Answer:
Step-by-step explanation:
1) [tex]\frac{1}{3}-(\frac{1}{3}*\frac{1}{3}) + (\frac{1}{3}[/tex] ÷[tex]\frac{1}{3}) =[/tex] [tex]\frac{1}{3}-\frac{1}{9} +(\frac{1}{3}*\frac{3}{1})[/tex]
[tex]=\frac{1}{3}-\frac{1}{9}+1\\\\=\frac{1*3}{3*3}-\frac{1}{9}+\frac{1*9}{1*9}\\\\=\frac{3}{9}-\frac{1}{9}+\frac{9}{9}\\\\=\frac{3-1+9}{9}\\\\=\frac{11}{9}\\\\=1\frac{2}{9}\\[/tex]
2)
[tex](3\frac{3}{4}-2\frac{2}{3})*1\frac{1}{2}=(\frac{15}{4}-\frac{8}{3})*\frac{3}{2}\\\\=(\frac{15*3}{4*3}-\frac{8*4}{3*4})*\frac{3}{2}\\\\=(\frac{45}{12}-\frac{24}{12})*\frac{3}{2}\\\\=(\frac{45-24}{12})*\frac{3}{2}\\\\=\frac{21}{12}*\frac{3}{2}\\\\=\frac{21}{4}*\frac{1}{2}\\\\=\frac{21}{8}\\\\=2\frac{5}{8}[/tex]
3) When finding equivalent fractions both numerator and denominator should be multiplied with the same number. But Lethna didn't multiply with the numerator.
[tex]\frac{2}{5}+\frac{1}{2}=\frac{2*2}{5*2}+\frac{1*5}{2*5}\\\\=\frac{4}{10}+\frac{5}{10}\\\\=\frac{9}{10}[/tex]
4) In fraction multiplication convert mixed fraction to improper fraction and reduce to smallest term
[tex]1\frac{1}{2}*5\frac{1}{3}=\frac{3}{2}*\frac{16}{3}\\\\=8[/tex]
5)
[tex]8\frac{2}{3}*5\frac{4}{9}=\frac{26}{3}*\frac{49}{9}\\\\=\frac{1274}{27}\\\\= 47\frac{5}{27}\\\\[/tex]
6) Use Keep Change Flip (KCF) method for fraction division
[tex]4\frac{2}{5}[/tex] ÷ [tex]6\frac{5}{8}[/tex] = [tex]\frac{22}{5}[/tex] ÷ [tex]\frac{53}{8}[/tex]
[tex]= \frac{22}{5}*\frac{8}{53}\\\\=\frac{176}{265}[/tex]
