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Isn't mine more accurate?

You make approximations along the way, while the explanation deals with exact numbers. Thus the correct answer is the exact value, while yours is an approximation. You may try to convert feet in the right side into inches instead of converting inches in the left side into feet.

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Don't you need to convert inches to feet before creating the proportions?

That is a good question indeed. If the units relate with some fixed coefficient, e.g. 1 foot = 12 × 1 inch, 1 meter = 100 × 1 cm, then that coefficient will be simplified in the fraction when we convert.

5 inch /7 inch = (x × 12) inch / (21 × 12) inch

Common length units relate in such manner. However, if we had a proportion defined for Celsius degrees, while a value given in Fahrenheit degrees, then we would have to convert the value into Celsius degrees before plugging it in. (C = (F – 32) × 5/9)