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Answer :
Final answer:
The simplest form ratios for the students are 13/15 for 7th-grade boys to 6th-grade boys, 17/15 for 7th-grade girls to 6th-grade boys, 15/13 for 7th graders to 6th graders, and 1/1 for the total number of boys to girls.
Explanation:
When writing each ratio as a fraction in simplest form, we start by expressing the ratio of two numbers as a fraction and then simplify it by finding the greatest common divisor (gcd) that both numerator and denominator share. Here are the simplified ratios for the provided numbers:
- 7th-grade boys to 6th-grade boys: There are 26 7th-grade boys and 30 6th-grade boys. To simplify, divide both numbers by their gcd which is 2, resulting in 13/15.
- 7th-grade girls to 6th-grade boys: There are 34 7th-grade girls and 30 6th-grade boys. To simplify, we find that both numbers are divisible by 2, resulting in 17/15.
- 7th graders to 6th graders: To find the ratio of 7th graders to 6th graders, we add the numbers of boys and girls in each grade. So, we have 26 boys + 34 girls = 60 7th graders, and 30 boys + 22 girls = 52 6th graders. Then we simplify 60/52 by dividing both numbers by 4, leading to 15/13.
- Boys to girls: Summing up the boys and girls across both grades gives us 26+30 boys and 34+22 girls. This ratio simplifies to 56/56 or 1/1, meaning there is an equal number of boys and girls in total.
Note: There's an error in the options given for the 7th-grade girls to 6th-grade boys ratio. The correct simplest form ratio should be 17/15 and for 7th graders to 6th graders should be 15/13, which are not found in the options. Moreover, the boys to girls ratio simplifies to 1/1, also not found in the options provided.
Learn more about Simplifying Ratios here:
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