Question Video: Expressing a Given Ratio in Its Simplest Form Mathematics

Video Transcript

Put the ratio five-sixths to 1.5 to three-tenths in its simplest form.

We recall that a ratio is written in its simplest form when all of our values are integers with no common factor except one. We will begin this question by turning the decimal 1.5 into a top-heavy or improper fraction. 1.5 is the same as one and a half. As there are two-halves in a whole, 1.5 is the same as three-halves or three over two. This means that we can rewrite the ratio as five-sixths to three-halves to three-tenths.

We need to ensure that these three values are integers. In order to convert them into integers, we need to begin by finding the lowest common denominator. This will be the lowest common multiple of six, two, and ten. This is equal to 30 as the lowest number in the six, two, and 10 times table is 30. We can then multiply each of our three fractions by 30.

Our first term becomes five-sixths multiplied by 30. As 30 divided by six is equal to five, we’re left with five multiplied by five. This gives us the integer 25. We can repeat this process for the second and third terms in our ratio. The second term simplifies to three multiplied by 15. This is equal to 45. The third term simplifies to three multiplied by three. This is equal to nine. 25, 45, and nine have no common factor apart from one. This means that the ratio five-sixths to 1.5 to three-tenths written in its simplest form is 25 to 45 to nine.