六年级数学题及答案：分数的四则混和运算 标签：分数、百分数应用题
<p>六年级数学题及答案：分数的四则混和运算</p><p>求1/3+1/15 +1/35+ 1/63 +1/99 +1/143</p><p>简便方法：</p><p>1/3=1×(1/3)=1/2(1-1/3)</p><p>1/15 =(1/3)×(1/5)=1/2(1/3-1/5)</p><p>1/35=（1/5)×(1/7)=1/2(1/5-1/7)</p><p>1/63 =(1/7)×(1/9)=1/2(1/7-1/9)</p><p>1/99 =(1/9)×(1/11)=1/2(1/9-1/11)</p><p>1/143=(1/11)×(1/13)=1/2(1/11-1/13)</p><p>所以1/3+1/15 +1/35+ 1/63 +1/99 +1/143</p><p>=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)</p><p>提公因式1/2得1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)</p><p>可观察到式子中间部分都抵消，最后只剩下1/2(1-1/13)=6/13</p><p>也就是1/3+1/15 +1/35+ 1/63 +1/99 +1/143=6/13。</p>
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