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1)
a) \(x+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=5\)
\(x+\frac{64}{128}+\frac{32}{128}+\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}=5\)
\(x+\frac{127}{128}=5\)
\(x=5-\frac{127}{128}=\frac{513}{128}\)
b) \(x+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}=3\)
\(x+\frac{729}{2187}+\frac{243}{2187}+\frac{81}{2187}+\frac{27}{2187}+\frac{9}{2187}+\frac{3}{2187}+\frac{1}{2187}=3\)
\(x+\frac{2186}{2187}=3\)
\(x=3-\frac{2186}{2187}=\frac{4375}{2187}\)
2)
a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=1-\frac{1}{6}=\frac{5}{6}\)
b) \(5\frac{1}{2}+3\frac{5}{6}+\frac{2}{3}\)
\(=\left(5+3\right)+\left(\frac{1}{2}+\frac{2}{3}+\frac{5}{6}\right)\)
\(=8+\left(\frac{3}{6}+\frac{4}{6}+\frac{5}{6}\right)\)
\(=8+2=10\)
c) \(7\frac{7}{8}+1\frac{4}{6}+3\frac{3}{5}\)
\(=\left(7+1+3\right)+\left(\frac{7}{8}+\frac{2}{3}+\frac{3}{5}\right)\)
\(=11+\left(\frac{105}{120}+\frac{80}{120}+\frac{72}{120}\right)\)
\(=11+\frac{257}{120}=\frac{1577}{120}\)
3) Gọi số đó là x. Theo đề ta có :
\(\frac{16-x}{21+x}=\frac{5}{7}\)
\(7\left(16-x\right)=5\left(21+x\right)\)
\(112-7x=105+5x\)
\(112-105=7x-5x\)
\(7=2x\)
\(x=\frac{7}{2}=3,5\) ( vô lí )
Vậy không có số tự nhiên để thõa mãn điều kiện trên.
a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)
\(=2\)
b) \(\frac{5}{9}\times\frac{1}{2}\times\frac{5}{9}\times\frac{6}{4}=\frac{25}{81}\times\frac{3}{4}=\frac{25}{108}\)
c) \(\frac{7}{8}\div\frac{1}{2}+\frac{9}{8}\div\frac{1}{2}=\left(\frac{7}{8}+\frac{9}{8}\right)\div\frac{1}{2}\)
\(=2\div\frac{1}{2}=4\)
d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)
\(=1+\frac{1}{2}=\frac{3}{2}\)
a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}\)
\(=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)
\(=1+1\)
\(=2\)
b) \(\frac{5}{9}.\frac{1}{2}.\frac{5}{9}.\frac{6}{4}\)
\(=\left(\frac{5}{9}\right)^2\left(\frac{1}{2}.\frac{6}{4}\right)\)
\(=\frac{25}{81}.\frac{3}{4}\)
\(=\frac{25}{108}\)
c) \(\frac{7}{8}:\frac{1}{2}+\frac{9}{8}:\frac{1}{2}\)
\(=\frac{7}{8}.2+\frac{9}{8}.2\)
\(=2\left(\frac{7}{8}+\frac{9}{8}\right)\)
\(=2.\frac{16}{8}\)
\(=2.2\)
\(=4\)
d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}\)
\(=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)
\(=1+\frac{1}{2}\)
\(=\frac{2}{2}+\frac{1}{2}\)
\(=\frac{3}{2}\)
a,(11/15+4/15)+(5/7+2/7)
=1+1
=2
b,5/9x(1/2+6/4)
=5/9x2
=10/9
c,1/2:(7/8+9/8)
=1/2:2
=1
d,(17/10-7/10)+1/2
=1+1/2
=3/2
\(x+\frac{15}{7}=\frac{9}{2}\)
\(x=\frac{9}{2}-\frac{15}{7}=\frac{33}{14}\)
\(x-\frac{3}{4}=\frac{7}{2}\)
\(x=\frac{7}{2}+\frac{3}{4}=\frac{17}{4}\)
