Question

g19b
(5) (left(1\frac{3}{7} - 1\frac{1}{5}
ight) div left(2\frac{2}{5} - 1\frac{1}{3}
ight) =)
(6) (1\frac{7}{20} div left(1\frac{1}{8} \times 2\frac{2}{11}
ight) =)
(7) (4\frac{3}{8} div left(5\frac{1}{4} div \frac{3}{5} div 3
ight) =)
(8) (\frac{5}{9} \times left(\frac{17}{20} - 0.65
ight) div \frac{2}{21} =)

Explanation:

(5)

Step1: Convert mixed numbers to improper fractions

\(1\frac{3}{7}=\frac{1\times7 + 3}{7}=\frac{10}{7}\), \(1\frac{1}{5}=\frac{1\times5 + 1}{5}=\frac{6}{5}\), \(2\frac{2}{5}=\frac{2\times5 + 2}{5}=\frac{12}{5}\), \(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\)

Step2: Calculate the numerator and denominator separately

Numerator: \(\frac{10}{7}-\frac{6}{5}=\frac{50 - 42}{35}=\frac{8}{35}\)
Denominator: \(\frac{12}{5}-\frac{4}{3}=\frac{36 - 20}{15}=\frac{16}{15}\)

Step3: Divide the numerator by the denominator

\(\frac{8}{35}\div\frac{16}{15}=\frac{8}{35}\times\frac{15}{16}=\frac{3}{14}\)

Step1: Convert mixed numbers to improper fractions

\(1\frac{7}{20}=\frac{1\times20 + 7}{20}=\frac{27}{20}\), \(1\frac{1}{8}=\frac{1\times8 + 1}{8}=\frac{9}{8}\), \(2\frac{2}{11}=\frac{2\times11 + 2}{11}=\frac{24}{11}\)

Step2: Calculate the product in the denominator

\(\frac{9}{8}\times\frac{24}{11}=\frac{27}{11}\)

Step3: Divide the numerator by the result from Step2

\(\frac{27}{20}\div\frac{27}{11}=\frac{27}{20}\times\frac{11}{27}=\frac{11}{20}\)

Step1: Convert mixed numbers to improper fractions

\(4\frac{3}{8}=\frac{4\times8 + 3}{8}=\frac{35}{8}\), \(5\frac{1}{4}=\frac{5\times4 + 1}{4}=\frac{21}{4}\)

Step2: Calculate the inner division

\(\frac{21}{4}\div\frac{3}{5}=\frac{21}{4}\times\frac{5}{3}=\frac{35}{4}\), then \(\frac{35}{4}\div3=\frac{35}{4}\times\frac{1}{3}=\frac{35}{12}\)

Step3: Divide the outer fraction by the result from Step2

\(\frac{35}{8}\div\frac{35}{12}=\frac{35}{8}\times\frac{12}{35}=\frac{3}{2}\)

Answer:

\(\frac{3}{14}\)

(6)