Video: Expressing a Given Ratio in Its Simplest Form

Put the ratio 3/4 : 1/9 : 8/9 in its simplest form.

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Video Transcript

Put the ratio three-quarters to one-ninth to eight-ninths in its simplest form.

This is a three-part ratio where each part of the ratio is a fraction. Putting it in its simplest form means to express it in the form 𝑎 to 𝑏 to 𝑐, where 𝑎, 𝑏, and 𝑐 are all integers with no common factors.

In order to convert these three fractions into integers, we need to eliminate the denominators. Two of the fractions have a denominator of nine. So we’ll begin by multiplying each part of the ratio by nine. This gives three multiplied by nine over four for the first part of the ratio and the integers one and eight for the second and third parts. This simplifies to 27 over four to one to eight.

This ratio still isn’t in its simplest form as we still have one fraction. In order to eliminate this, we need to multiply each part of the ratio by four. This gives 27 to four to 32. The three parts of the ratio are now all integers. And they don’t share any common factors other than one. Four and 32 do share common factors of two and four. But these aren’t also shared with 27.

So the ratio in its simplest form is 27 to four to 32. This is equivalent to the ratio we started off with as each time we multiplied every part of the ratio by the same numbers.

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