# Video: Calculating the Ratio between Two Quantities in Simplest Form

A student got 30 out of 90 marks in the first-term exam in physics, and he got 81 out of 90 in the second-term exam. Express the ratio of his total marks scored in the two exams to the total marks available in its simplest form.

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### Video Transcript

A student got 30 out of 90 marks in the first-term exam in physics, and he got 81 out of 90 in the second-term exam. Express the ratio of his total marks scored in the two exams to the total marks available in its simplest form.

In term one, the student scored 30 out of 90. In term two, he scored 81 out of 90. 30 plus 81 is equal to 111. This means that the student scored 111 marks altogether. 90 plus 90 is equal to 180. Therefore, the total number of marks available was 180. We were asked to find the ratio of the total marks scored to the total marks available.

As he scored 111 marks and there were 180 marks available, the ratio is 111 to 180. Both of these numbers are divisible by three. 111 divided by three is equal to 37. We could work this out using the bus stop method.

One divided by three is zero, so we need to carry the one. 11 divided by three is equal to three remainder two. We carry the two. Finally, 21 divided by three is equal to seven. Therefore, 111 divided by three is 37. 18 divided by three is equal to six. Therefore, 180 divided by three is equal to 60. 37 and 60 have no common factor apart from one. Therefore, the ratio is in its simplest form. The ratio of the student’s total marks scored to the total marks available in its simplest form is 37 to 60.