Question

perform the indicated operations and reduce your answers (no mixed numbers):

1. \\(\frac{9}{8} \times \frac{20}{63}\\)
2. \\(\frac{25}{18} \div \frac{15}{24}\\)
3. \\(\frac{55}{28} \times \frac{21}{19} \times \frac{38}{66}\\)
4. \\(\left(\frac{35}{26} \div \frac{45}{39}\

ight) \times \frac{9}{7}\\)

1. \\(\left(\frac{8}{9} - \frac{2}{3}\

ight) \div 4\\)

1. \\(\frac{11}{12} - \frac{4}{9}\\)
2. \\(\frac{1}{6} + \frac{2}{15}\\)
3. \\(\frac{9}{10} - \frac{5}{8}\\)
4. \\(\frac{5}{6} + \frac{3}{8}\\)

Explanation:

1)

Step1: Multiply numerators and denominators

$\frac{9\times20}{8\times63}=\frac{180}{504}$

Step2: Simplify the fraction

Divide numerator and denominator by 12: $\frac{180\div12}{504\div12}=\frac{15}{42}$
Divide numerator and denominator by 3: $\frac{15\div3}{42\div3}=\frac{5}{14}$

Step1: Convert division to multiplication

$\frac{25}{18}\div\frac{15}{24}=\frac{25}{18}\times\frac{24}{15}$

Step2: Multiply numerators and denominators

$\frac{25\times24}{18\times15}=\frac{600}{270}$

Step3: Simplify the fraction

Divide numerator and denominator by 30: $\frac{600\div30}{270\div30}=\frac{20}{9}$

Step1: Multiply numerators and denominators

$\frac{55\times21\times38}{28\times19\times66}$

Step2: Simplify before multiplying

55 and 66 can be simplified by 11: $\frac{5\times21\times38}{28\times19\times6}$
21 and 28 can be simplified by 7: $\frac{5\times3\times38}{4\times19\times6}$
38 and 19 can be simplified by 19: $\frac{5\times3\times2}{4\times1\times6}$

Step3: Multiply and simplify

$\frac{30}{24}=\frac{5}{4}$ (divide numerator and denominator by 6)

Answer:

$\frac{5}{14}$

2)