Question

Используя сочетательный закон сложения для натуральных чисел, проверьте равенство:а)(3/4+1/6)+7/12=3/4+(1/6+7/12); б)7/15+(2/9+5/6)=(7/15+2/9)+5/6.
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Answer 1

а)(3/4+1/6)+7/12=3/4+(1/6+7/12);

(3/4+1/6)+7/12 = $( frac{3*3}{3*4} + frac{2*1}{2*6} )+ frac{7}{12} = ( frac{9}{12} + frac{2}{12} )+ frac{7}{12} = frac{11}{12} + frac{7}{12} = frac{11+7}{12} = frac{18}{12} = frac{3}{2} =1 frac{1}{2}$

3/4+(1/6+7/12) = $frac{3}{4} + ( frac{2*1}{2*6} + frac{7}{12})= frac{3}{4} +( frac{2}{12} + frac{7}{12} ) = frac{3}{4} + frac{9}{12} = frac{3*3}{3*4} + frac{9}{12} = frac{9}{12} + frac{9}{12} = frac{18}{12}$=$1 frac{1}{2}$

$1 frac{1}{2} =1 frac{1}{2}$


б)7/15+(2/9+5/6)=(7/15+2/9)+5/6.

7/15+(2/9+5/6)=$frac{7}{15} +( frac{2*2}{2*9} + frac{3*5}{3*6} ) = frac{7}{15} +( frac{4}{18} + frac{15}{18} ) = frac{7}{15} + frac{19}{18} = frac{6*7}{6*15} + frac{5*19}{5*18} = frac{42}{90} + frac{95}{90}$=$frac{137}{90} =1 frac{47}{90}$

(7/15+2/9)+5/6 = $( frac{3*7}{3*15} + frac{5*2}{5*9} )+ frac{5}{6} =( frac{21}{45} + frac{10}{45} )+ frac{5}{6} = frac{31}{45} + frac{5}{6} = frac{2*31}{2*45} + frac{15*5}{15*6} = frac{62}{90} + frac{75}{90}$=$frac{137}{90} =1 frac{47}{90}$
$1 frac{47}{90} =1 frac{47}{90}$