Câu 58: Cộng các phân số sau:
a) \({\rm{}}{1 \over 6} + {2 \over 5}\) b) \({3 \over 5} + {{ – 7} \over 4}\) c) \(\left( { – 2} \right) + {{ – 5} \over 8}\)
a) \({\rm{}}{1 \over 6} + {2 \over 5} = {5 \over {30}} + {{12} \over {30}} = {{5 + 12} \over {30}} = {{17} \over {30}}\)
b) \({3 \over 5} + {{ – 7} \over 4} = {{12} \over {20}} + {{ – 35} \over {20}} = {{12 + ( – 35)} \over {20}} = {{ + 23} \over {20}}\)
c) \(\left( { – 2} \right) + {{ – 5} \over 8} = {{ – 16} \over 8} + {{ – 5} \over 8} = {{ – 16 + ( – 5)} \over 8} = {{ – 21} \over 8}\)
Câu 59: Cộng các phân số (rút gọn kết quả nếu có thể):
a) \({\rm{}}{1 \over { – 8}} + {{ – 5} \over 8}\) b) \({4 \over {13}} + {{ – 12} \over {39}}\) c) \({{ – 1} \over {21}} + {{ – 1} \over {28}}\)
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a) \({\rm{}}{1 \over { – 8}} + {{ – 5} \over 8} = {{ – 1} \over 8} + {{ – 5} \over 8} = {{ – 1 + ( – 5)} \over 8} = {{ – 6} \over 8} = {{ – 3} \over 4}\)
b) \({4 \over {13}} + {{ – 12} \over {39}} = {4 \over {13}} + {{ – 4} \over {13}} = {{4 + ( – 4)} \over {13}} = 0\)
c) \({{ – 1} \over {21}} + {{ – 1} \over {28}} = {{ – 4} \over {84}} + {{ – 3} \over {84}} = {{ – 4 + ( – 3)} \over {84}} = {{ – 7} \over {84}} = {{ – 1} \over {12}}\)
Câu 60: Tính các tổng dưới đây sau khi đã rút gọn phân số:
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a) \({\rm{}}{{ – 3} \over {29}} + {{16} \over {58}}\) b) \({8 \over {40}} + {{ – 36} \over {45}}\) c) \({{ – 8} \over {18}} + {{ – 15} \over {27}}\)
a) \({\rm{}}{{ – 3} \over {29}} + {{16} \over {58}} = {{ – 3} \over {29}} + {8 \over {29}} = {{ – 3 + 8} \over {29}} = {5 \over {29}}\)
b) \({8 \over {40}} + {{ – 36} \over {45}} = {1 \over 5} + {{ – 4} \over 5} = {{1 + ( – 4)} \over 5} = {{ – 3} \over 5}\)
c) \({{ – 8} \over {18}} + {{ – 15} \over {27}} = {{ – 4} \over 9} + {{ – 5} \over 9} = {{ – 4 + ( – 5)} \over 9} = {{ – 9} \over 9} = – 1\)
Câu 61: Tìm x, biết:
a) \(x = {1 \over 4} + {2 \over {13}}\)
b) \({x \over 3} = {2 \over 3} + {{ – 1} \over 7}\)
a) \(x = {1 \over 4} + {2 \over {13}} = {{13} \over {52}} + {8 \over {52}} = {{13 + 8} \over {52}} = {{21} \over {52}}\)
b) \({x \over 3} = {2 \over 3} + {{ – 1} \over 7} = {{14} \over {21}} + {{ – 3} \over {21}} = {{11} \over {21}} = {{11} \over {3.7}}\). Vậy \(x = {{11} \over 7}\)