\(x.\frac{7}{8}=\frac{12}{5}\)
\(x=\frac{12}{5}:\frac{7}{8}=\frac{96}{35}\)
\(\frac{5}{6}:x=\frac{4}{3}\)
\(x=\frac{5}{6}:\frac{4}{3}=\frac{5}{8}\)
- a) x=9/2-15/7=33/14
- b) x=7/2+3/4=17/4
- c) x=12/5:7/8=61/35
- d) x=5/6:4/3=5/8
- k nha
\(\frac{10}{18}+\frac{4}{9}+\frac{26}{10}+\frac{12}{5}+\frac{9}{15}\)
\(=\frac{5}{9}+\frac{4}{9}+\frac{13}{5}+\frac{12}{5}+\frac{3}{5}\)
\(=\left(\frac{5}{9}+\frac{4}{9}\right)+\left(\frac{13}{5}+\frac{12}{5}+\frac{3}{5}\right)\)
\(=1+\frac{28}{5}\)
\(=\frac{33}{5}\)
Ta có:
a) \(\frac{10}{18}+\frac{4}{9}+\frac{26}{10}+\frac{12}{5}+\frac{9}{15}=\frac{5}{9}+\frac{4}{9}+\frac{13}{5}+\frac{12}{5}+\frac{9}{15}=1+1+\frac{9}{15}=1\frac{9}{15}\)
b)\(\frac{10}{18}+\frac{4}{9}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=\left(\frac{5}{9}+\frac{4}{9}\right)+\left(\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}\right)\)
\(=1+\frac{31}{128}=1\frac{31}{128}\)
bài 6 \(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+\ldots+\frac{2}{80\times82}+\frac{2}{82\times84}\)
= \(\frac12-\frac14+\frac14-\frac16+\frac16-\cdots+\frac{1}{80}-\frac{1}{82}+\frac{1}{82}-\frac{1}{84}\)
= \(\frac12-\left(\frac14-\frac14\right)-\left(\frac16-\frac16\right)-\cdots-\left(\frac{1}{82}-\frac{1}{82}\right)-\frac{1}{84}\)
=\(\frac12-0-0-\frac{1}{84}\)
=\(\frac12\) - \(\frac{1}{84}\)
=\(\frac{42}{84}-\frac{1}{84}\)
=\(\frac{41}{84}\)
Bài 7
a)\(\frac{19}{4}=4\frac34\)
b)\(\frac{27}{5}=5\frac25\)
c)\(\frac{56}{8}=7\frac08\)
bài 8
a)\(\frac58=\frac{40}{x}\)
\(x=40:\frac58\)
\(x=40\times\frac85\)
\(x=64\)
b)\(\frac{12}{18}=\frac{9}{x}\)
\(x=9:\frac{12}{18}\)
\(x=9\times\frac{18}{12}\)
\(x=\frac{27}{2}\)
\(\frac{15}{20}=\frac{10}{x}\)
\(x=10:\frac{15}{20}\)
\(x=10\times\frac{20}{15}\)
x= \(\frac{40}{3}\)
Bài 8 c)
\(1<\frac54<\frac{6}{x}\)
Suy ra \(\frac{30}{24}<\frac{30}{5x}\)
24>\(5x\)
5\(x\le23\)
\(x\le\) 4
d)\(\frac35<\frac{4}{x}<1\)
\(\frac{12}{20}<\frac{12}{3x}<\frac{12}{12}\)
Suy ra \(3x<20\) ; \(3x>12\)
\(3x\le19\) ; \(x>4\)
\(x\le6\)
Vậy \(x=5\) hoặc 6
bài 9 a)
\(2\frac47+8\frac39+5\frac{15}{19}\)
= \(\frac{18}{7}+\frac{25}{3}+\frac{110}{19}\)
=\(\frac{1026}{399}+\frac{3325}{399}+\frac{2310}{399}\)
=\(\frac{4351}{399}\) +\(\frac{2310}{399}\)
=\(\frac{6661}{399}\)
Bài 9
b) \(\frac58+\frac69+33\frac59\)
= \(\frac58+\left(\frac69+\frac{302}{9}\right)\)
=\(\frac58+\frac{308}{9}\)
=\(\frac{45}{72}+\frac{2464}{72}\)
=\(\frac{2509}{72}\)
Bài 10
Người thứ ba được số phần tổng số tiền là
1 - \(\frac16-\frac49\) = \(\frac{7}{18}\) ( tổng số tiền)
56 nghìn ứng với phân số là
\(\frac{7}{18}-\frac49\) = - \(\frac{1}{18}\) (tổng số tiền)
Không có số tiền nào thỏa mãn đề bài.