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a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)
\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)
b)\(5+\dfrac{3}{5}=\dfrac{25}{5}+\dfrac{3}{5}=\dfrac{28}{5};10-\dfrac{9}{16}=\dfrac{160}{16}-\dfrac{9}{16}=\dfrac{151}{16}\)
\(\dfrac{2}{3}-\left(\dfrac{1}{6}+\dfrac{1}{8}\right)=\dfrac{2}{3}-\left(\dfrac{8}{48}+\dfrac{6}{48}\right)=\dfrac{2}{3}-\dfrac{14}{48}=\dfrac{32}{48}-\dfrac{14}{48}=\dfrac{3}{8}\)
a) \(A=\frac{27\text{x}45+27\text{x}25}{2+4+6+8+...+18}=\frac{27\left(45+25\right)}{\left(18+2\right)\text{x}\left(\frac{18-2}{2}+1\right)}\)
\(A=\frac{27\text{x}70}{20\text{x}9}=\frac{3\text{x}9\text{x}10\text{x}7}{10\text{x}2\text{x}9}\)
\(A=\frac{21}{2}\)
b) \(B=\frac{28\text{x}108-52\text{x}12}{32-28+24-20+16-12+8-4}\)
\(B=\frac{28\text{x}12\text{x}9\text{}\text{}-52\text{x}12}{\left(32-28\right)+\left(24-20\right)+\left(16-12\right)+\left(8-4\right)}\)
\(B=\frac{12\left(28\text{x}9-52\right)}{4+4+4+4}=\frac{12\text{x}200}{4\text{x}4}\)
\(B=\frac{4\text{x}3\text{x}4\text{x}50}{4\text{x}4}=150\)
1.
a) \(\frac{16}{24}-\frac{1}{3}=\frac{16}{24}-\frac{8}{24}=\)\(\frac{8}{24}=\frac{1}{3}\)
b) \(\frac{4}{5}-\frac{12}{60}=\frac{48}{60}-\frac{12}{60}=\frac{36}{60}=\frac{9}{15}\)
3.
a)\(\frac{17}{6}-\frac{2}{6}=\frac{17-2}{6}=\frac{15}{6}\)
b) \(\frac{16}{15}-\frac{11}{15}=\frac{16-11}{15}=\frac{5}{15}=\frac{1}{3}\)
c) \(\frac{19}{12}-\frac{13}{12}=\frac{19-13}{12}=\frac{6}{12}=\frac{1}{2}\)
a) 16 24 − 1 3 = 16 24 − 8 24 = 24 16 − 3 1 = 24 16 − 24 8 = 8 24 = 1 3 24 8 = 3 1 b) 4 5 − 12 60 = 48 60 − 12 60 = 36 60 = 9 15 5 4 − 60 12 = 60 48 − 60 12 = 60 36 = 15 9 3. a) 17 6 − 2 6 = 17 − 2 6 = 15 6 6 17 − 6 2 = 6 17−2 = 6 15 b) 16 15 − 11 15 = 16 − 11 15 = 5 15 = 1 3 15 16 − 15 11 = 15 16−11 = 15 5 = 3 1 c) 19 12 − 13 12 = 19 − 13 12 = 6 12 = 1 2 12 19 − 12 13 = 12 19−13 = 12 6 = 2 1
\(\frac{1}{2}+\frac{2}{4}+\frac{3}{6}+\frac{4}{8}+\frac{5}{10}+\frac{6}{12}+\frac{7}{14}+\frac{8}{16}+\frac{9}{18}+\frac{10}{20}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=\frac{1}{2}\times10\)
\(=\frac{10}{2}\)
\(=5\)
\(\frac{1}{2}\)+ \(\frac{2}{4}\)+ \(\frac{3}{6}\)+ \(\frac{4}{8}\)+ \(\frac{5}{10}\)+ \(\frac{6}{12}\)+ \(\frac{7}{14}\)+ \(\frac{8}{16}\)+ \(\frac{9}{18}\)+ \(\frac{10}{20}\)
= \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)
= \(\frac{1}{2}\)x 10
= 5
a) 1/2 = 2/4 = 3/6 = 4/8 = 5/10
b) 1/3 = 2/6 = 3/9 = 4/12 = 5/15
c) 3/4 = 6/8 = 9/12 = 12/16 = 18/24
d) 4/3 = 8/6 = 12/9 = 16/12 = 20/15
e) 6/4 = 3/2 ; 6/3 = 4/2
g) 4/2 12/6 = 24/12
a, \(\frac{2}{3}+\frac{2}{3}+\frac{6}{3}=\frac{10}{3}\)
b,\(\frac{3}{4}+\frac{3}{4}+\frac{3}{2}=\frac{6}{4}+\frac{3}{2}=\frac{3}{2}+\frac{3}{2}=\frac{6}{2}=3\)
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