Lesson 3 Rational Thinking Solidify Understanding

Ready

Perform the indicated operation. Show your work.

1.

$\frac{5}{17} + \frac{8}{17}$

2.

$\frac{3}{10} + \frac{16}{25}$

3.

$\frac{4}{5} + \frac{7}{11}$

4.

$(\frac{2}{3}) \cdot (\frac{4}{5})$

5.

$(\frac{2}{3}) \cdot (\frac{9}{16})$

6.

$(\frac{10}{33}) \cdot (\frac{11}{15})$

7.

Describe your procedure for adding two fractions.

a.

When the denominators are the same:

b.

When the denominators are different:

8.

Explain your procedure for multiplying two fractions.

Set

Complete the missing features of each rational function. Sketch the asymptotes on the graph and mark the location of the intercepts.

9.

$y = \frac{x^{2}}{(x + 6) (x - 4)}$

Degree of numerator:

Degree of denominator:

Equation of horizontal asymptote:

Equation of vertical asymptote(s):

$y$ -intercept:

$x$ -intercept(s):

10.

$y = \frac{x - 6}{x + 3}$

Degree of numerator:

Degree of denominator:

Equation of horizontal asymptote:

Equation of vertical asymptote(s):

$y$ -intercept:

$x$ -intercept(s):

11.

$y = \frac{10 x}{{(x + 3)}^{2}}$

Degree of numerator:

Degree of denominator:

Equation of horizontal asymptote:

Equation of vertical asymptote(s):

$y$ -intercept:

$x$ -intercept(s):

12.

$y = \frac{(x + 1)}{(x + 2) (x - 5)}$

Degree of numerator:

Degree of denominator:

Equation of horizontal asymptote:

Equation of vertical asymptote(s):

$y$ -intercept:

$x$ -intercept(s):

Go

Rewrite each fraction in an equivalent form. Then explain the mathematics that makes it possible to rewrite the fraction in its new form.

13.

$\frac{12}{15}$

14.

$\frac{26}{11}$

15.

$\frac{51}{17}$

16.

$\frac{6}{13}$

17.

$\frac{114}{27}$

18.

$\frac{- 14, 529}{14, 529}$

19.

$\frac{(23,796 a b c d) (a x^{2})}{(23,796 a b c d) (a x^{2})}$