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Determine the ratio between the three numbers π, π, and π given that π to π is equal to 10 to one and π to π is equal to two to one.
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So we want to know the ratio between all three numbers: π to π to π.
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We know that π to π is 10 to one.
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And π to π is two to one.
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So by presenting the two ratios vertically, we can use the least common multiple of the shared term π to make equivalent ratios.
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Then, we can write their ratio among all three terms.
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So we need to make π equal between the two ratios.
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So for π to π, we have 10 to one, so π is one.
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But for π to π, we have two to one, so π is two.
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So whatβll be the least common multiple between one and two?
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It would be two.
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So we need to make one turn into two.
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And we can do that by multiplying by two.
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However, if we multiply the one by two, we must also multiply the 10 by two to keep their ratio equivalent.
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10 times two is 20.
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And one times two is two.
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So we multiplied by two to get the 20 to two ratio.
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And then, we go ahead and just bring down the two to one ratio.
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So now notice the πs are identical.
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And now we can write a ratio among all three terms: 20 to two to one.
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So this would be our ratio between the three numbers π, π, and π.