Question

Carlos has a collection of balls. The ratio of blue balls to the red balls is $3:6,$ then

• A. Fraction of the blue balls out of the total balls is $\frac{1}{3}$
• B. Fraction of the blue balls out of the total balls is $\frac{1}{2}$
• C. Fraction of the red balls out of the total balls is $\frac{2}{3}$
• D. Fraction of the red balls out of the total balls is $2$

Answer 1

Answer: (A), (C)

Fraction of the red balls out of the total balls is $\frac{2}{3}$

The ratio of blue balls to the red balls is $3:6,$ that means there are 3 blue balls for every 6 red balls.

The number of blue balls = 3
The number of red balls = 6.

Total number of balls = Number of blue balls + Number of red balls
$=3+6$
$=9$

Fraction of the blue balls out of total balls
$=\frac{\text{Number of blue balls}}{\text{Total number of balls}}$
$=\frac{3}{9}$
$=\frac{3\times 1}{3\times 3}$
Cancel out the common factors, we get
$=\frac{1}{3}$

Fraction of the red balls out of total balls
$=\frac{\text{Number of red balls}}{\text{Total number of balls}}$
$=\frac{6}{9}$
$=\frac{3\times 2}{3\times 3}$
Cancel out the common factors, we get
$=\frac{2}{3}$