Question

foundations and pre-calculus 10

1. $\frac{34}{121} \div \frac{17}{55}$
2. $-\frac{38}{27} \div \frac{57}{18}$
3. $-\frac{13}{17} \div \frac{39}{34}$
4. $-\frac{343}{125} \div \frac{49}{25}$

answer the following, leave answer as a simplified fraction, improper if applicable.

1. $3\frac{1}{2} \cdot 2\frac{1}{3}$
2. $3\frac{1}{2} \div 2\frac{1}{3}$
3. $-5\frac{2}{5} \cdot 3\frac{1}{3}$
4. $-5\frac{2}{5} \div 3\frac{1}{3}$
5. $3\frac{3}{4} \div 1\frac{1}{8} \cdot 1\frac{2}{25}$
6. $3\frac{1}{4} \div 2\frac{7}{16} \cdot 1\frac{1}{8}$

25

Explanation:

Problem 11: $\boldsymbol{\frac{34}{121} \div \frac{17}{55}}$

Step1: Recall division of fractions rule

To divide fractions, multiply by the reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. So, $\frac{34}{121} \div \frac{17}{55} = \frac{34}{121} \times \frac{55}{17}$.

Step2: Simplify before multiplying

Notice that 34 and 17 have a common factor of 17: $\frac{34\div17}{121} \times \frac{55}{17\div17} = \frac{2}{121} \times \frac{55}{1}$. Also, 55 and 121 have a common factor of 11: $\frac{2}{121\div11} \times \frac{55\div11}{1} = \frac{2}{11} \times \frac{5}{1}$.

Step3: Multiply the numerators and denominators

$\frac{2\times5}{11\times1} = \frac{10}{11}$.

Problem 12: $\boldsymbol{-\frac{38}{27} \div \frac{57}{18}}$

Step1: Apply division of fractions rule

$-\frac{38}{27} \div \frac{57}{18} = -\frac{38}{27} \times \frac{18}{57}$.

Step2: Simplify the fractions

38 and 57 have a common factor of 19: $\frac{38\div19}{27} \times \frac{18}{57\div19} = -\frac{2}{27} \times \frac{18}{3}$. 18 and 27 have a common factor of 9: $-\frac{2}{27\div9} \times \frac{18\div9}{3} = -\frac{2}{3} \times \frac{2}{3}$.

Step3: Multiply the fractions

$-\frac{2\times2}{3\times3} = -\frac{4}{9}$.

Problem 13: $\boldsymbol{-\frac{13}{17} \div \frac{39}{34}}$

Step1: Use division of fractions formula

$-\frac{13}{17} \div \frac{39}{34} = -\frac{13}{17} \times \frac{34}{39}$.

Step2: Simplify the terms

34 and 17 have a common factor of 17: $-\frac{13}{17\div17} \times \frac{34\div17}{39} = -\frac{13}{1} \times \frac{2}{39}$. 13 and 39 have a common factor of 13: $-\frac{13\div13}{1} \times \frac{2}{39\div13} = -\frac{1}{1} \times \frac{2}{3}$.

Step3: Multiply the fractions

$-\frac{1\times2}{1\times3} = -\frac{2}{3}$.

Problem 14: $\boldsymbol{-\frac{343}{125} \div \frac{49}{25}}$

Answer:

$\frac{10}{11}$