your turn: q1 12 2/9 - 8 7/8 q2 find the volume of the cube below: 2 2/3 q3 21 1/6 - 16 4/5 q4 find the…

Explanation:

Q1:

Step1: Convert mixed - numbers to improper fractions

$12\frac{2}{9}=\frac{12\times9 + 2}{9}=\frac{108+2}{9}=\frac{110}{9}$ and $8\frac{7}{8}=\frac{8\times8 + 7}{8}=\frac{64 + 7}{8}=\frac{71}{8}$

Step2: Find a common denominator

The common denominator of 9 and 8 is 72. So $\frac{110}{9}=\frac{110\times8}{9\times8}=\frac{880}{72}$ and $\frac{71}{8}=\frac{71\times9}{8\times9}=\frac{639}{72}$

Step3: Subtract the fractions

$\frac{880}{72}-\frac{639}{72}=\frac{880 - 639}{72}=\frac{241}{72}=3\frac{25}{72}$

Q2:

Step1: Recall the volume formula for a cube

The volume formula for a cube is $V = s^3$, where $s = 2\frac{2}{3}=\frac{2\times3+2}{3}=\frac{8}{3}$

Step2: Calculate the volume

$V=(\frac{8}{3})^3=\frac{8\times8\times8}{3\times3\times3}=\frac{512}{27}=18\frac{26}{27}$

Q3:

Step1: Convert mixed - numbers to improper fractions

$21\frac{1}{6}=\frac{21\times6+1}{6}=\frac{126 + 1}{6}=\frac{127}{6}$ and $16\frac{4}{5}=\frac{16\times5+4}{5}=\frac{80 + 4}{5}=\frac{84}{5}$

Step2: Find a common denominator

The common denominator of 6 and 5 is 30. So $\frac{127}{6}=\frac{127\times5}{6\times5}=\frac{635}{30}$ and $\frac{84}{5}=\frac{84\times6}{5\times6}=\frac{504}{30}$

Step3: Subtract the fractions

$\frac{635}{30}-\frac{504}{30}=\frac{635 - 504}{30}=\frac{131}{30}=4\frac{11}{30}$

Q4:

Since only the height $h = 2\frac{2}{3}=\frac{8}{3}$ is given and no information about the base (length and width of the base of the prism), we cannot calculate the volume of the prism.

Answer:

Q1: $3\frac{25}{72}$ Q2: $18\frac{26}{27}$ Q3: $4\frac{11}{30}$ Q4: Cannot be calculated due to insufficient information.