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

Express the ratio 1 1/2 : 2 1/2 : 2 1/3 in its simplest form.

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### Video Transcript

Express the ratio one and a half to two and a half to two and one-third in its simplest form.

We recall that a ratio is written in its simplest form when all the values are integers with no common factor apart from one. In this question, we will begin by converting all three fractions into improper or top-heavy fractions. One and a half is equal to three-halves or three over two, as there are two-halves in one whole one. In the same way, two and a half is equal to five-halves or five over two. There are three-thirds in one whole one. This means there are six-thirds in two whole ones. Two and a third is therefore equal to seven-thirds.

We can actually convert any mixed number to an improper fraction by multiplying a whole number by the denominator and then adding the numerator. For two and a third, we multiply two by three and then add one. This gives us seven. The denominator stays the same. The ratio can therefore be rewritten as three over two to five over two to seven over three. None of these values are integers. So we need to get rid of the denominators by finding the lowest common multiple of two and three. This is equal to six, so we can multiply all three fractions by six.

Our first term becomes three over two multiplied by six. This simplifies to three multiplied by three, which equals nine. We can repeat this for the other two terms. The second term simplifies to five multiplied by three. This is equal to 15. Finally, the third term simplifies to seven multiplied by two, which is 14. Nine, 15, and 14 have no common factor apart from one. This means that the ratio one and a half to two and a half to two and one-third written in its simplest form is nine to 15 to 14.