Question

algebra evaluate the expression when $y = 2\frac{5}{6}$.

1. $\left(\frac{2}{3}\

ight)y$

1. $\left(1\frac{1}{9}\

ight)y$
41.

1. $\left(1\frac{1}{15}\

ight)y$

1. $\left(2\frac{9}{10}\

ight)y$
44.

Explanation:

Problem 39

Step1: Convert mixed number to improper fraction

$y = 2\frac{5}{6} = \frac{2\times6 + 5}{6} = \frac{17}{6}$

Step2: Multiply by $\frac{2}{3}$

$\frac{2}{3} \times \frac{17}{6} = \frac{2\times17}{3\times6} = \frac{34}{18} = \frac{17}{9}$

Problem 40

Step1: Convert mixed numbers to improper fractions

$1\frac{1}{9} = \frac{1\times9 + 1}{9} = \frac{10}{9}$; $y = \frac{17}{6}$

Step2: Multiply the two fractions

$\frac{10}{9} \times \frac{17}{6} = \frac{10\times17}{9\times6} = \frac{170}{54} = \frac{85}{27}$

Problem 42

Step1: Convert mixed numbers to improper fractions

$1\frac{1}{15} = \frac{1\times15 + 1}{15} = \frac{16}{15}$; $y = \frac{17}{6}$

Step2: Multiply the two fractions

$\frac{16}{15} \times \frac{17}{6} = \frac{16\times17}{15\times6} = \frac{272}{90} = \frac{136}{45}$

Problem 43

Step1: Convert mixed numbers to improper fractions

$2\frac{9}{10} = \frac{2\times10 + 9}{10} = \frac{29}{10}$; $y = \frac{17}{6}$

Step2: Multiply the two fractions

$\frac{29}{10} \times \frac{17}{6} = \frac{29\times17}{10\times6} = \frac{493}{60}$

Answer:

1. $\frac{17}{9}$
2. $\frac{85}{27}$
3. $\frac{136}{45}$
4. $\frac{493}{60}$