Of all the students in a certain dormitory, 1 2 are first-year students and the rest are second-year students. if 4 5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
a. 1/15b. 1/5c. 4/15d. 1/3e. 2/5

(B) 1/5

Step-by-step explanation:

First year student = 1/2 of the students in a certain dormitory. = x

Second year student = 1/2 of the students in a certain dormitory. = x

First year = second year = x

Total students in the dormitory = x+x = 2x

4/5 of the first year students have not declared a major = 4/5x

first year students who have declared a major = x -4/5x = 1/5x

Second year student who has declared a major is 3 times the fraction of the first year student who have declared major= 3/5x

Second year student who have not declared major= x - 3/5x = 2/5x

The fraction of all the students in the dormitory are second-year students who have not declared a major = (2/5x)/2x

= 2x/5 * 1/2x

= 1/5

no i do not : ( what is it?

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.