Question

in a school, 2/3 of students study a language. Of those who study a language, 2/5 study French. Find the Ratio of student who study French to students who do not study French. Give your answer in the simplest form.
Must be in Ratio __ : __

Answer 1

Answer: 4:11

Step-by-step explanation:

Given : Fraction of students study a language $=\dfrac{2}{3}$

Let x be the number of students in the school.

Then , No. of students study a language $=\dfrac{2}{3}x$

Fraction of students who study a language study French  $=\dfrac{2}{5}$

No. of of students who study a language study French  $=\dfrac{2}{5}x$

No. of students study French =$\dfrac{2}{5}\times\dfrac{2x}{3}=\dfrac{4x}{15}$

Then, the number of students do not study French = $x-\dfrac{4x}{15}=\dfrac{15x-4x}{15}=\dfrac{11x}{15}$

Now, the ratio of student who study French to students who do not study French:-

$\dfrac{\dfrac{4x}{15}}{\dfrac{11x}{15}}=\dfrac{4}{11}=4:11$

Hence, the required answer =  4:11

Answer 2

The ratio of students who study French to students who don't is 4 : 11

Ratio shows the relationship that exists between two or more numbers. It displays the number of times a value is contained in another value

The fraction of students that study a language = 2/3

fraction of students that study French = $\frac{2}{3}$ × $\frac{2}{5} = \frac{4}{15}$

Fraction of students that do not study French = 1 - $\frac{4}{15} = \frac{11}{15}$

The ratio ;$\frac{4}{15} : \frac{11}{15}$

$\frac{4}{15}$ ÷ $\frac{11}{15}$

$\frac{4}{15}$ × $\frac{15}{11}$

= 4 : 11

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