Question

Direction: Carefully read each statement below. Choose the letter that corresponds to the best answer. Write the chosen letter on a separate sheet of paper. 1. in a math club there are 30 girls and 20 boys. The ratio of boys to girls in simplest form is _______2. which ratio is expression in the simplest formA. 6:9B 10:24 C. 4:36D. 8:153. at xyz factory 18 employees work in the office while others work in the warehouse if there are a total of 48 employees in the factory what is the simplest from radio of employees to work in the office to the employees who work in the warehouseA. 3:5 B. 5:3 C. 3:8 D. 8:34. IF BOTH NUMBERS IN THE RAT YOU ARE RELATIVELY PRIME THEN THE RAT IS SAID TO BEA. EQUIVALENT B. EVEN C. IN SIMPLEST FORM D. ODD5. WHAT IS THE GREATEST COMMON FACTOR OF 36 AND 54 A. 6 B. 12C. 18D. 24

Answer 1

The ratio of boys to girls is 2:3 in simplest form. The ratio in simplest form from the options given is 8:15. The simplest form ratio of office to warehouse employees is 3:5, and the greatest common factor of 36 and 54 is 18.

Step-by-step explanation:

The question pertains to various concepts in ratios and proportions, which are fundamental topics in middle school mathematics. Below are the answers explained step-by-step for each of the given questions:

1. The ratio of boys to girls in simplest form is 2:3. This is because there are 20 boys and 30 girls, and both numbers can be divided by 10 to simplify the ratio.
2. The ratio that is expressed in the simplest form is D. 8:15. When we check each option for any common factors, we find that 8 and 15 have no common factors other than 1, which means the ratio is already in its simplest form.
3. For the third question, the simplest form ratio of employees who work in the office to the employees who work in the warehouse is A. 3:5. There are 18 employees in the office, so subtracting this from the total (48) gives us 30 employees in the warehouse. Dividing both numbers by 6 (their greatest common factor) simplifies the ratio to 3:5.
4. If both numbers in the ratio are relatively prime (have no common factors other than 1), then the ratio is said to be in C. IN SIMPLEST FORM.
5. The greatest common factor (GCF) of 36 and 54 is C. 18. This is because 18 is the largest number that divides both 36 and 54 without any remainder.

Remember, simplifying ratios involves dividing both terms by their greatest common factor until no common factor exists other than 1. Finding the greatest common factor is crucial for simplifying ratios to their simplest form.

Answer 2

Given:

Number of girls = 30

Number of boys = 20

The ratio of a to b is expressed as a:b

The ratio of boys to girls is given as,

`20\colon30=(20)/(30)=(2)/(3)=2\colon3`

Answer: The ratio of boys to girls is 2:3.