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1, =35 x 77-35 x 12+35x35-35 x 18 suy ra =35 x(77-12+35-18)=35 x 82=2870.
2, =2014 x (100-1)=201400-2014=199386.
3,=35x12+65x12+65=12x(65+35)+65=1200+65=1265.
4.=\(\frac{13\times\left(37-1\right)}{12\times\left(37+2\right)}\)=\(\frac{13\times36}{12\times39}=\frac{13\times3\times12}{12\times3\times13}=1\)
tck nha bạn
53x39+47x39-53x21-47x21
=39x ( 53+47) - 21x(53+47)
=39 x100 - 21x100
= 100x(39-21)
=100x18
=1800
2x53x12 +4x6x87 - 3x8x40
= (2x12)x53 + (4x16)x87 - (3x8) x40
= 24x53 + 24x87 + 24x40
= 24( 53+87+40)
= 24x180
=4320
Bài 3 :
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{99\times100}\)
Ta có : \(\frac{1}{1\times2}=\frac{2-1}{1\times2}=\frac{2}{1\times2}-\frac{1}{1\times2}=1-\frac{1}{2}\)
\(\frac{1}{2\times3}=\frac{3-2}{2\times3}=\frac{3}{2\times3}-\frac{2}{2\times3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{99\times100}=\frac{100-99}{99\times100}=\frac{100}{99\times100}-\frac{99}{99\times100}=\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10\times11}+\frac{1}{11\times12}+...+\frac{1}{38\times39}\)
Ta có : \(\frac{1}{10\times11}=\frac{11-10}{10\times11}=\frac{11}{10\times11}-\frac{10}{10\times11}=\frac{1}{10}-\frac{1}{11}\)
\(\frac{1}{11\times12}=\frac{12-11}{11\times12}=\frac{12}{11\times12}-\frac{11}{11\times12}=\frac{1}{11}-\frac{1}{12}\)
\(\frac{1}{38\times39}=\frac{39-38}{38\times39}=\frac{39}{38\times39}-\frac{38}{38\times39}=\frac{1}{38}-\frac{1}{39}\)
\(\frac{1}{39\times40}=\frac{40-39}{39\times40}=\frac{40}{39\times40}-\frac{39}{39\times40}=\frac{1}{39}-\frac{1}{40}\)
\(\Rightarrow B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
3.
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{38.39}+\frac{1}{39.40}\)
\(B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
5 x 7 x 77 - 7 x 60 + 49 x 25 -15 x 42
= 5x7x77 - 7x5x12 + 7x7x5x5 - 5x3x7x6
= 35 x77 - 35x12 + 35x35 - 35x18
= 35 x ( 77-12+35-18 )
= 35 x 82 = 2870
37 x 13 - \(\frac{13}{24}\) + 37 x 12
= 37 x ( 13 + 12) - \(\frac{13}{24}\)
= 37 x 25 - \(\frac{13}{24}\)
= 925 - \(\frac{13}{24}\)
= \(\frac{22187}{24}\)
123,45 + 23,56 +76,44 + 54,55
= (123,45 + 54,55) + (23,56 + 76,44)
= 178 + 100
= 278
456 x 45 + 456 x 10 + - 456 x 55
=456 x (45 +10-55)
=456 x 0
=0
2,5 x 8,5 + 7,5 x 8,5
=8,5 x (2,5 +7,5)
= 8,5 x 10
= 85
86 x 5 + 86 x 4 + 86
= 86 x (5+4+1)
= 86 x10
860