Middle School

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Write the ratio 42 inches to 9 feet as a fraction in simplest form.

Explain why you get the same result whether you convert feet to inches or convert inches to feet.

Answer :

1 ft= 12 inches
9 ft= 108 inches

ratio 12/108=1/9

doesn't matter the unit used as long as the are the same inches:inches or ft:ft
the ratio is still 1:9

hope this answers your question

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Rewritten by : Barada

Final answer:

The ratio of 42 inches to 9 feet can be converted to the same unit (inches) to yield a simplified fraction of 7/18. The ratio remains consistent regardless of whether we convert feet to inches or inches to feet because we are using the same conversion factor.

Explanation:

To write the ratio 42 inches to 9 feet as a fraction in simplest form, we must first ensure that both measurements are in the same unit. Since there are 12 inches in a foot, we can convert 9 feet to inches by multiplying 9 by 12, which gives us 108 inches. Now we can write the ratio as 42 inches to 108 inches.

The ratio in fraction form is 42/108. Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 6), we get 7/18. Therefore, the simplified fraction is 7/18.

No matter if we convert feet to inches or inches to feet, the result will be the same because we are simply scaling both measurements by the same conversion factor (12). This is exemplified in the proportion: 1 foot / 12 inches = w feet / 42 inches, where 'w' would be the number of feet equivalent to 42 inches.