题目内容
计算:(
-
+
-
+…+
-
)÷(1-
+
-
+…+
-
).
2+3+4 |
1 |
3+4+5 |
2 |
4+5+6 |
3 |
5+6+7 |
4 |
10+11+12 |
9 |
11+12+13 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
考点:分数的巧算
专题:计算问题(巧算速算)
分析:把原式进行变形,然后根据乘法分配律提取公因数3和2,然后根据乘一个数,再除以一个相同的数(0除外),相互抵消,即可得出结论.
解答:
解:(
-
+
-
+…+
-
)÷(1-
+
-
+…+
-
)
=(
-
+
-
+…+
-
)÷(1-
+
-
+…+
-
)
=3×(
-
+
-
+…+
-
)÷(1-
+
-
+…+
-
)
=3×[(1+2)-(1+
)+(1+
)-(1+
)+…+(1+
)-(1+
)]÷(1-
+
-
+…+
-
)
=3×(2-
+
-
+…+
-
)÷(1-
+
-
+…+
-
)
=3×2×(1-
+
-
+…+
-
)÷(1-
+
-
+…+
-
)
=6
2+3+4 |
1 |
3+4+5 |
2 |
4+5+6 |
3 |
5+6+7 |
4 |
10+11+12 |
9 |
11+12+13 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=(
3×3 |
1 |
3×4 |
2 |
3×5 |
3 |
3×6 |
4 |
3×11 |
9 |
3×12 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=3×(
3 |
1 |
4 |
2 |
5 |
3 |
6 |
4 |
11 |
9 |
12 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=3×[(1+2)-(1+
2 |
2 |
2 |
3 |
2 |
4 |
2 |
9 |
2 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=3×(2-
2 |
2 |
2 |
3 |
2 |
4 |
2 |
9 |
2 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=3×2×(1-
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
1 |
2 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=6
点评:灵活掌握分数乘法中的运算定律,并结合数字特点,进行解答即可.
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