Question

1. express the ratio $3\frac{2}{3}:7\frac{1}{3}$ in its simplest form.

a. 1:2 b. 3:7 c. 2:3 d. 2:7

1. the angles of a triangle are in the ratio 1:3:8. find the measures of the three angles of this triangle.

a. $20^\circ:50^\circ:110^\circ$ b. $15^\circ:45^\circ:120^\circ$
c. $15^\circ:30^\circ:135^\circ$ d. $20^\circ:45^\circ:115^\circ$

1. in a class, the ratio of the boys to the girls is 5:3. there are 15 girls in the class. which of the following equation represents the ratio of the number of boys to the number of girls in the class?

a. $\frac{5}{3}=\frac{x}{15}$ b. $\frac{5}{3}=\frac{15}{x}$ c. $\frac{5}{15}=\frac{3}{x}$ d. $\frac{3}{5}=\frac{x}{15}$

1. solve for the value of x in the given proportion, $\frac{x}{4}=\frac{15}{20}$

a. 2 b. 3 c. 4 d. 5

Explanation:

Question 7

Step1: Convert mixed numbers to improper fractions

$3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{11}{3}$, $7\frac{1}{3}=\frac{7\times3+1}{3}=\frac{22}{3}$

Step2: Find the ratio

The ratio $\frac{11}{3}:\frac{22}{3}$ is equivalent to $\frac{11}{3}\div\frac{22}{3}=\frac{11}{3}\times\frac{3}{22}=\frac{11}{22}=\frac{1}{2}$, so the ratio is $1:2$.

Step1: Sum of ratio parts

The ratio of angles is $1:3:8$, so the sum of the ratio parts is $1 + 3+8 = 12$.

Step2: Find each angle

The sum of angles in a triangle is $180^{\circ}$. So the first angle is $\frac{1}{12}\times180^{\circ}=15^{\circ}$, the second angle is $\frac{3}{12}\times180^{\circ}=45^{\circ}$, the third angle is $\frac{8}{12}\times180^{\circ}=120^{\circ}$.

Let the number of boys be $x$ and girls be $15$. The ratio of boys to girls is $5:3$, so $\frac{5}{3}=\frac{x}{15}$.

Answer:

a. 1:2

Question 8