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\(\frac{17}{25}\times\frac{29}{43}+\frac{14}{43}\times\frac{17}{25}\)
\(=\frac{17}{25}\times\left(\frac{29}{43}+\frac{14}{43}\right)\)
\(=\frac{17}{25}\times\frac{43}{43}\)
\(=\frac{17}{25}\times1\)
\(=\frac{17}{25}\)
a, \(\frac{5}{11}\times\frac{7}{25}+\frac{15}{11}\times\frac{1}{5}\)
\(=\frac{5}{11}\times\frac{7}{25}+\frac{5}{11}\times\frac{3}{5}\)
\(=\frac{5}{11}\times\left(\frac{7}{25}+\frac{3}{5}\right)\)
\(=\frac{5}{11}\times\frac{22}{25}\)
\(=\frac{2}{5}\)
b, \(\frac{3}{7}\times\frac{25}{19}-\frac{1}{7}\times\frac{18}{19}\)
\(=\frac{1}{7}\times\frac{75}{19}-\frac{1}{7}\times\frac{18}{19}\)
\(=\frac{1}{7}\times\left(\frac{75}{19}-\frac{18}{19}\right)\)
\(=\frac{1}{7}\times3\)
\(=\frac{3}{7}\)
a, \(\frac{6}{7}.\frac{16}{15}.\frac{7}{6}.\frac{21}{32}=\frac{6}{7}.\frac{7}{6}.\frac{16}{15}.\frac{21}{32}\)=\(1.\frac{16}{15}.\frac{21}{32}=\frac{7}{5.2}=\frac{7}{10}\)
Phần b T2
c,\(\frac{7}{4}.\frac{11}{21}+\frac{11}{21}.\frac{5}{4}=\frac{11}{21}.\left(\frac{7}{4}+\frac{5}{4}\right)\)=\(\frac{11}{21}.3=\frac{11}{7}\)
=(1+1+1+1+1+1+1+1)+(1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45)
Đặt A = 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
Ta có:
A x 1/2= 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
1/6=1/2x3=1/2-1/3
1/12=1/3x4=1/3-1/4
……………………
1/90=1/9x10=1/9-1/10
A x 1/2=1/2-1/3+1/3-1/4+1/4-1/5+…+1/9-1/10
A x 1/2=1/2-1/10=4/10
A=4/10:1/2=4/5
Vậy 4/3+7/6+11/10+16/15+22/21+29/28+37/36+46/45=1+1+1+1+1+1+1+1+4/5=8+4/5=44/5
\(\frac{4}{3}+\frac{7}{6}+\frac{11}{10}+...+\frac{46}{45}\)
\(=1+\frac{1}{3}+1+\frac{1}{6}+1+\frac{1}{10}+...+1+\frac{1}{45}\)
\(=\left(1+1+1+...+1\right)+\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)(8 chữ số 1)
\(=8+\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)
Đặt A = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
=> \(\frac{1}{2}\)A = \(\frac{1}{2}\times\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)
= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
Vậy A = \(\frac{2}{5}:\frac{1}{2}=\frac{4}{5}\)
Do đó biểu thức trên là 8 + \(\frac{4}{5}\) = \(\frac{44}{5}\)
Đáp số: \(\frac{44}{5}\)
\(\frac{8}{15}:\frac{2}{11}+\frac{7}{15}:\frac{2}{11}\)
\(=\left(\frac{8}{15}+\frac{7}{15}\right):\frac{2}{11}\)
\(=1:\frac{2}{11}\)
\(=\frac{11}{2}\)
\(\frac{4}{5}+\frac{2}{35}\times\frac{7}{2}=\frac{4}{5}+\frac{1}{5}=1\)
\(\frac{4}{5}+\left(\frac{1}{5}-\frac{1}{7}\right):\frac{2}{7}\)
\(=\left(\frac{4}{5}+\frac{1}{5}\right)-\frac{1}{7}:\frac{2}{7}\)
\(=\frac{5}{5}-\frac{1}{2}\)
\(=1-\frac{1}{2}=\frac{1}{2}\)
Câu 1:\(\frac{12}{23}\times\frac{9}{28}+\frac{11}{23}\times\frac{9}{28}\)
\(=\frac{9}{28}\times\left(\frac{12}{23}+\frac{11}{23}\right)\)
\(=\frac{9}{28}\times\frac{23}{23}\)
\(=\frac{9}{28}\times1\)
\(=\frac{9}{28}\)
Câu 2:
\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)
\(=\left(3+2+2+3\right)+\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)\)
\(=10+\frac{9}{9}\)
\(=10+1\)
\(=11\)
\(\frac{12}{23}x\frac{9}{28}+\frac{11}{23}x\frac{9}{28}=\)\(\left(\frac{12}{23}+\frac{11}{23}\right)x\frac{9}{28}\)\(=\) \(1x\frac{9}{28}=\frac{9}{28}\)
\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)\(=\) \(\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)+\left(3+2+3+2\right)\)\(=\) \(1+3+2+3+2=\)\(11\)
lấy (7/18+11/18)+(4/23+19/23)=2
vì 7/18+11/18=18/18=1
4/23+19/23=23/23=1
nên 1+1=2
Đ/s;2
=2
Vì 7 phần mười tám cộng 11 phần 18 bằng 1 và 4 phần 23 + 19 phần 23=1 nên 1+1=2
7/29+22/29 rồi cộng 2 phân số kia với nhau nha
\(\frac{7}{29}+\frac{17}{11}+\frac{22}{29}+\frac{5}{11}\)
\(=\left(\frac{7}{29}+\frac{22}{29}\right)+\left(\frac{17}{11}+\frac{5}{11}\right)\)
\(=\frac{29}{29}+\frac{22}{11}\)
\(=1+2\)
\(=3\)