In part textbooks, a distinction is made between a ratio, i m sorry is presume to have a usual unit because that both quantities, and a rate, i m sorry is characterized to it is in a quotient of two quantities with various units (e.g. A proportion of the variety of miles to the number of hours). No such distinction is made in the usual core and hence, the two amounts in a ratio might or may not have actually a typical unit. However, as soon as there is a common unit, as in this problem, the is possible to add the two quantities and also then uncover the proportion of each quantity with respect come the whole (often explained as a part-whole relationship). like these aid build ideal connections between ratios and also fractions. Students often write ratios as fractions, yet in truth we reserve fractions to stand for numbers or quantities rather 보다 relationships between quantities. Because that example, if we were to take into consideration the ratio $4:5$ in this situation, climate two possible ways to translate $frac45$ in the context room to say,

"The number of boys is $frac45$ the number of girls,"

or to say,

"The ratio of the variety of boys to the variety of girls is $frac45 : 1$."

This 2nd interpretation shows the reality that $frac45$ is the unit rate (which is a number) for the ratio $4:5$.

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Solution:Using a ice cream diagram

For every 4 boys there are 5 girls and also 9 students at the school. Therefore that method that $frac49$ of the students are boys. $frac49$ the the total variety of students is 120 students:$$frac49 imes ? = 120$$If $frac49$ the number of students is 120, climate $frac14$ of 120 is $frac19$ that the total variety of students. In various other words, $frac14 imes 120 = 30$ is $frac19$ the total number of students. Climate 9 time this lot will provide the total variety of students:$$9 imes 30 = 270$$So over there is a total of 270 students in ~ the school. Note that this is equivalent to detect the answer come the division problem:$$120div frac49 =?$$We have the right to see all of this an extremely succinctly by making use of a ice diagram:


There room 4 units of boys and also 9 units of students. Because of this 4/9 the the students room boys.

4 units = 120

1 unit = 30

9 units = 270

There room 270 college student altogether.

Solution:Using a table

boys girl all students
4 5 9
40 50 90
80 100 180
120 150 270

Students can multiply the numbers in the first row by 10 to get the second row, and also then dual that amount to gain the 3rd row. Including the entries in the second and third row gives the fourth row that has the solution.

Alternatively, since $120 div 4 = 30$, students have the right to just main point the numbers in the very first row by 30 to get the worths in the fourth row.

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In every row, we deserve to see the the fraction of the students that are boys is$frac49 $.looking in ~ the critical row, we deserve to see the the total variety of students will certainly be $4 imes 30 + 5 imes 30 = 120 + 150 = 270$.