
10
a
−
6
{\displaystyle {\frac {5a-3}{7}}\times 14={\frac {(5a-3)\times 14}{7}}=2(5a-3)=10a-6}
12
x
÷
6
=
12
x
×
1
6
=
2
x
{\displaystyle 12x\div 6=12x\times {\frac {1}{6}}=2x}
9
a
÷
3
4
=
9
a
×
4
3
=
12
a
{\displaystyle 9a\div {\frac {3}{4}}=9a\times {\frac {4}{3}}=12a}
(
18
a
−
15
)
÷
3
=
(
18
a
−
15
)
×
1
3
=
6
a
−
5
{\displaystyle (18a-15)\div 3=(18a-15)\times {\frac {1}{3}}=6a-5}
(
24
a
−
8
)
÷
(
−
8
)
=
(
24
a
−
8
)
×
(
−
1
8
)
=
−
3
a
+
1
{\displaystyle (24a-8)\div (-8)=(24a-8)\times \left(-{\frac {1}{8}}\right)=-3a+1}
6
(
a
+
2
)
+
5
(
2
a
−
3
)
=
6
a
+
12
+
10
a
−
15
=
16
a
−
3
{\displaystyle 6(a+2)+5(2a-3)=6a+12+10a-15=16a-3}
2
(
x
+
3
)
−
3
(
2
x
−
1
)
=
2
x
+
6
−
6
x
+
3
=
−
4
x
+
9
{\displaystyle 2(x+3)-3(2x-1)=2x+6-6x+3=-4x+9}
