A class of 48 students has 22 boys and 26 girls. What is ratio of girls to boys in the class?
A.
26:11
B.
13:11
C.
13:22
D.
11:13
The Correct Answer and Explanation is:
The correct answer is B. 13:11.
Explanation:
To determine the ratio of girls to boys in the class, you begin by identifying the number of girls and boys in the class. In this case, there are 26 girls and 22 boys.
Step 1: Understand the Concept of Ratio A ratio is a way of comparing two quantities by division. The ratio of girls to boys can be expressed as the number of girls divided by the number of boys. This gives you the ratio in the simplest form.
Step 2: Write the Initial Ratio The initial ratio of girls to boys is:Ratio of girls to boys=26 girls22 boys\text{Ratio of girls to boys} = \frac{26 \text{ girls}}{22 \text{ boys}}Ratio of girls to boys=22 boys26 girls
So, the ratio is 26:22.
Step 3: Simplify the Ratio To simplify this ratio, you need to find the greatest common divisor (GCD) of the two numbers (26 and 22) and divide both numbers by that GCD.
- The factors of 26 are 1, 2, 13, and 26.
- The factors of 22 are 1, 2, 11, and 22.
- The common factors are 1 and 2, with 2 being the greatest common divisor.
So, divide both the number of girls (26) and the number of boys (22) by 2:26÷222÷2=1311\frac{26 \div 2}{22 \div 2} = \frac{13}{11}22÷226÷2=1113
The simplified ratio is 13:11.
Step 4: Interpret the Simplified Ratio The simplified ratio, 13:11, means that for every 13 girls in the class, there are 11 boys. Ratios are a useful way to compare quantities, especially when the numbers are large, as they allow for a more straightforward comparison.
Answer Analysis:
- Option A (26:11) is incorrect because it incorrectly simplifies the ratio.
- Option C (13:22) is incorrect as it does not simplify the ratio properly.
- Option D (11:13) is incorrect because it reverses the intended comparison (boys to girls instead of girls to boys).
Thus, Option B (13:11) is the correct answer, representing the simplified ratio of girls to boys in the class.